%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW194+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 : n001.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 09:04:47 AM UTC 2026
% Result : Theorem 55.88s 56.17s
% Output : Proof 56.00s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(fact_ext,axiom,
! [V_g_2,V_f_2] :
( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
=> V_f_2 = V_g_2 ),
file('theBenchmark.p',fact_ext) ).
fof(fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096) ).
fof(fact__096abs_A_I2_A_K_Ay_J_A_060_061_A1_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact__096abs_A_I2_A_K_Ay_J_A_060_061_A1_096) ).
fof(fact__0962_A_K_Ax_A_060_061_A1_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact__0962_A_K_Ax_A_060_061_A1_096) ).
fof(fact__0962_A_K_Ay_A_060_061_A1_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact__0962_A_K_Ay_A_060_061_A1_096) ).
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),hAPP(hAPP(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_four__x__squared,axiom,
! [V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(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))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
file('theBenchmark.p',fact_four__x__squared) ).
fof(fact_power2__eq__square__number__of,axiom,
! [V_w,T_b] :
( ( class_Int_Onumber(T_b)
& class_Groups_Omonoid__mult(T_b) )
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w)) ),
file('theBenchmark.p',fact_power2__eq__square__number__of) ).
fof(fact_abs__power2,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(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))))) = hAPP(hAPP(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)
=> hAPP(hAPP(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)))) = hAPP(hAPP(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__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> hAPP(hAPP(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_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(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)))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).
fof(fact_power2__eq__square,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(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)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
file('theBenchmark.p',fact_power2__eq__square) ).
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)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(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__096_N1_A_060_061_A2_A_K_Ax_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),
file('theBenchmark.p',fact__096_N1_A_060_061_A2_A_K_Ax_096) ).
fof(fact_power3__eq__cube,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ),
file('theBenchmark.p',fact_power3__eq__cube) ).
fof(fact__096_N1_A_060_061_A2_A_K_Ay_096,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____)),
file('theBenchmark.p',fact__096_N1_A_060_061_A2_A_K_Ay_096) ).
fof(fact_eq__number__of__Pls__Min,axiom,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
file('theBenchmark.p',fact_eq__number__of__Pls__Min) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
! [V_q,V_p,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(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_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_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_power__m1__even,axiom,
! [V_n,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)),hAPP(hAPP(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_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_power__m1__even) ).
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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(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_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_real__mult__assoc,axiom,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(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] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z),
file('theBenchmark.p',fact_real__mult__commute) ).
fof(fact_power__even__eq,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
file('theBenchmark.p',fact_power__even__eq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(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_I11_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(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_I30_J,axiom,
! [V_q,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(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_real__mult__1,axiom,
! [V_z] : hAPP(hAPP(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_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_xy,axiom,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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_xy) ).
fof(fact_abs__power__minus__one,axiom,
! [V_n,T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)),V_n)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_abs__power__minus__one) ).
fof(fact_le__special_I4_J,axiom,
! [V_xa_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_xa_2),c_Groups_Oone__class_Oone(T_a))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)) ) ),
file('theBenchmark.p',fact_le__special_I4_J) ).
fof(fact_le__special_I2_J,axiom,
! [V_ya_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_ya_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2) ) ),
file('theBenchmark.p',fact_le__special_I2_J) ).
fof(fact_csqrt,axiom,
! [V_z] : hAPP(hAPP(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_abs__minus__one,axiom,
! [T_a] :
( ( class_Rings_Olinordered__idom(T_a)
& class_Int_Onumber__ring(T_a) )
=> c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_abs__minus__one) ).
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_mult__numeral__1,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))),V_a) = V_a ),
file('theBenchmark.p',fact_mult__numeral__1) ).
fof(fact_mult__numeral__1__right,axiom,
! [V_a,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))) = V_a ),
file('theBenchmark.p',fact_mult__numeral__1__right) ).
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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ),
file('theBenchmark.p',fact_power__increasing) ).
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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
file('theBenchmark.p',fact_one__le__power) ).
fof(fact_z,axiom,
v_z = c_Complex_Ocomplex_OComplex(v_x____,v_y____),
file('theBenchmark.p',fact_z) ).
fof(fact_assms,axiom,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_assms) ).
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_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_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_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_times__numeral__code_I5_J,axiom,
! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)),
file('theBenchmark.p',fact_times__numeral__code_I5_J) ).
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_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_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_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_rel__simps_I24_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
file('theBenchmark.p',fact_rel__simps_I24_J) ).
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_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).
fof(fact_crossproduct__noteq,axiom,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
<=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ),
file('theBenchmark.p',fact_crossproduct__noteq) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
! [V_b,V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) ).
fof(fact_crossproduct__eq,axiom,
! [V_za_2,V_xa_2,V_ya_2,V_w_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_ya_2))
<=> ( V_ya_2 = V_za_2
| V_w_2 = V_xa_2 ) ) ),
file('theBenchmark.p',fact_crossproduct__eq) ).
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_real__add__mult__distrib,axiom,
! [V_w,V_z2,V_z1] : hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)),
file('theBenchmark.p',fact_real__add__mult__distrib) ).
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) )
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(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) )
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(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_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_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_rel__simps_I30_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ),
file('theBenchmark.p',fact_rel__simps_I30_J) ).
fof(fact_rel__simps_I26_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,V_k_2) ),
file('theBenchmark.p',fact_rel__simps_I26_J) ).
fof(fact_rel__simps_I20_J,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
file('theBenchmark.p',fact_rel__simps_I20_J) ).
fof(fact_rel__simps_I23_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
file('theBenchmark.p',fact_rel__simps_I23_J) ).
fof(fact_rel__simps_I28_J,axiom,
! [V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin)
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) ),
file('theBenchmark.p',fact_rel__simps_I28_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_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
! [V_a,V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
! [V_m,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) ).
fof(fact_double__number__of__Bit0,axiom,
! [V_w,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w)) ),
file('theBenchmark.p',fact_double__number__of__Bit0) ).
fof(fact_number__of__reorient,axiom,
! [V_xa_2,V_w_2,T_a] :
( class_Int_Onumber(T_a)
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = V_xa_2
<=> V_xa_2 = c_Int_Onumber__class_Onumber__of(T_a,V_w_2) ) ),
file('theBenchmark.p',fact_number__of__reorient) ).
fof(fact_eq__number__of,axiom,
! [V_ya_2,V_xa_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_xa_2) = c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)
<=> V_xa_2 = V_ya_2 ) ),
file('theBenchmark.p',fact_eq__number__of) ).
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_power__one__right,axiom,
! [V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(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_mult__Pls,axiom,
! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
file('theBenchmark.p',fact_mult__Pls) ).
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_mult__Bit0,axiom,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),
file('theBenchmark.p',fact_mult__Bit0) ).
fof(fact_zpower__zpower,axiom,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)),
file('theBenchmark.p',fact_zpower__zpower) ).
fof(fact_mult__2__right,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ),
file('theBenchmark.p',fact_mult__2__right) ).
fof(fact_mult__2,axiom,
! [V_z,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z) ),
file('theBenchmark.p',fact_mult__2) ).
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_pos__zmult__eq__1__iff__lemma,axiom,
! [V_n,V_m] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> ( V_m = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_pos__zmult__eq__1__iff__lemma) ).
fof(fact_zmult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( ( V_n_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
& V_m_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) )
| ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_zmult__eq__1__iff) ).
fof(fact_le__number__of,axiom,
! [V_ya_2,V_xa_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_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,V_ya_2) ) ),
file('theBenchmark.p',fact_le__number__of) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(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_arith__simps_I32_J,axiom,
! [V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ),
file('theBenchmark.p',fact_arith__simps_I32_J) ).
fof(fact_mult__number__of__left,axiom,
! [V_z,V_w,V_v,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ),
file('theBenchmark.p',fact_mult__number__of__left) ).
fof(fact_power__commutes,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__commutes) ).
fof(fact_power__mult__distrib,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ),
file('theBenchmark.p',fact_power__mult__distrib) ).
fof(fact_power__one,axiom,
! [V_n,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(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_power2__sum,axiom,
! [V_y,V_x,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,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(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
file('theBenchmark.p',fact_power2__sum) ).
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_I46_J,axiom,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
file('theBenchmark.p',fact_rel__simps_I46_J) ).
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_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_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_Bit0__Pls,axiom,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
file('theBenchmark.p',fact_Bit0__Pls) ).
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_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_power__mult,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n) ),
file('theBenchmark.p',fact_power__mult) ).
fof(fact_power__abs,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(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_Bit1__Min,axiom,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
file('theBenchmark.p',fact_Bit1__Min) ).
fof(fact_rel__simps_I43_J,axiom,
! [V_l_2] :
( c_Int_OMin = c_Int_OBit1(V_l_2)
<=> c_Int_OMin = V_l_2 ),
file('theBenchmark.p',fact_rel__simps_I43_J) ).
fof(fact_rel__simps_I47_J,axiom,
! [V_k_2] :
( c_Int_OBit1(V_k_2) = c_Int_OMin
<=> V_k_2 = c_Int_OMin ),
file('theBenchmark.p',fact_rel__simps_I47_J) ).
fof(fact_rel__simps_I40_J,axiom,
c_Int_OMin != c_Int_OPls,
file('theBenchmark.p',fact_rel__simps_I40_J) ).
fof(fact_rel__simps_I37_J,axiom,
c_Int_OPls != c_Int_OMin,
file('theBenchmark.p',fact_rel__simps_I37_J) ).
fof(fact_rel__simps_I42_J,axiom,
! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
file('theBenchmark.p',fact_rel__simps_I42_J) ).
fof(fact_rel__simps_I45_J,axiom,
! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
file('theBenchmark.p',fact_rel__simps_I45_J) ).
fof(fact_real__sum__squared__expand,axiom,
! [V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)),
file('theBenchmark.p',fact_real__sum__squared__expand) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [B_x,B_y] : v_z != c_Complex_Ocomplex_OComplex(B_x,B_y),
file('theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
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_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_power__m1__odd,axiom,
! [V_n,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)),c_Nat_OSuc(hAPP(hAPP(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_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin) ),
file('theBenchmark.p',fact_power__m1__odd) ).
fof(fact_power__power__power,axiom,
! [T_a] :
( class_Power_Opower(T_a)
=> c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a)) ),
file('theBenchmark.p',fact_power__power__power) ).
fof(fact_power2__diff,axiom,
! [V_y,V_x,T_a] :
( class_Int_Onumber__ring(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)) ),
file('theBenchmark.p',fact_power2__diff) ).
fof(fact_zero__le__even__power_H,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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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))) ),
file('theBenchmark.p',fact_zero__le__even__power_H) ).
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,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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_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,hAPP(hAPP(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)))),hAPP(hAPP(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_C_I2_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
file('theBenchmark.p',fact_C_I2_J) ).
fof(fact_C_I1_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
file('theBenchmark.p',fact_C_I1_J) ).
fof(fact_C_I4_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))),
file('theBenchmark.p',fact_C_I4_J) ).
fof(fact_C_I3_J,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))),
file('theBenchmark.p',fact_C_I3_J) ).
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_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_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_zmult__1,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
file('theBenchmark.p',fact_zmult__1) ).
fof(fact_zmult__1__right,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
file('theBenchmark.p',fact_zmult__1__right) ).
fof(fact_zmult__commute,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
file('theBenchmark.p',fact_zmult__commute) ).
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_zpower__zadd__distrib,axiom,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
file('theBenchmark.p',fact_zpower__zadd__distrib) ).
fof(fact_zadd__zmult__distrib2,axiom,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
file('theBenchmark.p',fact_zadd__zmult__distrib2) ).
fof(fact_zdiff__zmult__distrib2,axiom,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
file('theBenchmark.p',fact_zdiff__zmult__distrib2) ).
fof(fact_power__Suc__0,axiom,
! [V_n] : hAPP(hAPP(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_zmult__assoc,axiom,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
file('theBenchmark.p',fact_zmult__assoc) ).
fof(fact_zadd__zmult__distrib,axiom,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
file('theBenchmark.p',fact_zadd__zmult__distrib) ).
fof(fact_zdiff__zmult__distrib,axiom,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
file('theBenchmark.p',fact_zdiff__zmult__distrib) ).
fof(fact_nat__power__eq__Suc__0__iff,axiom,
! [V_m_2,V_xa_2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( V_xa_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_abs__zmult__eq__1,axiom,
! [V_n,V_m] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('theBenchmark.p',fact_abs__zmult__eq__1) ).
fof(fact_power_Opower_Opower__Suc,axiom,
! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)),
file('theBenchmark.p',fact_power_Opower_Opower__Suc) ).
fof(fact_power_Opower_Opower__0,axiom,
! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
file('theBenchmark.p',fact_power_Opower_Opower__0) ).
fof(fact_complex__diff,axiom,
! [V_d,V_c,V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)),
file('theBenchmark.p',fact_complex__diff) ).
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_Complex__eq__0,axiom,
! [V_b_2,V_a_2] :
( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_Complex__eq__0) ).
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_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_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_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__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_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_complex__zero__def,axiom,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_complex__zero__def) ).
fof(fact_zero__reorient,axiom,
! [V_xa_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = V_xa_2
<=> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__reorient) ).
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__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_real__sqrt__eq__iff,axiom,
! [V_ya_2,V_xa_2] :
( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2)
<=> V_xa_2 = V_ya_2 ),
file('theBenchmark.p',fact_real__sqrt__eq__iff) ).
fof(fact_real__sqrt__eq__0__iff,axiom,
! [V_xa_2] :
( c_NthRoot_Osqrt(V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_xa_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_real__sqrt__ge__0__iff,axiom,
! [V_ya_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2) ),
file('theBenchmark.p',fact_real__sqrt__ge__0__iff) ).
fof(fact_real__sqrt__le__0__iff,axiom,
! [V_xa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_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__le__eq__diff,axiom,
! [V_ya_2,V_xa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__le__eq__diff) ).
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_power__0__Suc,axiom,
! [V_n,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Power_Opower(T_a) )
=> hAPP(hAPP(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_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_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)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) ),
file('theBenchmark.p',fact_nat__one__le__power) ).
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_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) )
=> ( hAPP(hAPP(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_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_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_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_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_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__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_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_mult__eq__if,axiom,
! [V_n,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__eq__if) ).
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_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_realpow__two__diff,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y)) ),
file('theBenchmark.p',fact_realpow__two__diff) ).
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_power__inject__base,axiom,
! [V_b,V_n,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(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__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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(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_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_ya_2,V_xa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) ),
file('theBenchmark.p',fact_real__sqrt__le__iff) ).
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)
=> hAPP(hAPP(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)
=> hAPP(hAPP(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_power__eq__if,axiom,
! [V_p,V_m] :
( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_power__eq__if) ).
fof(fact_real__sqrt__mult,axiom,
! [V_y,V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(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__sqrt__power,axiom,
! [V_k,V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_k)) = hAPP(hAPP(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__1__iff,axiom,
! [V_xa_2] :
( c_NthRoot_Osqrt(V_xa_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
<=> V_xa_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_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_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_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_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__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_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_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(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_I9_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(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_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__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_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)
=> hAPP(hAPP(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_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_Pls__def) ).
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),hAPP(hAPP(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_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_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)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(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_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)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(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__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_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_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_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_add__nonneg__eq__0__iff,axiom,
! [V_ya_2,V_xa_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_xa_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ya_2)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
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__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__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_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_complex__add,axiom,
! [V_d,V_c,V_b,V_a] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d)),
file('theBenchmark.p',fact_complex__add) ).
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_real__sqrt__mult__self__sum__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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),V_y)))),
file('theBenchmark.p',fact_real__sqrt__mult__self__sum__ge__zero) ).
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,hAPP(hAPP(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_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_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_Complex__eq__number__of,axiom,
! [V_w_2,V_b_2,V_a_2] :
( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w_2)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w_2) ) ),
file('theBenchmark.p',fact_Complex__eq__number__of) ).
fof(fact_Complex__eq__1,axiom,
! [V_b_2,V_a_2] :
( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
<=> ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_Complex__eq__1) ).
fof(fact_complex__one__def,axiom,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_complex__one__def) ).
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_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_xa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_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_ya_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2) ),
file('theBenchmark.p',fact_real__sqrt__ge__1__iff) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(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_left__diff__distrib__number__of,axiom,
! [V_v,V_b,V_a,T_b] :
( ( class_Rings_Oring(T_b)
& class_Int_Onumber(T_b) )
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(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_right__diff__distrib__number__of,axiom,
! [V_c,V_b,V_v,T_b] :
( ( class_Rings_Oring(T_b)
& class_Int_Onumber(T_b) )
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(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_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_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_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_real__sqrt__abs2,axiom,
! [V_x] : c_NthRoot_Osqrt(hAPP(hAPP(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_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_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_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_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(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_I27_J,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(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_I35_J,axiom,
! [V_q,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(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_power__Suc2,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__Suc) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
! [V_q,V_p,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) ).
fof(fact_power__add,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__add) ).
fof(fact_mult__Bit1,axiom,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),V_l),
file('theBenchmark.p',fact_mult__Bit1) ).
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_sum__squares__eq__zero__iff,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_add__scale__eq__noteq,axiom,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( V_r != c_Groups_Ozero__class_Ozero(T_a)
=> ( ( V_c != V_d
& V_a = V_b )
=> c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d)) ) ) ),
file('theBenchmark.p',fact_add__scale__eq__noteq) ).
fof(fact_complex__mult,axiom,
! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))),
file('theBenchmark.p',fact_complex__mult) ).
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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
file('theBenchmark.p',fact_zero__le__power) ).
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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(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_power__0,axiom,
! [V_a,T_a] :
( class_Power_Opower(T_a)
=> hAPP(hAPP(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_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_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_real__two__squares__add__zero__iff,axiom,
! [V_ya_2,V_xa_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_ya_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( V_ya_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
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_complex__norm,axiom,
! [V_y,V_x] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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_complex__norm) ).
fof(fact_le__real__sqrt__sumsq,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),V_y)))),
file('theBenchmark.p',fact_le__real__sqrt__sumsq) ).
fof(fact_real__sqrt__unique,axiom,
! [V_x,V_y] :
( hAPP(hAPP(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,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> hAPP(hAPP(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__pow2__iff,axiom,
! [V_xa_2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_xa_2)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_xa_2
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) ),
file('theBenchmark.p',fact_real__sqrt__pow2__iff) ).
fof(fact_real__squared__diff__one__factored,axiom,
! [V_x,T_a] :
( class_Rings_Oring__1(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))) ),
file('theBenchmark.p',fact_real__squared__diff__one__factored) ).
fof(fact_real__sqrt__sum__squares__eq__cancel2,axiom,
! [V_y,V_x] :
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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__eq__cancel,axiom,
! [V_y,V_x] :
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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_diff__bin__simps_I4_J,axiom,
! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I4_J) ).
fof(fact_diff__bin__simps_I6_J,axiom,
! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I6_J) ).
fof(fact_diff__bin__simps_I5_J,axiom,
! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,V_l)),
file('theBenchmark.p',fact_diff__bin__simps_I5_J) ).
fof(fact_sum__squares__le__zero__iff,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)),c_Groups_Ozero__class_Ozero(T_a))
<=> ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_sum__squares__ge__zero,axiom,
! [V_y,V_x,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_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y))) ),
file('theBenchmark.p',fact_sum__squares__ge__zero) ).
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_xa_2,V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_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_xa_2,V_ya_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
<=> V_xa_2 = V_ya_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_le__funD,axiom,
! [V_xa_2,V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
=> c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_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_ya_2,V_xa_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_xa_2 = V_ya_2
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_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_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
<=> ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) ) ),
file('theBenchmark.p',fact_le__fun__def) ).
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)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(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_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_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_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),hAPP(hAPP(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_one__reorient,axiom,
! [V_xa_2,T_a] :
( class_Groups_Oone(T_a)
=> ( c_Groups_Oone__class_Oone(T_a) = V_xa_2
<=> V_xa_2 = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_one__reorient) ).
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_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,hAPP(hAPP(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)))),hAPP(hAPP(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_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_odd__0__le__power__imp__0__le,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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(hAPP(hAPP(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_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) ) ),
file('theBenchmark.p',fact_odd__0__le__power__imp__0__le) ).
fof(fact_complex_Oinject,axiom,
! [V_real2_H_2,V_real1_H_2,V_real2_2,V_real1_2] :
( c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) = c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)
<=> ( V_real2_2 = V_real2_H_2
& V_real1_2 = V_real1_H_2 ) ),
file('theBenchmark.p',fact_complex_Oinject) ).
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(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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_le__special_I3_J,axiom,
! [V_xa_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_xa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,c_Int_OPls) ) ),
file('theBenchmark.p',fact_le__special_I3_J) ).
fof(fact_le__special_I1_J,axiom,
! [V_ya_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_ya_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_ya_2) ) ),
file('theBenchmark.p',fact_le__special_I1_J) ).
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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__decreasing) ).
fof(fact_nat__mult__2,axiom,
! [V_z] : hAPP(hAPP(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_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
file('theBenchmark.p',fact_nat__mult__2) ).
fof(fact_nat__mult__2__right,axiom,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
file('theBenchmark.p',fact_nat__mult__2__right) ).
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_zero__eq__power2,axiom,
! [V_a_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( hAPP(hAPP(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_zero__power2,axiom,
! [T_a] :
( class_Rings_Osemiring__1(T_a)
=> hAPP(hAPP(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_real__sqrt__abs,axiom,
! [V_x] : c_NthRoot_Osqrt(hAPP(hAPP(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_power2__eq__imp__eq,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( hAPP(hAPP(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)))) = hAPP(hAPP(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__le__imp__le,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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_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),hAPP(hAPP(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_sum__power2__eq__zero__iff,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_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_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__power2__eq__zero__iff) ).
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,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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__mult__squared__eq,axiom,
! [V_ya,V_xa,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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)))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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__squared__eq) ).
fof(fact_realpow__two__sum__zero__iff,axiom,
! [V_ya_2,V_xa_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_ya_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_ya_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_realpow__two__sum__zero__iff) ).
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_mult_Ocomm__neutral,axiom,
! [V_a,T_a] :
( class_Groups_Ocomm__monoid__mult(T_a)
=> hAPP(hAPP(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)
=> hAPP(hAPP(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)
=> hAPP(hAPP(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)
=> hAPP(hAPP(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_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
! [V_n,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(hAPP(hAPP(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))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) ).
fof(fact_power__odd__eq,axiom,
! [V_n,V_a,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(hAPP(hAPP(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))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
file('theBenchmark.p',fact_power__odd__eq) ).
fof(fact_sum__power2__le__zero__iff,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_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_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__power2__le__zero__iff) ).
fof(fact_even__power__le__0__imp__0,axiom,
! [V_k,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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_k)),c_Groups_Ozero__class_Ozero(T_a))
=> V_a = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_even__power__le__0__imp__0) ).
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_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_convex__bound__le,axiom,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( class_Rings_Olinordered__semiring__1(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__le) ).
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_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_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(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__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_complex__i__not__one,axiom,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',fact_complex__i__not__one) ).
fof(fact_complex__i__not__number__of,axiom,
! [V_w] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w),
file('theBenchmark.p',fact_complex__i__not__number__of) ).
fof(fact_complex__i__not__zero,axiom,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',fact_complex__i__not__zero) ).
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_i__squared,axiom,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
file('theBenchmark.p',fact_i__squared) ).
fof(fact_Complex__eq__i,axiom,
! [V_ya_2,V_xa_2] :
( c_Complex_Ocomplex_OComplex(V_xa_2,V_ya_2) = c_Complex_Oii
<=> ( V_ya_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_Complex__eq__i) ).
fof(fact_i__def,axiom,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_i__def) ).
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_mult__zero__left,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> hAPP(hAPP(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_Ozero__left,axiom,
! [V_b,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(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)
=> hAPP(hAPP(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__zero__right,axiom,
! [V_a,T_a] :
( class_Rings_Omult__zero(T_a)
=> hAPP(hAPP(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_Ozero__right,axiom,
! [V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(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)
=> hAPP(hAPP(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_mult__eq__0__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Oring__no__zero__divisors(T_a)
=> ( hAPP(hAPP(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)
=> hAPP(hAPP(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)
=> ( hAPP(hAPP(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_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_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_mult_Oadd__right,axiom,
! [V_b_H,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(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)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_y)) ),
file('theBenchmark.p',fact_mult__right_Oadd) ).
fof(fact_comm__semiring__class_Odistrib,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring(T_a)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ),
file('theBenchmark.p',fact_comm__semiring__class_Odistrib) ).
fof(fact_mult_Oadd__left,axiom,
! [V_b,V_a_H,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(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)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ),
file('theBenchmark.p',fact_mult__left_Oadd) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_mult_Odiff__right,axiom,
! [V_b_H,V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(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)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(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)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(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)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_ya)) ),
file('theBenchmark.p',fact_mult__left_Odiff) ).
fof(fact_norm__eq__zero,axiom,
! [V_xa_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_norm__eq__zero) ).
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_abs__mult,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(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)
=> hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
file('theBenchmark.p',fact_abs__mult__self) ).
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_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_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_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_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_Nat__Transfer_Otransfer__nat__int__function__closures_I2_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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ),
file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) ).
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_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),hAPP(hAPP(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_power2__i,axiom,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
file('theBenchmark.p',fact_power2__i) ).
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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)) ),
file('theBenchmark.p',fact_zero__le__square) ).
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),hAPP(hAPP(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_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,hAPP(hAPP(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_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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonneg__nonneg) ).
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,hAPP(hAPP(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__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,hAPP(hAPP(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__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,hAPP(hAPP(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__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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__nonpos__nonpos) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__left__mono) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__right__mono__neg) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__left__mono__neg) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono_H) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__mono) ).
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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ),
file('theBenchmark.p',fact_split__mult__pos__le) ).
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,hAPP(hAPP(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_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_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(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,hAPP(hAPP(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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
<=> c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_power__eq__0__iff__number__of,axiom,
! [V_w_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) )
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_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_norm__le__zero__iff,axiom,
! [V_xa_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_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_norm__le__zero__iff) ).
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_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_norm__mult,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(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_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_norm__power,axiom,
! [V_n,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(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_mult__right__le__one__le,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),V_x)
=> ( 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_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x) ) ) ) ),
file('theBenchmark.p',fact_mult__right__le__one__le) ).
fof(fact_mult__left__le__one__le,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),V_x)
=> ( 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_y,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x) ) ) ) ),
file('theBenchmark.p',fact_mult__left__le__one__le) ).
fof(fact_le__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_le__add__iff2) ).
fof(fact_le__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_le__add__iff1) ).
fof(fact_abs__mult__pos,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),V_x)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x)) ) ),
file('theBenchmark.p',fact_abs__mult__pos) ).
fof(fact_abs__eq__mult,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oordered__ring__abs(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_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,c_Groups_Ozero__class_Ozero(T_a),V_a) ) )
=> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(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__eq__mult) ).
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)
=> hAPP(hAPP(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)
=> hAPP(hAPP(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_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(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_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_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_realpow__num__eq__if,axiom,
! [V_m,V_n,T_a] :
( class_Power_Opower(T_a)
=> ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
& ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_realpow__num__eq__if) ).
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_lemma__realpow__diff,axiom,
! [V_y,V_n,V_p,T_a] :
( class_Groups_Omonoid__mult(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y) ) ),
file('theBenchmark.p',fact_lemma__realpow__diff) ).
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_norm__ratiotest__lemma,axiom,
! [V_y,V_x,V_c,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
=> V_x = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_norm__ratiotest__lemma) ).
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_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_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_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_nat__mult__commute,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
file('theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_nat__mult__assoc,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
file('theBenchmark.p',fact_nat__mult__assoc) ).
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_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_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_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_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_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_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__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_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_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_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_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__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_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_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_mult__0,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_mult__0) ).
fof(fact_mult__0__right,axiom,
! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_mult__0__right) ).
fof(fact_mult__is__0,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_mult__is__0) ).
fof(fact_mult__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mult__cancel2,axiom,
! [V_n_2,V_k_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
<=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel2) ).
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_Suc__mult__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
<=> V_m_2 = V_n_2 ),
file('theBenchmark.p',fact_Suc__mult__cancel1) ).
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_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__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_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_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_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_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_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_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__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__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__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_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_add__mult__distrib2,axiom,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
file('theBenchmark.p',fact_add__mult__distrib2) ).
fof(fact_add__mult__distrib,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
file('theBenchmark.p',fact_add__mult__distrib) ).
fof(fact_le__square,axiom,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)),
file('theBenchmark.p',fact_le__square) ).
fof(fact_le__cube,axiom,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
file('theBenchmark.p',fact_le__cube) ).
fof(fact_mult__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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ),
file('theBenchmark.p',fact_mult__le__mono1) ).
fof(fact_mult__le__mono2,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ),
file('theBenchmark.p',fact_mult__le__mono2) ).
fof(fact_mult__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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_l)) ) ),
file('theBenchmark.p',fact_mult__le__mono) ).
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_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__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__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__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__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_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__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__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_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_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_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_diff__mult__distrib2,axiom,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
file('theBenchmark.p',fact_diff__mult__distrib2) ).
fof(fact_diff__mult__distrib,axiom,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
file('theBenchmark.p',fact_diff__mult__distrib) ).
fof(fact_nat__mult__1,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
file('theBenchmark.p',fact_nat__mult__1) ).
fof(fact_nat__1__eq__mult__iff,axiom,
! [V_n_2,V_m_2] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).
fof(fact_nat__mult__1__right,axiom,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
file('theBenchmark.p',fact_nat__mult__1__right) ).
fof(fact_nat__mult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__1__iff) ).
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_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_mult__eq__1__iff,axiom,
! [V_n_2,V_m_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_mult__eq__1__iff) ).
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_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_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_mult__Suc__right,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_mult__Suc__right) ).
fof(fact_mult__Suc,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_mult__Suc) ).
fof(fact_Suc__mult__le__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(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_Suc__mult__le__cancel1) ).
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_mult__eq__self__implies__10,axiom,
! [V_n,V_m] :
( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
=> ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__eq__self__implies__10) ).
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_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_one__le__mult__iff,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
<=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) ),
file('theBenchmark.p',fact_one__le__mult__iff) ).
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_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_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_rabs__ratiotest__lemma,axiom,
! [V_y,V_x,V_c] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
=> V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_rabs__ratiotest__lemma) ).
fof(fact_complex_Osize_I1_J,axiom,
! [V_real2,V_real1] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_complex_Osize_I1_J) ).
fof(fact_nat__le__add__iff1,axiom,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) ) ),
file('theBenchmark.p',fact_nat__le__add__iff1) ).
fof(fact_nat__diff__add__eq1,axiom,
! [V_n,V_m,V_u,V_i,V_j] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n) ),
file('theBenchmark.p',fact_nat__diff__add__eq1) ).
fof(fact_nat__eq__add__iff1,axiom,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
<=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) = V_n_2 ) ),
file('theBenchmark.p',fact_nat__eq__add__iff1) ).
fof(fact_nat__mult__eq__cancel__disj,axiom,
! [V_n_2,V_m_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> ( V_m_2 = V_n_2
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel__disj) ).
fof(fact_left__add__mult__distrib,axiom,
! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k),
file('theBenchmark.p',fact_left__add__mult__distrib) ).
fof(fact_nat__eq__add__iff2,axiom,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
<=> V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) ) ),
file('theBenchmark.p',fact_nat__eq__add__iff2) ).
fof(fact_nat__diff__add__eq2,axiom,
! [V_n,V_m,V_u,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n)) ),
file('theBenchmark.p',fact_nat__diff__add__eq2) ).
fof(fact_nat__le__add__iff2,axiom,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) ) ),
file('theBenchmark.p',fact_nat__le__add__iff2) ).
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,hAPP(hAPP(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)))),hAPP(hAPP(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_complex_Osize_I2_J,axiom,
! [V_real2,V_real1] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_complex_Osize_I2_J) ).
fof(fact_complex_Osimps_I2_J,axiom,
! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2),
file('theBenchmark.p',fact_complex_Osimps_I2_J) ).
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_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_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_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_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_times__divide__eq__right,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Odivision__ring(T_a)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c) ),
file('theBenchmark.p',fact_times__divide__eq__right) ).
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_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_power__divide,axiom,
! [V_n,V_b,V_a,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> hAPP(hAPP(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ),
file('theBenchmark.p',fact_power__divide) ).
fof(fact_real__divide__square__eq,axiom,
! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a),hAPP(hAPP(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__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_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_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_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)
=> ( hAPP(hAPP(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_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 = hAPP(hAPP(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_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 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ),
file('theBenchmark.p',fact_nonzero__divide__eq__eq) ).
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)
<=> hAPP(hAPP(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_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_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_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_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)
=> hAPP(hAPP(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ),
file('theBenchmark.p',fact_nonzero__power__divide) ).
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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(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_real__0__le__divide__iff,axiom,
! [V_ya_2,V_xa_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_xa_2,V_ya_2))
<=> ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_ya_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_xa_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ) ),
file('theBenchmark.p',fact_real__0__le__divide__iff) ).
fof(fact_divide__eq__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_a_2
<=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of1) ).
fof(fact_divide__eq__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = c_Int_Onumber__class_Onumber__of(T_a,V_w_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2) ) ) ) ),
file('theBenchmark.p',fact_divide__eq__eq__number__of) ).
fof(fact_eq__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
<=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a)
=> c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of) ).
fof(fact_eq__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Ofield__inverse__zero(T_a) )
=> ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
<=> ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_b_2 ) ) ) ),
file('theBenchmark.p',fact_eq__divide__eq__number__of1) ).
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_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_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_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)
=> hAPP(hAPP(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
file('theBenchmark.p',fact_power__diff) ).
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_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_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_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_lemma__MVT,axiom,
! [V_b_2,V_a_2,V_f_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_2,V_a_2),hAPP(hAPP(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_f_2,V_b_2),hAPP(V_f_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_f_2,V_b_2),hAPP(hAPP(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_f_2,V_b_2),hAPP(V_f_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_DERIV__mult__lemma,axiom,
! [V_h,V_d,V_c,V_b,V_a,T_a] :
( class_RealVector_Oreal__field(T_a)
=> c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)),V_h) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d),V_h)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c),V_h)),V_d)) ),
file('theBenchmark.p',fact_DERIV__mult__lemma) ).
fof(fact_eq__divide__2__times__iff,axiom,
! [V_za_2,V_ya_2,V_xa_2] :
( V_xa_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_ya_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2))
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_xa_2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_ya_2,V_za_2) ),
file('theBenchmark.p',fact_eq__divide__2__times__iff) ).
fof(fact_diff__divide__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z) ) ),
file('theBenchmark.p',fact_diff__divide__eq__iff) ).
fof(fact_divide__diff__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z) ) ),
file('theBenchmark.p',fact_divide__diff__eq__iff) ).
fof(fact_diff__frac__eq,axiom,
! [V_w,V_x,V_z,V_y,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_diff__frac__eq) ).
fof(fact_times__divide__times__eq,axiom,
! [V_w,V_z,V_y,V_x,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_w)) ),
file('theBenchmark.p',fact_times__divide__times__eq) ).
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_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_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_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__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_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)
=> hAPP(hAPP(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 = hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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_w_2,V_xa_2,V_za_2,V_ya_2,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_ya_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_xa_2,V_ya_2) = c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_za_2)
<=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_za_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2) ) ) ) ),
file('theBenchmark.p',fact_frac__eq__eq) ).
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_add__frac__eq,axiom,
! [V_w,V_x,V_z,V_y,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
file('theBenchmark.p',fact_add__frac__eq) ).
fof(fact_divide__add__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z) ) ),
file('theBenchmark.p',fact_divide__add__eq__iff) ).
fof(fact_add__frac__num,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y) ) ),
file('theBenchmark.p',fact_add__frac__num) ).
fof(fact_add__divide__eq__iff,axiom,
! [V_y,V_x,V_z,T_a] :
( class_Fields_Ofield(T_a)
=> ( V_z != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z) ) ),
file('theBenchmark.p',fact_add__divide__eq__iff) ).
fof(fact_add__num__frac,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Ofield__inverse__zero(T_a)
=> ( V_y != c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y) ) ),
file('theBenchmark.p',fact_add__num__frac) ).
fof(fact_arctan__half,axiom,
! [V_x] : c_Transcendental_Oarctan(V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(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_arctan__half) ).
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,hAPP(hAPP(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)))),hAPP(hAPP(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_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,hAPP(hAPP(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)))),hAPP(hAPP(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_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono__neg) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono__neg) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_comm__mult__strict__left__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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__strict__left__mono) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ) ),
file('theBenchmark.p',fact_mult__strict__right__mono) ).
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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__neg__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,hAPP(hAPP(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__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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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_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),hAPP(hAPP(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_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),hAPP(hAPP(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_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,hAPP(hAPP(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_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,hAPP(hAPP(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__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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__pos__pos) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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__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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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__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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(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_not__square__less__zero,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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_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_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_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_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_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_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_arctan__zero__zero,axiom,
c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_arctan__zero__zero) ).
fof(fact_arctan__monotone_H,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_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)) ),
file('theBenchmark.p',fact_arctan__monotone_H) ).
fof(fact_arctan__monotone,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_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)) ),
file('theBenchmark.p',fact_arctan__monotone) ).
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_real__sqrt__less__iff,axiom,
! [V_ya_2,V_xa_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) ),
file('theBenchmark.p',fact_real__sqrt__less__iff) ).
fof(fact_less__special_I3_J,axiom,
! [V_xa_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_xa_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OPls) ) ),
file('theBenchmark.p',fact_less__special_I3_J) ).
fof(fact_less__special_I1_J,axiom,
! [V_ya_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_ya_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_ya_2) ) ),
file('theBenchmark.p',fact_less__special_I1_J) ).
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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__strict__decreasing) ).
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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
file('theBenchmark.p',fact_one__less__power) ).
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_ya_2,V_xa_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_xa_2 != V_ya_2
<=> ( c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)
| c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_not__less__iff__gr__or__eq,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
<=> ( V_xa_2 = V_ya_2
| c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_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_xa_2,V_ya_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
<=> V_xa_2 = V_ya_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_less__eq__real__def,axiom,
! [V_ya_2,V_xa_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
<=> ( V_xa_2 = V_ya_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ),
file('theBenchmark.p',fact_less__eq__real__def) ).
fof(fact_real__less__def,axiom,
! [V_ya_2,V_xa_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)
<=> ( V_xa_2 != V_ya_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ),
file('theBenchmark.p',fact_real__less__def) ).
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_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_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__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__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__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__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__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_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_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_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__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_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__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_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_linorder__antisym__conv2,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
<=> V_xa_2 = V_ya_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
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_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_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_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_linorder__antisym__conv1,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
<=> V_xa_2 = V_ya_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
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_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_order__le__less,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
<=> ( V_xa_2 = V_ya_2
| c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_less__le__not__le,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__less__le,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
<=> ( V_xa_2 != V_ya_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) ) ) ),
file('theBenchmark.p',fact_order__less__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_linorder__not__le,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__not__less,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N)) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing) ).
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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(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__iff,axiom,
! [V_ya_2,V_xa_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing__iff) ).
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_less__number__of,axiom,
! [V_ya_2,V_xa_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_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2) ) ),
file('theBenchmark.p',fact_less__number__of) ).
fof(fact_less__special_I4_J,axiom,
! [V_xa_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_xa_2),c_Groups_Oone__class_Oone(T_a))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)) ) ),
file('theBenchmark.p',fact_less__special_I4_J) ).
fof(fact_less__special_I2_J,axiom,
! [V_ya_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_ya_2))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2) ) ),
file('theBenchmark.p',fact_less__special_I2_J) ).
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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)) ) ) ) ),
file('theBenchmark.p',fact_power__strict__mono) ).
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_le__number__of__eq__not__less,axiom,
! [V_w_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_w_2))
<=> ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Int_Onumber__class_Onumber__of(T_a,V_v_2)) ) ),
file('theBenchmark.p',fact_le__number__of__eq__not__less) ).
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_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_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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),V_n)) ) ) ),
file('theBenchmark.p',fact_less__1__mult) ).
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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ),
file('theBenchmark.p',fact_zero__less__power) ).
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_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_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)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(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_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_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__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_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,hAPP(hAPP(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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)) ) ) ),
file('theBenchmark.p',fact_abs__mult__less) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_y)) ) ),
file('theBenchmark.p',fact_real__mult__less__mono2) ).
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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) ) ),
file('theBenchmark.p',fact_real__mult__order) ).
fof(fact_real__mult__less__iff1,axiom,
! [V_ya_2,V_xa_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_za_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ),
file('theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_not__real__square__gt__zero,axiom,
! [V_xa_2] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2))
<=> V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_not__real__square__gt__zero) ).
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_real__sqrt__gt__0__iff,axiom,
! [V_ya_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2) ),
file('theBenchmark.p',fact_real__sqrt__gt__0__iff) ).
fof(fact_real__sqrt__lt__0__iff,axiom,
! [V_xa_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_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__lt__1__iff,axiom,
! [V_xa_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_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_ya_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2) ),
file('theBenchmark.p',fact_real__sqrt__gt__1__iff) ).
fof(fact_mult__le__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__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_mult__le__cancel__left__pos) ).
fof(fact_mult__le__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__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) ) ) ),
file('theBenchmark.p',fact_mult__le__cancel__left__neg) ).
fof(fact_mult__strict__mono,axiom,
! [V_d,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,V_c,V_d)
=> ( 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_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono) ).
fof(fact_mult__strict__mono_H,axiom,
! [V_d,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,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(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__strict__mono_H) ).
fof(fact_mult__less__le__imp__less,axiom,
! [V_d,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__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(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__less__le__imp__less) ).
fof(fact_mult__le__less__imp__less,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(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_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(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d)) ) ) ) ) ),
file('theBenchmark.p',fact_mult__le__less__imp__less) ).
fof(fact_mult__right__less__imp__less,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__right__less__imp__less) ).
fof(fact_mult__less__imp__less__right,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__right) ).
fof(fact_mult__left__less__imp__less,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__left__less__imp__less) ).
fof(fact_mult__less__imp__less__left,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__less__imp__less__left) ).
fof(fact_mult__right__le__imp__le,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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__eq(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__right__le__imp__le) ).
fof(fact_mult__left__le__imp__le,axiom,
! [V_b,V_a,V_c,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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__eq(T_a,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_mult__left__le__imp__le) ).
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_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__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__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__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__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_not__sum__squares__lt__zero,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__ring(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_not__sum__squares__lt__zero) ).
fof(fact_sum__squares__gt__zero__iff,axiom,
! [V_ya_2,V_xa_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)))
<=> ( V_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__gt__zero__iff) ).
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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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_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_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_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_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_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__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_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_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_less__add__iff2,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_less__add__iff2) ).
fof(fact_less__add__iff1,axiom,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( class_Rings_Oordered__ring(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_less__add__iff1) ).
fof(fact_less__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_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_c_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_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq) ).
fof(fact_divide__less__eq,axiom,
! [V_a_2,V_c_2,V_b_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_b_2,V_c_2),V_a_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_c_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,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq) ).
fof(fact_pos__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Fields_Olinordered__field(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,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ),
file('theBenchmark.p',fact_pos__less__divide__eq) ).
fof(fact_pos__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_a] :
( class_Fields_Olinordered__field(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_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ),
file('theBenchmark.p',fact_pos__divide__less__eq) ).
fof(fact_mult__imp__div__pos__less,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Olinordered__field(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ),
file('theBenchmark.p',fact_mult__imp__div__pos__less) ).
fof(fact_mult__imp__less__div__pos,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Olinordered__field(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)
=> c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_mult__imp__less__div__pos) ).
fof(fact_neg__less__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Fields_Olinordered__field(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,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ),
file('theBenchmark.p',fact_neg__less__divide__eq) ).
fof(fact_neg__divide__less__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_a] :
( class_Fields_Olinordered__field(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_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
<=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ),
file('theBenchmark.p',fact_neg__divide__less__eq) ).
fof(fact_divide__strict__left__mono,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,c_Groups_Ozero__class_Ozero(T_a),V_c)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ),
file('theBenchmark.p',fact_divide__strict__left__mono) ).
fof(fact_divide__strict__left__mono__neg,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,V_c,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
=> c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ),
file('theBenchmark.p',fact_divide__strict__left__mono__neg) ).
fof(fact_power__gt1__lemma,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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_power__gt1__lemma) ).
fof(fact_power__less__power__Suc,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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
file('theBenchmark.p',fact_power__less__power__Suc) ).
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_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),hAPP(hAPP(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_r_2,V_a_2,V_xa_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_xa_2,V_a_2)),V_r_2)
<=> ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_r_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_r_2),V_xa_2) ) ) ),
file('theBenchmark.p',fact_abs__diff__less__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_zero__less__norm__iff,axiom,
! [V_xa_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_xa_2))
<=> V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [V_ya_2,V_xa_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__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_za_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ),
file('theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [V_ya_2,V_xa_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__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_ya_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ),
file('theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_s)) ) ) ),
file('theBenchmark.p',fact_norm__mult__less) ).
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_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_arctan__add,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_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
=> c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)) = c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)))) ) ),
file('theBenchmark.p',fact_arctan__add) ).
fof(fact_divide__left__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(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono__neg) ).
fof(fact_divide__left__mono,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( 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)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b)) ) ) ) ),
file('theBenchmark.p',fact_divide__left__mono) ).
fof(fact_neg__divide__le__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ),
file('theBenchmark.p',fact_neg__divide__le__eq) ).
fof(fact_neg__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ),
file('theBenchmark.p',fact_neg__le__divide__eq) ).
fof(fact_mult__imp__le__div__pos,axiom,
! [V_x,V_z,V_y,T_a] :
( class_Fields_Olinordered__field(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) ) ) ),
file('theBenchmark.p',fact_mult__imp__le__div__pos) ).
fof(fact_mult__imp__div__pos__le,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Fields_Olinordered__field(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) ) ) ),
file('theBenchmark.p',fact_mult__imp__div__pos__le) ).
fof(fact_pos__divide__le__eq,axiom,
! [V_a_2,V_b_2,V_c_2,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ),
file('theBenchmark.p',fact_pos__divide__le__eq) ).
fof(fact_pos__le__divide__eq,axiom,
! [V_b_2,V_a_2,V_c_2,T_a] :
( class_Fields_Olinordered__field(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ),
file('theBenchmark.p',fact_pos__le__divide__eq) ).
fof(fact_divide__le__eq,axiom,
! [V_a_2,V_c_2,V_b_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_b_2,V_c_2),V_a_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_c_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(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq) ).
fof(fact_le__divide__eq,axiom,
! [V_c_2,V_b_2,V_a_2,T_a] :
( class_Fields_Olinordered__field__inverse__zero(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_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_c_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(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq) ).
fof(fact_power__Suc__less,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ) ) ),
file('theBenchmark.p',fact_power__Suc__less) ).
fof(fact_divide__less__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_a] :
( ( class_Int_Onumber(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_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_a_2)
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of1) ).
fof(fact_divide__less__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_a] :
( ( class_Int_Onumber(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_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_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_c_2,c_Groups_Ozero__class_Ozero(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_w_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__less__eq__number__of) ).
fof(fact_less__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_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_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of) ).
fof(fact_less__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
=> c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_less__divide__eq__number__of1) ).
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,hAPP(hAPP(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__increasing__iff,axiom,
! [V_ya_2,V_xa_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_xa_2,V_ya_2) ) ) ),
file('theBenchmark.p',fact_power__increasing__iff) ).
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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(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_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_convex__bound__lt,axiom,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( class_Rings_Olinordered__semiring__1__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) = c_Groups_Oone__class_Oone(T_a)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a) ) ) ) ) ) ),
file('theBenchmark.p',fact_convex__bound__lt) ).
fof(fact_divide__le__eq__number__of1,axiom,
! [V_a_2,V_w_2,V_b_2,T_a] :
( ( class_Int_Onumber(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_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_a_2)
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of1) ).
fof(fact_divide__le__eq__number__of,axiom,
! [V_w_2,V_c_2,V_b_2,T_a] :
( ( class_Int_Onumber(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_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_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_c_2,c_Groups_Ozero__class_Ozero(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_w_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2)) ) ) ) ),
file('theBenchmark.p',fact_divide__le__eq__number__of) ).
fof(fact_le__divide__eq__number__of,axiom,
! [V_c_2,V_b_2,V_w_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_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_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2)) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of) ).
fof(fact_le__divide__eq__number__of1,axiom,
! [V_w_2,V_b_2,V_a_2,T_a] :
( ( class_Int_Onumber(T_a)
& class_Fields_Olinordered__field__inverse__zero(T_a) )
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
<=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) ) ) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2) ) ) ) ),
file('theBenchmark.p',fact_le__divide__eq__number__of1) ).
fof(fact_half__gt__zero__iff,axiom,
! [V_r_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_r_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_r_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_power2__less__0,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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),hAPP(hAPP(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_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__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_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_power2__less__imp__less,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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_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_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,hAPP(hAPP(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)))),hAPP(hAPP(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_ya_2,V_xa_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
<=> ( V_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__power2__gt__zero__iff) ).
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),hAPP(hAPP(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__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_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,hAPP(hAPP(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_odd__power__less__zero,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(hAPP(hAPP(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_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_odd__power__less__zero) ).
fof(fact_machin,axiom,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))))))))),
file('theBenchmark.p',fact_machin) ).
fof(fact_complex_Orecs,axiom,
! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2),
file('theBenchmark.p',fact_complex_Orecs) ).
fof(fact_natceiling__add__one,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_natceiling__add__one) ).
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_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_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_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_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_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__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_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_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_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_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_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_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_pi__not__less__zero,axiom,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Opi,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_pi__not__less__zero) ).
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_pi__gt__zero,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi),
file('theBenchmark.p',fact_pi__gt__zero) ).
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_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_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_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_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_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_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_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_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__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__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__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_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_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_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_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__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_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_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_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_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_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_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__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_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_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_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_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_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_rel__simps_I7_J,axiom,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
file('theBenchmark.p',fact_rel__simps_I7_J) ).
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_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_zless__le,axiom,
! [V_w_2,V_za_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_w_2)
<=> ( V_za_2 != V_w_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_w_2) ) ),
file('theBenchmark.p',fact_zless__le) ).
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_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_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_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__fun__def,axiom,
! [V_g_2,V_f_2,T_a,T_b] :
( class_Orderings_Oord(T_b)
=> ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) ) ),
file('theBenchmark.p',fact_less__fun__def) ).
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_pi__ge__zero,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi),
file('theBenchmark.p',fact_pi__ge__zero) ).
fof(fact_pi__neq__zero,axiom,
c_Transcendental_Opi != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_pi__neq__zero) ).
fof(fact_bin__less__0__simps_I4_J,axiom,
! [V_w_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_bin__less__0__simps_I4_J) ).
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_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_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_bin__less__0__simps_I3_J,axiom,
! [V_w_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_bin__less__0__simps_I3_J) ).
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_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_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_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_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_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_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_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__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_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_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_nat__0__less__mult__iff,axiom,
! [V_n_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_nat__0__less__mult__iff) ).
fof(fact_mult__less__cancel1,axiom,
! [V_n_2,V_m_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) ),
file('theBenchmark.p',fact_mult__less__cancel1) ).
fof(fact_mult__less__cancel2,axiom,
! [V_n_2,V_k_2,V_m_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ) ),
file('theBenchmark.p',fact_mult__less__cancel2) ).
fof(fact_mult__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_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k)) ) ),
file('theBenchmark.p',fact_mult__less__mono1) ).
fof(fact_mult__less__mono2,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_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j)) ) ),
file('theBenchmark.p',fact_mult__less__mono2) ).
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_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__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1__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__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring__1) ).
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__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__semiring) ).
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_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring__abs) ).
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,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__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__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
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__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__semiring,axiom,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Olinordered__semiring) ).
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,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__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__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_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__Rings_Olinordered__semiring__1__strict,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict) ).
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__Rings_Olinordered__semiring__1,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring__1) ).
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__Rings_Olinordered__semiring,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__semiring) ).
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_Oordered__ring__abs,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oordered__ring__abs) ).
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__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__RealVector_Oreal__field) ).
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__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__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
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__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__RealVector_Oreal__field,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__RealVector_Oreal__field) ).
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__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__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
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__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(conj_0,conjecture,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('theBenchmark.p',conj_0) ).
fof(f_1_1,plain,
! [V_g_2,V_f_2] :
( V_f_2 = V_g_2
| ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_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]) ).
fof(f_1_4,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(definitional_conversion,[status(esa)],[f_1_3]) ).
cnf(f_1_5,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_4]) ).
fof(f_2_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096]) ).
fof(f_2_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_2_1]) ).
cnf(f_2_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact__096abs_A_I2_A_K_Ay_J_A_060_061_A1_096]) ).
fof(f_3_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_3_1]) ).
cnf(f_3_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact__0962_A_K_Ax_A_060_061_A1_096]) ).
fof(f_4_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_4_1]) ).
cnf(f_4_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_4_2]) ).
fof(f_5_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact__0962_A_K_Ay_A_060_061_A1_096]) ).
fof(f_5_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_5_1]) ).
cnf(f_5_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_5_2]) ).
fof(f_6_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(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_6_2,plain,
! [U_3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(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_3)),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_3] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(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_3)),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(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_3)),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [V_x] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(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))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),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_four__x__squared]) ).
fof(f_7_2,plain,
! [U_4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_4] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_4),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_4)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [V_w,T_b] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_w)),c_Int_Onumber__class_Onumber__of(T_b,V_w))
| ~ class_Int_Onumber(T_b)
| ~ class_Groups_Omonoid__mult(T_b) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__square__number__of]) ).
fof(f_8_2,plain,
! [U_6,U_5] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5),c_Int_Onumber__class_Onumber__of(U_5,U_6)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5),c_Int_Onumber__class_Onumber__of(U_5,U_6)),c_Int_Onumber__class_Onumber__of(U_5,U_6))
| ~ class_Int_Onumber(U_5)
| ~ class_Groups_Omonoid__mult(U_5) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_6,U_5] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5),c_Int_Onumber__class_Onumber__of(U_5,U_6)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5),c_Int_Onumber__class_Onumber__of(U_5,U_6)),c_Int_Onumber__class_Onumber__of(U_5,U_6))
| ~ class_Int_Onumber(U_5)
| ~ class_Groups_Omonoid__mult(U_5) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_5),c_Int_Onumber__class_Onumber__of(U_5,U_6)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5),c_Int_Onumber__class_Onumber__of(U_5,U_6)),c_Int_Onumber__class_Onumber__of(U_5,U_6))
| ~ class_Int_Onumber(U_5)
| ~ class_Groups_Omonoid__mult(U_5) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(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))))) = hAPP(hAPP(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_9_2,plain,
! [U_8,U_7] :
( c_Groups_Oabs__class_Oabs(U_7,hAPP(hAPP(c_Power_Opower__class_Opower(U_7),U_8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7),U_8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
! [U_8,U_7] :
( c_Groups_Oabs__class_Oabs(U_7,hAPP(hAPP(c_Power_Opower__class_Opower(U_7),U_8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7),U_8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7) ),
inference(definitional_conversion,[status(esa)],[f_9_2]) ).
cnf(f_9_4,plain,
( c_Groups_Oabs__class_Oabs(U_7,hAPP(hAPP(c_Power_Opower__class_Opower(U_7),U_8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_7),U_8),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_7) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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)))) = hAPP(hAPP(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_10_2,plain,
! [U_10,U_9] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_9),c_Groups_Oabs__class_Oabs(U_9,U_10)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9),U_10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_9) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_9,U_10] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_9),c_Groups_Oabs__class_Oabs(U_9,U_10)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9),U_10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_9) ),
inference(definitional_conversion,[status(esa)],[f_10_2]) ).
cnf(f_10_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_9),c_Groups_Oabs__class_Oabs(U_9,U_10)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_9),U_10),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__idom(U_9) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [T_a] :
( hAPP(hAPP(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_11_2,plain,
! [U_11] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11),c_Groups_Oone__class_Oone(U_11)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_11)
| ~ class_Rings_Osemiring__1(U_11) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_11] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11),c_Groups_Oone__class_Oone(U_11)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_11)
| ~ class_Rings_Osemiring__1(U_11) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_11),c_Groups_Oone__class_Oone(U_11)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(U_11)
| ~ class_Rings_Osemiring__1(U_11) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(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))))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J]) ).
fof(f_12_2,plain,
! [U_13,U_12] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12),U_13),U_13) = hAPP(hAPP(c_Power_Opower__class_Opower(U_12),U_13),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(U_12) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_12,U_13] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12),U_13),U_13) = hAPP(hAPP(c_Power_Opower__class_Opower(U_12),U_13),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(U_12) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12),U_13),U_13) = hAPP(hAPP(c_Power_Opower__class_Opower(U_12),U_13),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Ocomm__semiring__1(U_12) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__eq__square]) ).
fof(f_13_2,plain,
! [U_15,U_14] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_14),U_15),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14),U_15),U_15)
| ~ class_Groups_Omonoid__mult(U_14) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_14,U_15] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_14),U_15),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14),U_15),U_15)
| ~ class_Groups_Omonoid__mult(U_14) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_14),U_15),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14),U_15),U_15)
| ~ class_Groups_Omonoid__mult(U_14) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [V_n,V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(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_14_2,plain,
! [U_18,U_17,U_16] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_16),U_17),hAPP(hAPP(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_18)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_16),hAPP(hAPP(c_Power_Opower__class_Opower(U_16),U_17),U_18)),hAPP(hAPP(c_Power_Opower__class_Opower(U_16),U_17),U_18))
| ~ class_Rings_Ocomm__semiring__1(U_16) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_16,U_17,U_18] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_16),U_17),hAPP(hAPP(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_18)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_16),hAPP(hAPP(c_Power_Opower__class_Opower(U_16),U_17),U_18)),hAPP(hAPP(c_Power_Opower__class_Opower(U_16),U_17),U_18))
| ~ class_Rings_Ocomm__semiring__1(U_16) ),
inference(definitional_conversion,[status(esa)],[f_14_2]) ).
cnf(f_14_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_16),U_17),hAPP(hAPP(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_18)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_16),hAPP(hAPP(c_Power_Opower__class_Opower(U_16),U_17),U_18)),hAPP(hAPP(c_Power_Opower__class_Opower(U_16),U_17),U_18))
| ~ class_Rings_Ocomm__semiring__1(U_16) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),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__096_N1_A_060_061_A2_A_K_Ax_096]) ).
fof(f_15_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),
inference(definitional_conversion,[status(esa)],[f_15_1]) ).
cnf(f_15_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power3__eq__cube]) ).
fof(f_16_2,plain,
! [U_20,U_19] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_19),U_20),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_19),U_20),U_20)),U_20)
| ~ class_Groups_Omonoid__mult(U_19) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_19,U_20] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_19),U_20),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_19),U_20),U_20)),U_20)
| ~ class_Groups_Omonoid__mult(U_19) ),
inference(definitional_conversion,[status(esa)],[f_16_2]) ).
cnf(f_16_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_19),U_20),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_19),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_19),U_20),U_20)),U_20)
| ~ class_Groups_Omonoid__mult(U_19) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____)),
inference(fof_nnf,[status(thm)],[fact__096_N1_A_060_061_A2_A_K_Ay_096]) ).
fof(f_17_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____)),
inference(definitional_conversion,[status(esa)],[f_17_1]) ).
cnf(f_17_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OMin),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_y____)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_eq__number__of__Pls__Min]) ).
fof(f_18_2,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
inference(definitional_conversion,[status(esa)],[f_18_1]) ).
cnf(f_18_3,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls) != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [V_q,V_p,V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),V_q) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J]) ).
fof(f_19_2,plain,
! [U_24,U_23,U_22,U_21] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_21),hAPP(hAPP(c_Power_Opower__class_Opower(U_21),U_22),U_23)),U_24) = hAPP(hAPP(c_Power_Opower__class_Opower(U_21),U_22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_23),U_24))
| ~ class_Rings_Ocomm__semiring__1(U_21) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_21,U_22,U_23,U_24] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_21),hAPP(hAPP(c_Power_Opower__class_Opower(U_21),U_22),U_23)),U_24) = hAPP(hAPP(c_Power_Opower__class_Opower(U_21),U_22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_23),U_24))
| ~ class_Rings_Ocomm__semiring__1(U_21) ),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_21),hAPP(hAPP(c_Power_Opower__class_Opower(U_21),U_22),U_23)),U_24) = hAPP(hAPP(c_Power_Opower__class_Opower(U_21),U_22),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_23),U_24))
| ~ class_Rings_Ocomm__semiring__1(U_21) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(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_20_2,plain,
! [U_26,U_25] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_25),U_26),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_26
| ~ class_Rings_Ocomm__semiring__1(U_25) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_26,U_25] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_25),U_26),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_26
| ~ class_Rings_Ocomm__semiring__1(U_25) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_25),U_26),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_26
| ~ class_Rings_Ocomm__semiring__1(U_25) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_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]) ).
fof(f_21_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(definitional_conversion,[status(esa)],[f_21_1]) ).
cnf(f_21_3,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_21_2]) ).
fof(f_22_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]) ).
fof(f_22_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(definitional_conversion,[status(esa)],[f_22_1]) ).
cnf(f_22_3,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_22_2]) ).
fof(f_23_1,plain,
! [V_n,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)),hAPP(hAPP(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_Oone__class_Oone(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__m1__even]) ).
fof(f_23_2,plain,
! [U_28,U_27] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_27),c_Int_Onumber__class_Onumber__of(U_27,c_Int_OMin)),hAPP(hAPP(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_28)) = c_Groups_Oone__class_Oone(U_27)
| ~ class_Int_Onumber__ring(U_27) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_27,U_28] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_27),c_Int_Onumber__class_Onumber__of(U_27,c_Int_OMin)),hAPP(hAPP(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_28)) = c_Groups_Oone__class_Oone(U_27)
| ~ class_Int_Onumber__ring(U_27) ),
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_27),c_Int_Onumber__class_Onumber__of(U_27,c_Int_OMin)),hAPP(hAPP(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_28)) = c_Groups_Oone__class_Oone(U_27)
| ~ class_Int_Onumber__ring(U_27) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_rx)),hAPP(hAPP(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_24_2,plain,
! [U_33,U_32,U_31,U_30,U_29] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_30),U_31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_32),U_33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_30),U_32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_31),U_33))
| ~ class_Rings_Ocomm__semiring__1(U_29) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_29,U_30,U_31,U_32,U_33] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_30),U_31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_32),U_33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_30),U_32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_31),U_33))
| ~ class_Rings_Ocomm__semiring__1(U_29) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_30),U_31)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_32),U_33)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_30),U_32)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_29),U_31),U_33))
| ~ class_Rings_Ocomm__semiring__1(U_29) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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_25_2,plain,
! [U_38,U_37,U_36,U_35,U_34] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_35),U_36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_37),U_38)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_35),U_36)),U_38))
| ~ class_Rings_Ocomm__semiring__1(U_34) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_34,U_35,U_36,U_37,U_38] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_35),U_36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_37),U_38)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_35),U_36)),U_38))
| ~ class_Rings_Ocomm__semiring__1(U_34) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_35),U_36)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_37),U_38)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_37),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_34),U_35),U_36)),U_38))
| ~ class_Rings_Ocomm__semiring__1(U_34) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_1,plain,
! [V_ry,V_rx,V_ly,V_lx,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),hAPP(hAPP(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_26_2,plain,
! [U_43,U_42,U_41,U_40,U_39] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_40),U_41)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_42),U_43)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_40),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_41),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_42),U_43)))
| ~ class_Rings_Ocomm__semiring__1(U_39) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_39,U_40,U_41,U_42,U_43] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_40),U_41)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_42),U_43)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_40),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_41),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_42),U_43)))
| ~ class_Rings_Ocomm__semiring__1(U_39) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_40),U_41)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_42),U_43)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_40),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_41),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_39),U_42),U_43)))
| ~ class_Rings_Ocomm__semiring__1(U_39) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [V_rx,V_ly,V_lx,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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_27_2,plain,
! [U_47,U_46,U_45,U_44] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),U_45),U_46)),U_47) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),U_45),U_47)),U_46)
| ~ class_Rings_Ocomm__semiring__1(U_44) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
! [U_44,U_45,U_46,U_47] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),U_45),U_46)),U_47) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),U_45),U_47)),U_46)
| ~ class_Rings_Ocomm__semiring__1(U_44) ),
inference(definitional_conversion,[status(esa)],[f_27_2]) ).
cnf(f_27_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),U_45),U_46)),U_47) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_44),U_45),U_47)),U_46)
| ~ class_Rings_Ocomm__semiring__1(U_44) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [V_rx,V_ly,V_lx,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(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_28_2,plain,
! [U_51,U_50,U_49,U_48] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),U_49),U_50)),U_51) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),U_49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),U_50),U_51))
| ~ class_Rings_Ocomm__semiring__1(U_48) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_48,U_49,U_50,U_51] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),U_49),U_50)),U_51) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),U_49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),U_50),U_51))
| ~ class_Rings_Ocomm__semiring__1(U_48) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),U_49),U_50)),U_51) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),U_49),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_48),U_50),U_51))
| ~ class_Rings_Ocomm__semiring__1(U_48) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_1,plain,
! [V_ry,V_rx,V_lx,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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_29_2,plain,
! [U_55,U_54,U_53,U_52] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),U_53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),U_54),U_55)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),U_53),U_54)),U_55)
| ~ class_Rings_Ocomm__semiring__1(U_52) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_52,U_53,U_54,U_55] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),U_53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),U_54),U_55)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),U_53),U_54)),U_55)
| ~ class_Rings_Ocomm__semiring__1(U_52) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),U_53),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),U_54),U_55)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_52),U_53),U_54)),U_55)
| ~ class_Rings_Ocomm__semiring__1(U_52) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [V_ry,V_rx,V_lx,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),V_ry)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_rx),hAPP(hAPP(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_30_2,plain,
! [U_59,U_58,U_57,U_56] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_58),U_59)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_57),U_59))
| ~ class_Rings_Ocomm__semiring__1(U_56) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
! [U_56,U_57,U_58,U_59] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_58),U_59)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_57),U_59))
| ~ class_Rings_Ocomm__semiring__1(U_56) ),
inference(definitional_conversion,[status(esa)],[f_30_2]) ).
cnf(f_30_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_57),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_58),U_59)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_58),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_56),U_57),U_59))
| ~ class_Rings_Ocomm__semiring__1(U_56) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(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_31_2,plain,
! [U_62,U_61,U_60] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_60),U_61),U_62) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_60),U_62),U_61)
| ~ class_Rings_Ocomm__semiring__1(U_60) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_60,U_61,U_62] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_60),U_61),U_62) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_60),U_62),U_61)
| ~ class_Rings_Ocomm__semiring__1(U_60) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_60),U_61),U_62) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_60),U_62),U_61)
| ~ class_Rings_Ocomm__semiring__1(U_60) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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_32_2,plain,
! [U_64,U_63] :
( U_63 = U_64
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_64,U_63)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_63,U_64) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_64,U_63] :
( U_63 = U_64
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_64,U_63)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_63,U_64) ),
inference(definitional_conversion,[status(esa)],[f_32_2]) ).
cnf(f_32_4,plain,
( U_63 = U_64
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_64,U_63)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_63,U_64) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_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_33_2,plain,
! [U_67,U_66,U_65] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_65,U_67)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_66,U_67)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_65,U_66) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_66,U_65,U_67] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_65,U_67)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_66,U_67)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_65,U_66) ),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_65,U_67)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_66,U_67)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_65,U_66) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_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_34_2,plain,
! [U_69,U_68] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_69,U_68)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_68,U_69) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_69,U_68] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_69,U_68)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_68,U_69) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_69,U_68)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_68,U_69) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_70] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_70,U_70),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_70] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_70,U_70),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_70,U_70),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,plain,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_z3)),
inference(fof_nnf,[status(thm)],[fact_real__mult__assoc]) ).
fof(f_36_2,plain,
! [U_73,U_72,U_71] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_71),U_72)),U_73) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_72),U_73)),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_71,U_72,U_73] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_71),U_72)),U_73) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_72),U_73)),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_71),U_72)),U_73) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_71),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_72),U_73)),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,plain,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_w),V_z),
inference(fof_nnf,[status(thm)],[fact_real__mult__commute]) ).
fof(f_37_2,plain,
! [U_75,U_74] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_74),U_75) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_75),U_74),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_74,U_75] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_74),U_75) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_75),U_74),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_74),U_75) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_75),U_74),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__even__eq]) ).
fof(f_38_2,plain,
! [U_78,U_77,U_76] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_76),U_77),hAPP(hAPP(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_78)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_76),hAPP(hAPP(c_Power_Opower__class_Opower(U_76),U_77),U_78)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_76) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_76,U_77,U_78] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_76),U_77),hAPP(hAPP(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_78)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_76),hAPP(hAPP(c_Power_Opower__class_Opower(U_76),U_77),U_78)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_76) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_76),U_77),hAPP(hAPP(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_78)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_76),hAPP(hAPP(c_Power_Opower__class_Opower(U_76),U_77),U_78)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Groups_Omonoid__mult(U_76) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_39_2,plain,
! [U_80,U_79] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),c_Groups_Oone__class_Oone(U_79)) = U_80
| ~ class_Rings_Ocomm__semiring__1(U_79) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_79,U_80] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),c_Groups_Oone__class_Oone(U_79)) = U_80
| ~ class_Rings_Ocomm__semiring__1(U_79) ),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_79),U_80),c_Groups_Oone__class_Oone(U_79)) = U_80
| ~ class_Rings_Ocomm__semiring__1(U_79) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_40_2,plain,
! [U_82,U_81] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_81),c_Groups_Oone__class_Oone(U_81)),U_82) = U_82
| ~ class_Rings_Ocomm__semiring__1(U_81) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_81,U_82] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_81),c_Groups_Oone__class_Oone(U_81)),U_82) = U_82
| ~ class_Rings_Ocomm__semiring__1(U_81) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_81),c_Groups_Oone__class_Oone(U_81)),U_82) = U_82
| ~ class_Rings_Ocomm__semiring__1(U_81) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_1,plain,
! [V_q,V_y,V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),V_q) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),hAPP(hAPP(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_41_2,plain,
! [U_86,U_85,U_84,U_83] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_84),U_85)),U_86) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),hAPP(hAPP(c_Power_Opower__class_Opower(U_83),U_84),U_86)),hAPP(hAPP(c_Power_Opower__class_Opower(U_83),U_85),U_86))
| ~ class_Rings_Ocomm__semiring__1(U_83) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_83,U_84,U_85,U_86] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_84),U_85)),U_86) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),hAPP(hAPP(c_Power_Opower__class_Opower(U_83),U_84),U_86)),hAPP(hAPP(c_Power_Opower__class_Opower(U_83),U_85),U_86))
| ~ class_Rings_Ocomm__semiring__1(U_83) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_83),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),U_84),U_85)),U_86) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_83),hAPP(hAPP(c_Power_Opower__class_Opower(U_83),U_84),U_86)),hAPP(hAPP(c_Power_Opower__class_Opower(U_83),U_85),U_86))
| ~ class_Rings_Ocomm__semiring__1(U_83) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_1,plain,
! [V_z] : hAPP(hAPP(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_42_2,plain,
! [U_87] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_87) = U_87,
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_87] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_87) = U_87,
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_87) = U_87,
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_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_43_2,plain,
! [U_88] :
( c_Groups_Oone__class_Oone(U_88) = c_Int_Onumber__class_Onumber__of(U_88,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_88) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_88] :
( c_Groups_Oone__class_Oone(U_88) = c_Int_Onumber__class_Onumber__of(U_88,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_88) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( c_Groups_Oone__class_Oone(U_88) = c_Int_Onumber__class_Onumber__of(U_88,c_Int_OBit1(c_Int_OPls))
| ~ class_Int_Onumber__ring(U_88) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_1,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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_xy]) ).
fof(f_44_2,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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(definitional_conversion,[status(esa)],[f_44_1]) ).
cnf(f_44_3,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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(clausify,[status(thm)],[f_44_2]) ).
fof(f_45_1,plain,
! [V_n,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)),V_n)) = 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_abs__power__minus__one]) ).
fof(f_45_2,plain,
! [U_90,U_89] :
( c_Groups_Oabs__class_Oabs(U_89,hAPP(hAPP(c_Power_Opower__class_Opower(U_89),c_Int_Onumber__class_Onumber__of(U_89,c_Int_OMin)),U_90)) = c_Groups_Oone__class_Oone(U_89)
| ~ class_Rings_Olinordered__idom(U_89)
| ~ class_Int_Onumber__ring(U_89) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_89,U_90] :
( c_Groups_Oabs__class_Oabs(U_89,hAPP(hAPP(c_Power_Opower__class_Opower(U_89),c_Int_Onumber__class_Onumber__of(U_89,c_Int_OMin)),U_90)) = c_Groups_Oone__class_Oone(U_89)
| ~ class_Rings_Olinordered__idom(U_89)
| ~ class_Int_Onumber__ring(U_89) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( c_Groups_Oabs__class_Oabs(U_89,hAPP(hAPP(c_Power_Opower__class_Opower(U_89),c_Int_Onumber__class_Onumber__of(U_89,c_Int_OMin)),U_90)) = c_Groups_Oone__class_Oone(U_89)
| ~ class_Rings_Olinordered__idom(U_89)
| ~ class_Int_Onumber__ring(U_89) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_1,plain,
! [V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_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_46_2,plain,
! [U_92,U_91] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_91,c_Int_Onumber__class_Onumber__of(U_91,U_92),c_Groups_Oone__class_Oone(U_91))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_92,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_92,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(U_91,c_Int_Onumber__class_Onumber__of(U_91,U_92),c_Groups_Oone__class_Oone(U_91)) ) )
| ~ class_Rings_Olinordered__idom(U_91)
| ~ class_Int_Onumber__ring(U_91) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
( ! [U_91,U_92] :
( c_Orderings_Oord__class_Oless__eq(U_91,c_Int_Onumber__class_Onumber__of(U_91,U_92),c_Groups_Oone__class_Oone(U_91))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_92,c_Int_OBit1(c_Int_OPls))
| ~ sP0(U_91,U_92) )
& ! [U_91,U_92] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_92,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(U_91,c_Int_Onumber__class_Onumber__of(U_91,U_92),c_Groups_Oone__class_Oone(U_91))
| ~ sP0(U_91,U_92) )
& ! [U_91,U_92] :
( sP0(U_91,U_92)
| ~ class_Rings_Olinordered__idom(U_91)
| ~ class_Int_Onumber__ring(U_91) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_46_2]) ).
cnf(f_46_4,plain,
( sP0(U_91,U_92)
| ~ class_Rings_Olinordered__idom(U_91)
| ~ class_Int_Onumber__ring(U_91) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_92,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless__eq(U_91,c_Int_Onumber__class_Onumber__of(U_91,U_92),c_Groups_Oone__class_Oone(U_91))
| ~ sP0(U_91,U_92) ),
inference(clausify,[status(thm)],[f_46_3]) ).
cnf(f_46_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_91,c_Int_Onumber__class_Onumber__of(U_91,U_92),c_Groups_Oone__class_Oone(U_91))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_92,c_Int_OBit1(c_Int_OPls))
| ~ sP0(U_91,U_92) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_1,plain,
! [V_ya_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_ya_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_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_ya_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_47_2,plain,
! [U_94,U_93] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Oone__class_Oone(U_93),c_Int_Onumber__class_Onumber__of(U_93,U_94))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_94) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_94)
| ~ c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Oone__class_Oone(U_93),c_Int_Onumber__class_Onumber__of(U_93,U_94)) ) )
| ~ class_Rings_Olinordered__idom(U_93)
| ~ class_Int_Onumber__ring(U_93) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
( ! [U_93,U_94] :
( c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Oone__class_Oone(U_93),c_Int_Onumber__class_Onumber__of(U_93,U_94))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_94)
| ~ sP1(U_93,U_94) )
& ! [U_93,U_94] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_94)
| ~ c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Oone__class_Oone(U_93),c_Int_Onumber__class_Onumber__of(U_93,U_94))
| ~ sP1(U_93,U_94) )
& ! [U_93,U_94] :
( sP1(U_93,U_94)
| ~ class_Rings_Olinordered__idom(U_93)
| ~ class_Int_Onumber__ring(U_93) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_47_2]) ).
cnf(f_47_4,plain,
( sP1(U_93,U_94)
| ~ class_Rings_Olinordered__idom(U_93)
| ~ class_Int_Onumber__ring(U_93) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_94)
| ~ c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Oone__class_Oone(U_93),c_Int_Onumber__class_Onumber__of(U_93,U_94))
| ~ sP1(U_93,U_94) ),
inference(clausify,[status(thm)],[f_47_3]) ).
cnf(f_47_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_93,c_Groups_Oone__class_Oone(U_93),c_Int_Onumber__class_Onumber__of(U_93,U_94))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_94)
| ~ sP1(U_93,U_94) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_1,plain,
! [V_z] : hAPP(hAPP(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_48_2,plain,
! [U_95] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(U_95)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_95,
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_95] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(U_95)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_95,
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Fundamental__Theorem__Algebra__Mirabelle_Ocsqrt(U_95)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_95,
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)) = 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_abs__minus__one]) ).
fof(f_49_2,plain,
! [U_96] :
( c_Groups_Oabs__class_Oabs(U_96,c_Int_Onumber__class_Onumber__of(U_96,c_Int_OMin)) = c_Groups_Oone__class_Oone(U_96)
| ~ class_Rings_Olinordered__idom(U_96)
| ~ class_Int_Onumber__ring(U_96) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
! [U_96] :
( c_Groups_Oabs__class_Oabs(U_96,c_Int_Onumber__class_Onumber__of(U_96,c_Int_OMin)) = c_Groups_Oone__class_Oone(U_96)
| ~ class_Rings_Olinordered__idom(U_96)
| ~ class_Int_Onumber__ring(U_96) ),
inference(definitional_conversion,[status(esa)],[f_49_2]) ).
cnf(f_49_4,plain,
( c_Groups_Oabs__class_Oabs(U_96,c_Int_Onumber__class_Onumber__of(U_96,c_Int_OMin)) = c_Groups_Oone__class_Oone(U_96)
| ~ class_Rings_Olinordered__idom(U_96)
| ~ class_Int_Onumber__ring(U_96) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_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_50_2,plain,
! [U_97] :
( c_Int_Onumber__class_Onumber__of(U_97,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_97)
| ~ class_Int_Onumber__ring(U_97) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_97] :
( c_Int_Onumber__class_Onumber__of(U_97,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_97)
| ~ class_Int_Onumber__ring(U_97) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( c_Int_Onumber__class_Onumber__of(U_97,c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_97)
| ~ class_Int_Onumber__ring(U_97) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit1(c_Int_OPls))),V_a) = V_a
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__numeral__1]) ).
fof(f_51_2,plain,
! [U_99,U_98] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_98),c_Int_Onumber__class_Onumber__of(U_98,c_Int_OBit1(c_Int_OPls))),U_99) = U_99
| ~ class_Int_Onumber__ring(U_98) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
! [U_98,U_99] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_98),c_Int_Onumber__class_Onumber__of(U_98,c_Int_OBit1(c_Int_OPls))),U_99) = U_99
| ~ class_Int_Onumber__ring(U_98) ),
inference(definitional_conversion,[status(esa)],[f_51_2]) ).
cnf(f_51_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_98),c_Int_Onumber__class_Onumber__of(U_98,c_Int_OBit1(c_Int_OPls))),U_99) = U_99
| ~ class_Int_Onumber__ring(U_98) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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) ),
inference(fof_nnf,[status(thm)],[fact_mult__numeral__1__right]) ).
fof(f_52_2,plain,
! [U_101,U_100] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_100),U_101),c_Int_Onumber__class_Onumber__of(U_100,c_Int_OBit1(c_Int_OPls))) = U_101
| ~ class_Int_Onumber__ring(U_100) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
! [U_100,U_101] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_100),U_101),c_Int_Onumber__class_Onumber__of(U_100,c_Int_OBit1(c_Int_OPls))) = U_101
| ~ class_Int_Onumber__ring(U_100) ),
inference(definitional_conversion,[status(esa)],[f_52_2]) ).
cnf(f_52_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_100),U_101),c_Int_Onumber__class_Onumber__of(U_100,c_Int_OBit1(c_Int_OPls))) = U_101
| ~ class_Int_Onumber__ring(U_100) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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_53_2,plain,
! [U_105,U_104,U_103,U_102] :
( c_Orderings_Oord__class_Oless__eq(U_102,hAPP(hAPP(c_Power_Opower__class_Opower(U_102),U_105),U_103),hAPP(hAPP(c_Power_Opower__class_Opower(U_102),U_105),U_104))
| ~ c_Orderings_Oord__class_Oless__eq(U_102,c_Groups_Oone__class_Oone(U_102),U_105)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_103,U_104)
| ~ class_Rings_Olinordered__semidom(U_102) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_102,U_103,U_104,U_105] :
( c_Orderings_Oord__class_Oless__eq(U_102,hAPP(hAPP(c_Power_Opower__class_Opower(U_102),U_105),U_103),hAPP(hAPP(c_Power_Opower__class_Opower(U_102),U_105),U_104))
| ~ c_Orderings_Oord__class_Oless__eq(U_102,c_Groups_Oone__class_Oone(U_102),U_105)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_103,U_104)
| ~ class_Rings_Olinordered__semidom(U_102) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_102,hAPP(hAPP(c_Power_Opower__class_Opower(U_102),U_105),U_103),hAPP(hAPP(c_Power_Opower__class_Opower(U_102),U_105),U_104))
| ~ c_Orderings_Oord__class_Oless__eq(U_102,c_Groups_Oone__class_Oone(U_102),U_105)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_103,U_104)
| ~ class_Rings_Olinordered__semidom(U_102) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(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_54_2,plain,
! [U_108,U_107,U_106] :
( c_Orderings_Oord__class_Oless__eq(U_106,c_Groups_Oone__class_Oone(U_106),hAPP(hAPP(c_Power_Opower__class_Opower(U_106),U_107),U_108))
| ~ c_Orderings_Oord__class_Oless__eq(U_106,c_Groups_Oone__class_Oone(U_106),U_107)
| ~ class_Rings_Olinordered__semidom(U_106) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_108,U_106,U_107] :
( c_Orderings_Oord__class_Oless__eq(U_106,c_Groups_Oone__class_Oone(U_106),hAPP(hAPP(c_Power_Opower__class_Opower(U_106),U_107),U_108))
| ~ c_Orderings_Oord__class_Oless__eq(U_106,c_Groups_Oone__class_Oone(U_106),U_107)
| ~ class_Rings_Olinordered__semidom(U_106) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_106,c_Groups_Oone__class_Oone(U_106),hAPP(hAPP(c_Power_Opower__class_Opower(U_106),U_107),U_108))
| ~ c_Orderings_Oord__class_Oless__eq(U_106,c_Groups_Oone__class_Oone(U_106),U_107)
| ~ class_Rings_Olinordered__semidom(U_106) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_1,plain,
v_z = c_Complex_Ocomplex_OComplex(v_x____,v_y____),
inference(fof_nnf,[status(thm)],[fact_z]) ).
fof(f_55_2,plain,
v_z = c_Complex_Ocomplex_OComplex(v_x____,v_y____),
inference(definitional_conversion,[status(esa)],[f_55_1]) ).
cnf(f_55_3,plain,
v_z = c_Complex_Ocomplex_OComplex(v_x____,v_y____),
inference(clausify,[status(thm)],[f_55_2]) ).
fof(f_56_1,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_assms]) ).
fof(f_56_2,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_56_1]) ).
cnf(f_56_3,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_56_2]) ).
fof(f_57_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_57_2,plain,
! [U_109] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_109) = U_109,
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_109] : c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_109) = U_109,
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_109) = U_109,
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_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_58_2,plain,
! [U_112,U_111,U_110] :
( c_Int_Onumber__class_Onumber__of(U_110,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_111,U_112)) = c_Groups_Oplus__class_Oplus(U_110,c_Int_Onumber__class_Onumber__of(U_110,U_111),c_Int_Onumber__class_Onumber__of(U_110,U_112))
| ~ class_Int_Onumber__ring(U_110) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
! [U_110,U_111,U_112] :
( c_Int_Onumber__class_Onumber__of(U_110,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_111,U_112)) = c_Groups_Oplus__class_Oplus(U_110,c_Int_Onumber__class_Onumber__of(U_110,U_111),c_Int_Onumber__class_Onumber__of(U_110,U_112))
| ~ class_Int_Onumber__ring(U_110) ),
inference(definitional_conversion,[status(esa)],[f_58_2]) ).
cnf(f_58_4,plain,
( c_Int_Onumber__class_Onumber__of(U_110,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_111,U_112)) = c_Groups_Oplus__class_Oplus(U_110,c_Int_Onumber__class_Onumber__of(U_110,U_111),c_Int_Onumber__class_Onumber__of(U_110,U_112))
| ~ class_Int_Onumber__ring(U_110) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_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_59_2,plain,
! [U_115,U_114,U_113] :
( c_Groups_Oplus__class_Oplus(U_113,U_114,U_115) = c_Groups_Oplus__class_Oplus(U_113,U_115,U_114)
| ~ class_Rings_Ocomm__semiring__1(U_113) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
! [U_114,U_113,U_115] :
( c_Groups_Oplus__class_Oplus(U_113,U_114,U_115) = c_Groups_Oplus__class_Oplus(U_113,U_115,U_114)
| ~ class_Rings_Ocomm__semiring__1(U_113) ),
inference(definitional_conversion,[status(esa)],[f_59_2]) ).
cnf(f_59_4,plain,
( c_Groups_Oplus__class_Oplus(U_113,U_114,U_115) = c_Groups_Oplus__class_Oplus(U_113,U_115,U_114)
| ~ class_Rings_Ocomm__semiring__1(U_113) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_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_60_2,plain,
! [U_119,U_118,U_117,U_116] :
( c_Groups_Oplus__class_Oplus(U_116,U_117,c_Groups_Oplus__class_Oplus(U_116,U_118,U_119)) = c_Groups_Oplus__class_Oplus(U_116,U_118,c_Groups_Oplus__class_Oplus(U_116,U_117,U_119))
| ~ class_Rings_Ocomm__semiring__1(U_116) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_116,U_117,U_118,U_119] :
( c_Groups_Oplus__class_Oplus(U_116,U_117,c_Groups_Oplus__class_Oplus(U_116,U_118,U_119)) = c_Groups_Oplus__class_Oplus(U_116,U_118,c_Groups_Oplus__class_Oplus(U_116,U_117,U_119))
| ~ class_Rings_Ocomm__semiring__1(U_116) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( c_Groups_Oplus__class_Oplus(U_116,U_117,c_Groups_Oplus__class_Oplus(U_116,U_118,U_119)) = c_Groups_Oplus__class_Oplus(U_116,U_118,c_Groups_Oplus__class_Oplus(U_116,U_117,U_119))
| ~ class_Rings_Ocomm__semiring__1(U_116) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_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_61_2,plain,
! [U_123,U_122,U_121,U_120] :
( c_Groups_Oplus__class_Oplus(U_120,U_121,c_Groups_Oplus__class_Oplus(U_120,U_122,U_123)) = c_Groups_Oplus__class_Oplus(U_120,c_Groups_Oplus__class_Oplus(U_120,U_121,U_122),U_123)
| ~ class_Rings_Ocomm__semiring__1(U_120) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_121,U_120,U_122,U_123] :
( c_Groups_Oplus__class_Oplus(U_120,U_121,c_Groups_Oplus__class_Oplus(U_120,U_122,U_123)) = c_Groups_Oplus__class_Oplus(U_120,c_Groups_Oplus__class_Oplus(U_120,U_121,U_122),U_123)
| ~ class_Rings_Ocomm__semiring__1(U_120) ),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
( c_Groups_Oplus__class_Oplus(U_120,U_121,c_Groups_Oplus__class_Oplus(U_120,U_122,U_123)) = c_Groups_Oplus__class_Oplus(U_120,c_Groups_Oplus__class_Oplus(U_120,U_121,U_122),U_123)
| ~ class_Rings_Ocomm__semiring__1(U_120) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_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_62_2,plain,
! [U_126,U_125,U_124] :
( c_Groups_Oplus__class_Oplus(U_124,c_Int_Onumber__class_Onumber__of(U_124,U_125),c_Int_Onumber__class_Onumber__of(U_124,U_126)) = c_Int_Onumber__class_Onumber__of(U_124,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_125,U_126))
| ~ class_Int_Onumber__ring(U_124) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_124,U_125,U_126] :
( c_Groups_Oplus__class_Oplus(U_124,c_Int_Onumber__class_Onumber__of(U_124,U_125),c_Int_Onumber__class_Onumber__of(U_124,U_126)) = c_Int_Onumber__class_Onumber__of(U_124,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_125,U_126))
| ~ class_Int_Onumber__ring(U_124) ),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
( c_Groups_Oplus__class_Oplus(U_124,c_Int_Onumber__class_Onumber__of(U_124,U_125),c_Int_Onumber__class_Onumber__of(U_124,U_126)) = c_Int_Onumber__class_Onumber__of(U_124,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_125,U_126))
| ~ class_Int_Onumber__ring(U_124) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_1,plain,
! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)),
inference(fof_nnf,[status(thm)],[fact_times__numeral__code_I5_J]) ).
fof(f_63_2,plain,
! [U_128,U_127] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_127)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_128)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_127),U_128)),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_127,U_128] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_127)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_128)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_127),U_128)),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_127)),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_128)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_127),U_128)),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_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_64_2,plain,
! [U_130,U_129] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_129),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_130))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_129,U_130) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_129,U_130)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_129),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_130)) ) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
( ! [U_134,U_132] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_132),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_134))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_132,U_134) )
& ! [U_133,U_131] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_131,U_133)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_131),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_133)) ) ),
inference(miniscope,[status(thm)],[f_64_2]) ).
fof(f_64_4,plain,
( ! [U_132,U_134] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_132),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_134))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_132,U_134) )
& ! [U_133,U_131] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_131,U_133)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_131),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_133)) ) ),
inference(definitional_conversion,[status(esa)],[f_64_3]) ).
cnf(f_64_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_131,U_133)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_131),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_133)) ),
inference(clausify,[status(thm)],[f_64_4]) ).
cnf(f_64_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_132),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_134))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_132,U_134) ),
inference(clausify,[status(thm)],[f_64_4]) ).
fof(f_65_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_65_2,plain,
! [U_138,U_137,U_136,U_135] :
( c_Groups_Oplus__class_Oplus(U_135,c_Int_Onumber__class_Onumber__of(U_135,U_136),c_Groups_Oplus__class_Oplus(U_135,c_Int_Onumber__class_Onumber__of(U_135,U_137),U_138)) = c_Groups_Oplus__class_Oplus(U_135,c_Int_Onumber__class_Onumber__of(U_135,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_136,U_137)),U_138)
| ~ class_Int_Onumber__ring(U_135) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_138,U_136,U_137,U_135] :
( c_Groups_Oplus__class_Oplus(U_135,c_Int_Onumber__class_Onumber__of(U_135,U_136),c_Groups_Oplus__class_Oplus(U_135,c_Int_Onumber__class_Onumber__of(U_135,U_137),U_138)) = c_Groups_Oplus__class_Oplus(U_135,c_Int_Onumber__class_Onumber__of(U_135,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_136,U_137)),U_138)
| ~ class_Int_Onumber__ring(U_135) ),
inference(definitional_conversion,[status(esa)],[f_65_2]) ).
cnf(f_65_4,plain,
( c_Groups_Oplus__class_Oplus(U_135,c_Int_Onumber__class_Onumber__of(U_135,U_136),c_Groups_Oplus__class_Oplus(U_135,c_Int_Onumber__class_Onumber__of(U_135,U_137),U_138)) = c_Groups_Oplus__class_Oplus(U_135,c_Int_Onumber__class_Onumber__of(U_135,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_136,U_137)),U_138)
| ~ class_Int_Onumber__ring(U_135) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_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_66_2,plain,
! [U_142,U_141,U_140,U_139] :
( c_Groups_Oplus__class_Oplus(U_139,c_Groups_Oplus__class_Oplus(U_139,U_140,U_141),U_142) = c_Groups_Oplus__class_Oplus(U_139,U_140,c_Groups_Oplus__class_Oplus(U_139,U_141,U_142))
| ~ class_Rings_Ocomm__semiring__1(U_139) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_140,U_139,U_142,U_141] :
( c_Groups_Oplus__class_Oplus(U_139,c_Groups_Oplus__class_Oplus(U_139,U_140,U_141),U_142) = c_Groups_Oplus__class_Oplus(U_139,U_140,c_Groups_Oplus__class_Oplus(U_139,U_141,U_142))
| ~ class_Rings_Ocomm__semiring__1(U_139) ),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
( c_Groups_Oplus__class_Oplus(U_139,c_Groups_Oplus__class_Oplus(U_139,U_140,U_141),U_142) = c_Groups_Oplus__class_Oplus(U_139,U_140,c_Groups_Oplus__class_Oplus(U_139,U_141,U_142))
| ~ class_Rings_Ocomm__semiring__1(U_139) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_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_67_2,plain,
! [U_146,U_145,U_144,U_143] :
( c_Groups_Oplus__class_Oplus(U_143,c_Groups_Oplus__class_Oplus(U_143,U_144,U_145),U_146) = c_Groups_Oplus__class_Oplus(U_143,c_Groups_Oplus__class_Oplus(U_143,U_144,U_146),U_145)
| ~ class_Rings_Ocomm__semiring__1(U_143) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
! [U_144,U_143,U_145,U_146] :
( c_Groups_Oplus__class_Oplus(U_143,c_Groups_Oplus__class_Oplus(U_143,U_144,U_145),U_146) = c_Groups_Oplus__class_Oplus(U_143,c_Groups_Oplus__class_Oplus(U_143,U_144,U_146),U_145)
| ~ class_Rings_Ocomm__semiring__1(U_143) ),
inference(definitional_conversion,[status(esa)],[f_67_2]) ).
cnf(f_67_4,plain,
( c_Groups_Oplus__class_Oplus(U_143,c_Groups_Oplus__class_Oplus(U_143,U_144,U_145),U_146) = c_Groups_Oplus__class_Oplus(U_143,c_Groups_Oplus__class_Oplus(U_143,U_144,U_146),U_145)
| ~ class_Rings_Ocomm__semiring__1(U_143) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_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_68_2,plain,
! [U_151,U_150,U_149,U_148,U_147] :
( c_Groups_Oplus__class_Oplus(U_147,c_Groups_Oplus__class_Oplus(U_147,U_148,U_149),c_Groups_Oplus__class_Oplus(U_147,U_150,U_151)) = c_Groups_Oplus__class_Oplus(U_147,c_Groups_Oplus__class_Oplus(U_147,U_148,U_150),c_Groups_Oplus__class_Oplus(U_147,U_149,U_151))
| ~ class_Rings_Ocomm__semiring__1(U_147) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_147,U_148,U_149,U_150,U_151] :
( c_Groups_Oplus__class_Oplus(U_147,c_Groups_Oplus__class_Oplus(U_147,U_148,U_149),c_Groups_Oplus__class_Oplus(U_147,U_150,U_151)) = c_Groups_Oplus__class_Oplus(U_147,c_Groups_Oplus__class_Oplus(U_147,U_148,U_150),c_Groups_Oplus__class_Oplus(U_147,U_149,U_151))
| ~ class_Rings_Ocomm__semiring__1(U_147) ),
inference(definitional_conversion,[status(esa)],[f_68_2]) ).
cnf(f_68_4,plain,
( c_Groups_Oplus__class_Oplus(U_147,c_Groups_Oplus__class_Oplus(U_147,U_148,U_149),c_Groups_Oplus__class_Oplus(U_147,U_150,U_151)) = c_Groups_Oplus__class_Oplus(U_147,c_Groups_Oplus__class_Oplus(U_147,U_148,U_150),c_Groups_Oplus__class_Oplus(U_147,U_149,U_151))
| ~ class_Rings_Ocomm__semiring__1(U_147) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_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_69_2,plain,
! [U_153,U_152] :
( U_152 = U_153
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_153,U_152)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_152,U_153) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_153,U_152] :
( U_152 = U_153
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_153,U_152)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_152,U_153) ),
inference(definitional_conversion,[status(esa)],[f_69_2]) ).
cnf(f_69_4,plain,
( U_152 = U_153
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_153,U_152)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_152,U_153) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_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_70_2,plain,
! [U_156,U_155,U_154] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_154,U_156)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_155,U_156)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_154,U_155) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_156,U_155,U_154] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_154,U_156)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_155,U_156)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_154,U_155) ),
inference(definitional_conversion,[status(esa)],[f_70_2]) ).
cnf(f_70_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_154,U_156)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_155,U_156)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_154,U_155) ),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_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_71_2,plain,
! [U_158,U_157] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_158,U_157)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_157,U_158) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_158,U_157] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_158,U_157)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_157,U_158) ),
inference(definitional_conversion,[status(esa)],[f_71_2]) ).
cnf(f_71_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_158,U_157)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_157,U_158) ),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_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_72_2,plain,
! [U_159] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_159,U_159),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
! [U_159] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_159,U_159),
inference(definitional_conversion,[status(esa)],[f_72_2]) ).
cnf(f_72_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_159,U_159),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_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_73_2,plain,
! [U_161,U_160] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_160),c_Int_OBit1(U_161))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_160,U_161) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_160,U_161)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_160),c_Int_OBit1(U_161)) ) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
( ! [U_165,U_163] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_163),c_Int_OBit1(U_165))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_163,U_165) )
& ! [U_164,U_162] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_162,U_164)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_162),c_Int_OBit1(U_164)) ) ),
inference(miniscope,[status(thm)],[f_73_2]) ).
fof(f_73_4,plain,
( ! [U_163,U_165] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_163),c_Int_OBit1(U_165))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_163,U_165) )
& ! [U_164,U_162] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_162,U_164)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_162),c_Int_OBit1(U_164)) ) ),
inference(definitional_conversion,[status(esa)],[f_73_3]) ).
cnf(f_73_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_162,U_164)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_162),c_Int_OBit1(U_164)) ),
inference(clausify,[status(thm)],[f_73_4]) ).
cnf(f_73_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_163),c_Int_OBit1(U_165))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_163,U_165) ),
inference(clausify,[status(thm)],[f_73_4]) ).
fof(f_74_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_74_2,plain,
! [U_167,U_166] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_166),c_Int_OBit1(U_167))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_166,U_167) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_166,U_167)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_166),c_Int_OBit1(U_167)) ) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
( ! [U_171,U_169] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_169),c_Int_OBit1(U_171))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_169,U_171) )
& ! [U_170,U_168] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_168,U_170)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_168),c_Int_OBit1(U_170)) ) ),
inference(miniscope,[status(thm)],[f_74_2]) ).
fof(f_74_4,plain,
( ! [U_169,U_171] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_169),c_Int_OBit1(U_171))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_169,U_171) )
& ! [U_170,U_168] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_168,U_170)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_168),c_Int_OBit1(U_170)) ) ),
inference(definitional_conversion,[status(esa)],[f_74_3]) ).
cnf(f_74_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_168,U_170)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_168),c_Int_OBit1(U_170)) ),
inference(clausify,[status(thm)],[f_74_4]) ).
cnf(f_74_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_169),c_Int_OBit1(U_171))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_169,U_171) ),
inference(clausify,[status(thm)],[f_74_4]) ).
fof(f_75_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]) ).
fof(f_75_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_75_1]) ).
cnf(f_75_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(clausify,[status(thm)],[f_75_2]) ).
fof(f_76_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_76_2,plain,
! [U_173,U_172] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_172),c_Int_OBit0(U_173))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_172,U_173) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_172,U_173)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_172),c_Int_OBit0(U_173)) ) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_177,U_175] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_175),c_Int_OBit0(U_177))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_175,U_177) )
& ! [U_176,U_174] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_174,U_176)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_174),c_Int_OBit0(U_176)) ) ),
inference(miniscope,[status(thm)],[f_76_2]) ).
fof(f_76_4,plain,
( ! [U_177,U_175] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_175),c_Int_OBit0(U_177))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_175,U_177) )
& ! [U_176,U_174] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_174,U_176)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_174),c_Int_OBit0(U_176)) ) ),
inference(definitional_conversion,[status(esa)],[f_76_3]) ).
cnf(f_76_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_174,U_176)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_174),c_Int_OBit0(U_176)) ),
inference(clausify,[status(thm)],[f_76_4]) ).
cnf(f_76_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_175),c_Int_OBit0(U_177))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_175,U_177) ),
inference(clausify,[status(thm)],[f_76_4]) ).
fof(f_77_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_77_2,plain,
! [U_179,U_178] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_178),c_Int_OBit0(U_179))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_178,U_179) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_178,U_179)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_178),c_Int_OBit0(U_179)) ) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
( ! [U_183,U_181] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_181),c_Int_OBit0(U_183))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_181,U_183) )
& ! [U_182,U_180] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_180,U_182)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_180),c_Int_OBit0(U_182)) ) ),
inference(miniscope,[status(thm)],[f_77_2]) ).
fof(f_77_4,plain,
( ! [U_183,U_181] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_181),c_Int_OBit0(U_183))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_181,U_183) )
& ! [U_182,U_180] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_180,U_182)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_180),c_Int_OBit0(U_182)) ) ),
inference(definitional_conversion,[status(esa)],[f_77_3]) ).
cnf(f_77_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_180,U_182)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_180),c_Int_OBit0(U_182)) ),
inference(clausify,[status(thm)],[f_77_4]) ).
cnf(f_77_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_181),c_Int_OBit0(U_183))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_181,U_183) ),
inference(clausify,[status(thm)],[f_77_4]) ).
fof(f_78_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I24_J]) ).
fof(f_78_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(definitional_conversion,[status(esa)],[f_78_1]) ).
cnf(f_78_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(clausify,[status(thm)],[f_78_2]) ).
fof(f_79_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_79_2,plain,
! [U_185,U_184] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_184),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_185))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_184,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_184,U_185) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_184,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_184,U_185)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_184),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_185)) ) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
( ! [U_189,U_187] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_187),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_189))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_187,c_Int_OPls)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_187,U_189) ) )
& ! [U_188,U_186] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_186,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_186,U_188)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_186),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_188)) ) ),
inference(miniscope,[status(thm)],[f_79_2]) ).
fof(f_79_4,plain,
( ! [U_187,U_189] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_187,c_Int_OPls)
| ~ sP2(U_187,U_189) )
& ! [U_187,U_189] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_187,U_189)
| ~ sP2(U_187,U_189) )
& ! [U_187,U_189] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_187),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_189))
| sP2(U_187,U_189) )
& ! [U_186,U_188] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_186,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_186,U_188)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_186),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_188)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_79_3]) ).
cnf(f_79_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_186,c_Int_OPls)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_186,U_188)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_186),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_188)) ),
inference(clausify,[status(thm)],[f_79_4]) ).
cnf(f_79_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_187),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_189))
| sP2(U_187,U_189) ),
inference(clausify,[status(thm)],[f_79_4]) ).
cnf(f_79_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_187,U_189)
| ~ sP2(U_187,U_189) ),
inference(clausify,[status(thm)],[f_79_4]) ).
cnf(f_79_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_187,c_Int_OPls)
| ~ sP2(U_187,U_189) ),
inference(clausify,[status(thm)],[f_79_4]) ).
fof(f_80_1,plain,
! [V_z,V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Oplus__class_Oplus(T_a,V_y,V_z)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J]) ).
fof(f_80_2,plain,
! [U_193,U_192,U_191,U_190] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_190),U_191),c_Groups_Oplus__class_Oplus(U_190,U_192,U_193)) = c_Groups_Oplus__class_Oplus(U_190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_190),U_191),U_192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_190),U_191),U_193))
| ~ class_Rings_Ocomm__semiring__1(U_190) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
! [U_190,U_192,U_191,U_193] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_190),U_191),c_Groups_Oplus__class_Oplus(U_190,U_192,U_193)) = c_Groups_Oplus__class_Oplus(U_190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_190),U_191),U_192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_190),U_191),U_193))
| ~ class_Rings_Ocomm__semiring__1(U_190) ),
inference(definitional_conversion,[status(esa)],[f_80_2]) ).
cnf(f_80_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_190),U_191),c_Groups_Oplus__class_Oplus(U_190,U_192,U_193)) = c_Groups_Oplus__class_Oplus(U_190,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_190),U_191),U_192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_190),U_191),U_193))
| ~ class_Rings_Ocomm__semiring__1(U_190) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_1,plain,
! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] :
( ( ( ( V_c_2 != V_d_2
& V_a_2 != V_b_2 )
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) )
& ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))
| V_c_2 = V_d_2
| V_a_2 = V_b_2 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__noteq]) ).
fof(f_81_2,plain,
! [U_198,U_197,U_196,U_195,U_194] :
( ( ( ( U_197 != U_198
& U_195 != U_196 )
| c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_198)) = c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_197)) )
& ( c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_198)) != c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_197))
| U_197 = U_198
| U_195 = U_196 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_194) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
( ! [U_195,U_196,U_197,U_198] :
( U_197 != U_198
| ~ sP3(U_195,U_196,U_197,U_198) )
& ! [U_195,U_196,U_197,U_198] :
( U_195 != U_196
| ~ sP3(U_195,U_196,U_197,U_198) )
& ! [U_194,U_195,U_196,U_197,U_198] :
( sP3(U_195,U_196,U_197,U_198)
| c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_198)) = c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_197))
| ~ sP4(U_194,U_195,U_196,U_197,U_198) )
& ! [U_194,U_195,U_196,U_197,U_198] :
( c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_198)) != c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_197))
| U_197 = U_198
| U_195 = U_196
| ~ sP4(U_194,U_195,U_196,U_197,U_198) )
& ! [U_194,U_195,U_196,U_197,U_198] :
( sP4(U_194,U_195,U_196,U_197,U_198)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_194) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4])],[f_81_2]) ).
cnf(f_81_4,plain,
( sP4(U_194,U_195,U_196,U_197,U_198)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_194) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_5,plain,
( c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_198)) != c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_197))
| U_197 = U_198
| U_195 = U_196
| ~ sP4(U_194,U_195,U_196,U_197,U_198) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_6,plain,
( sP3(U_195,U_196,U_197,U_198)
| c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_197),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_198)) = c_Groups_Oplus__class_Oplus(U_194,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_195),U_198),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_194),U_196),U_197))
| ~ sP4(U_194,U_195,U_196,U_197,U_198) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_7,plain,
( U_195 != U_196
| ~ sP3(U_195,U_196,U_197,U_198) ),
inference(clausify,[status(thm)],[f_81_3]) ).
cnf(f_81_8,plain,
( U_197 != U_198
| ~ sP3(U_195,U_196,U_197,U_198) ),
inference(clausify,[status(thm)],[f_81_3]) ).
fof(f_82_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_I8_J]) ).
fof(f_82_2,plain,
! [U_202,U_201,U_200,U_199] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_199),c_Groups_Oplus__class_Oplus(U_199,U_200,U_201)),U_202) = c_Groups_Oplus__class_Oplus(U_199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_199),U_200),U_202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_199),U_201),U_202))
| ~ class_Rings_Ocomm__semiring__1(U_199) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_201,U_202,U_200,U_199] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_199),c_Groups_Oplus__class_Oplus(U_199,U_200,U_201)),U_202) = c_Groups_Oplus__class_Oplus(U_199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_199),U_200),U_202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_199),U_201),U_202))
| ~ class_Rings_Ocomm__semiring__1(U_199) ),
inference(definitional_conversion,[status(esa)],[f_82_2]) ).
cnf(f_82_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_199),c_Groups_Oplus__class_Oplus(U_199,U_200,U_201)),U_202) = c_Groups_Oplus__class_Oplus(U_199,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_199),U_200),U_202),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_199),U_201),U_202))
| ~ class_Rings_Ocomm__semiring__1(U_199) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_1,plain,
! [V_b,V_m,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J]) ).
fof(f_83_2,plain,
! [U_206,U_205,U_204,U_203] :
( c_Groups_Oplus__class_Oplus(U_203,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_203),U_204),U_205),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_203),U_206),U_205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_203),c_Groups_Oplus__class_Oplus(U_203,U_204,U_206)),U_205)
| ~ class_Rings_Ocomm__semiring__1(U_203) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
! [U_203,U_204,U_205,U_206] :
( c_Groups_Oplus__class_Oplus(U_203,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_203),U_204),U_205),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_203),U_206),U_205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_203),c_Groups_Oplus__class_Oplus(U_203,U_204,U_206)),U_205)
| ~ class_Rings_Ocomm__semiring__1(U_203) ),
inference(definitional_conversion,[status(esa)],[f_83_2]) ).
cnf(f_83_4,plain,
( c_Groups_Oplus__class_Oplus(U_203,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_203),U_204),U_205),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_203),U_206),U_205)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_203),c_Groups_Oplus__class_Oplus(U_203,U_204,U_206)),U_205)
| ~ class_Rings_Ocomm__semiring__1(U_203) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [V_za_2,V_xa_2,V_ya_2,V_w_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_za_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_ya_2))
| ( V_ya_2 != V_za_2
& V_w_2 != V_xa_2 ) )
& ( V_ya_2 = V_za_2
| V_w_2 = V_xa_2
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_za_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_ya_2)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).
fof(f_84_2,plain,
! [U_211,U_210,U_209,U_208,U_207] :
( ( ( c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_211)) = c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_209))
| ( U_209 != U_211
& U_208 != U_210 ) )
& ( U_209 = U_211
| U_208 = U_210
| c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_211)) != c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_209)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_207) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( ! [U_208,U_209,U_210,U_211] :
( U_209 != U_211
| ~ sP5(U_208,U_209,U_210,U_211) )
& ! [U_208,U_209,U_210,U_211] :
( U_208 != U_210
| ~ sP5(U_208,U_209,U_210,U_211) )
& ! [U_207,U_208,U_209,U_210,U_211] :
( c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_211)) = c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_209))
| sP5(U_208,U_209,U_210,U_211)
| ~ sP6(U_207,U_208,U_209,U_210,U_211) )
& ! [U_207,U_208,U_209,U_210,U_211] :
( U_209 = U_211
| U_208 = U_210
| c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_211)) != c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_209))
| ~ sP6(U_207,U_208,U_209,U_210,U_211) )
& ! [U_207,U_208,U_209,U_210,U_211] :
( sP6(U_207,U_208,U_209,U_210,U_211)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_207) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5,sP6])],[f_84_2]) ).
cnf(f_84_4,plain,
( sP6(U_207,U_208,U_209,U_210,U_211)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_207) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_5,plain,
( U_209 = U_211
| U_208 = U_210
| c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_211)) != c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_209))
| ~ sP6(U_207,U_208,U_209,U_210,U_211) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_6,plain,
( c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_209),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_211)) = c_Groups_Oplus__class_Oplus(U_207,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_208),U_211),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_207),U_210),U_209))
| sP5(U_208,U_209,U_210,U_211)
| ~ sP6(U_207,U_208,U_209,U_210,U_211) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_7,plain,
( U_208 != U_210
| ~ sP5(U_208,U_209,U_210,U_211) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_8,plain,
( U_209 != U_211
| ~ sP5(U_208,U_209,U_210,U_211) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_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_85_2,plain,
! [U_214,U_213,U_212] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_214,U_212),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_214,U_213))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_212,U_213) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_213,U_214,U_212] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_214,U_212),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_214,U_213))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_212,U_213) ),
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_214,U_212),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_214,U_213))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_212,U_213) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [V_w,V_z2,V_z1] : hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z2),V_w)),
inference(fof_nnf,[status(thm)],[fact_real__add__mult__distrib]) ).
fof(f_86_2,plain,
! [U_217,U_216,U_215] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_215,U_216)),U_217) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_215),U_217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_216),U_217)),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_215,U_217,U_216] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_215,U_216)),U_217) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_215),U_217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_216),U_217)),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_215,U_216)),U_217) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_215),U_217),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_216),U_217)),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,plain,
! [V_c,V_b,V_v,T_b] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(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_87_2,plain,
! [U_221,U_220,U_219,U_218] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_218),c_Int_Onumber__class_Onumber__of(U_218,U_219)),c_Groups_Oplus__class_Oplus(U_218,U_220,U_221)) = c_Groups_Oplus__class_Oplus(U_218,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_218),c_Int_Onumber__class_Onumber__of(U_218,U_219)),U_220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_218),c_Int_Onumber__class_Onumber__of(U_218,U_219)),U_221))
| ~ class_Rings_Osemiring(U_218)
| ~ class_Int_Onumber(U_218) ),
inference(variable_rename,[status(thm)],[f_87_1]) ).
fof(f_87_3,plain,
! [U_220,U_221,U_218,U_219] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_218),c_Int_Onumber__class_Onumber__of(U_218,U_219)),c_Groups_Oplus__class_Oplus(U_218,U_220,U_221)) = c_Groups_Oplus__class_Oplus(U_218,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_218),c_Int_Onumber__class_Onumber__of(U_218,U_219)),U_220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_218),c_Int_Onumber__class_Onumber__of(U_218,U_219)),U_221))
| ~ class_Rings_Osemiring(U_218)
| ~ class_Int_Onumber(U_218) ),
inference(definitional_conversion,[status(esa)],[f_87_2]) ).
cnf(f_87_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_218),c_Int_Onumber__class_Onumber__of(U_218,U_219)),c_Groups_Oplus__class_Oplus(U_218,U_220,U_221)) = c_Groups_Oplus__class_Oplus(U_218,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_218),c_Int_Onumber__class_Onumber__of(U_218,U_219)),U_220),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_218),c_Int_Onumber__class_Onumber__of(U_218,U_219)),U_221))
| ~ class_Rings_Osemiring(U_218)
| ~ class_Int_Onumber(U_218) ),
inference(clausify,[status(thm)],[f_87_3]) ).
fof(f_88_1,plain,
! [V_v,V_b,V_a,T_b] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(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_88_2,plain,
! [U_225,U_224,U_223,U_222] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_222),c_Groups_Oplus__class_Oplus(U_222,U_223,U_224)),c_Int_Onumber__class_Onumber__of(U_222,U_225)) = c_Groups_Oplus__class_Oplus(U_222,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_222),U_223),c_Int_Onumber__class_Onumber__of(U_222,U_225)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_222),U_224),c_Int_Onumber__class_Onumber__of(U_222,U_225)))
| ~ class_Rings_Osemiring(U_222)
| ~ class_Int_Onumber(U_222) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_222,U_223,U_224,U_225] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_222),c_Groups_Oplus__class_Oplus(U_222,U_223,U_224)),c_Int_Onumber__class_Onumber__of(U_222,U_225)) = c_Groups_Oplus__class_Oplus(U_222,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_222),U_223),c_Int_Onumber__class_Onumber__of(U_222,U_225)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_222),U_224),c_Int_Onumber__class_Onumber__of(U_222,U_225)))
| ~ class_Rings_Osemiring(U_222)
| ~ class_Int_Onumber(U_222) ),
inference(definitional_conversion,[status(esa)],[f_88_2]) ).
cnf(f_88_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_222),c_Groups_Oplus__class_Oplus(U_222,U_223,U_224)),c_Int_Onumber__class_Onumber__of(U_222,U_225)) = c_Groups_Oplus__class_Oplus(U_222,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_222),U_223),c_Int_Onumber__class_Onumber__of(U_222,U_225)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_222),U_224),c_Int_Onumber__class_Onumber__of(U_222,U_225)))
| ~ class_Rings_Osemiring(U_222)
| ~ class_Int_Onumber(U_222) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_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_89_2,plain,
! [U_227,U_226] :
( c_Groups_Oplus__class_Oplus(U_226,U_227,c_Int_Onumber__class_Onumber__of(U_226,c_Int_OPls)) = U_227
| ~ class_Int_Onumber__ring(U_226) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
! [U_226,U_227] :
( c_Groups_Oplus__class_Oplus(U_226,U_227,c_Int_Onumber__class_Onumber__of(U_226,c_Int_OPls)) = U_227
| ~ class_Int_Onumber__ring(U_226) ),
inference(definitional_conversion,[status(esa)],[f_89_2]) ).
cnf(f_89_4,plain,
( c_Groups_Oplus__class_Oplus(U_226,U_227,c_Int_Onumber__class_Onumber__of(U_226,c_Int_OPls)) = U_227
| ~ class_Int_Onumber__ring(U_226) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_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_90_2,plain,
! [U_229,U_228] :
( c_Groups_Oplus__class_Oplus(U_228,c_Int_Onumber__class_Onumber__of(U_228,c_Int_OPls),U_229) = U_229
| ~ class_Int_Onumber__ring(U_228) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_228,U_229] :
( c_Groups_Oplus__class_Oplus(U_228,c_Int_Onumber__class_Onumber__of(U_228,c_Int_OPls),U_229) = U_229
| ~ class_Int_Onumber__ring(U_228) ),
inference(definitional_conversion,[status(esa)],[f_90_2]) ).
cnf(f_90_4,plain,
( c_Groups_Oplus__class_Oplus(U_228,c_Int_Onumber__class_Onumber__of(U_228,c_Int_OPls),U_229) = U_229
| ~ class_Int_Onumber__ring(U_228) ),
inference(clausify,[status(thm)],[f_90_3]) ).
fof(f_91_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_91_2,plain,
! [U_230] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_230))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_230) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_230)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_230)) ) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
( ! [U_232] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_232))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_232) )
& ! [U_231] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_231)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_231)) ) ),
inference(miniscope,[status(thm)],[f_91_2]) ).
fof(f_91_4,plain,
( ! [U_232] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_232))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_232) )
& ! [U_231] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_231)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_231)) ) ),
inference(definitional_conversion,[status(esa)],[f_91_3]) ).
cnf(f_91_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_231)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_231)) ),
inference(clausify,[status(thm)],[f_91_4]) ).
cnf(f_91_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_232))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_232) ),
inference(clausify,[status(thm)],[f_91_4]) ).
fof(f_92_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_92_2,plain,
! [U_234,U_233] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_233),c_Int_OBit1(U_234))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_233,U_234) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_233,U_234)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_233),c_Int_OBit1(U_234)) ) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
( ! [U_238,U_236] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_236),c_Int_OBit1(U_238))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_236,U_238) )
& ! [U_237,U_235] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_235,U_237)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_235),c_Int_OBit1(U_237)) ) ),
inference(miniscope,[status(thm)],[f_92_2]) ).
fof(f_92_4,plain,
( ! [U_236,U_238] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_236),c_Int_OBit1(U_238))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_236,U_238) )
& ! [U_237,U_235] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_235,U_237)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_235),c_Int_OBit1(U_237)) ) ),
inference(definitional_conversion,[status(esa)],[f_92_3]) ).
cnf(f_92_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_235,U_237)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_235),c_Int_OBit1(U_237)) ),
inference(clausify,[status(thm)],[f_92_4]) ).
cnf(f_92_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_236),c_Int_OBit1(U_238))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_236,U_238) ),
inference(clausify,[status(thm)],[f_92_4]) ).
fof(f_93_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_93_2,plain,
! [U_240,U_239] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_239),c_Int_OBit1(U_240))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_239,U_240) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_239,U_240)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_239),c_Int_OBit1(U_240)) ) ),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
( ! [U_244,U_242] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_242),c_Int_OBit1(U_244))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_242,U_244) )
& ! [U_243,U_241] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_241,U_243)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_241),c_Int_OBit1(U_243)) ) ),
inference(miniscope,[status(thm)],[f_93_2]) ).
fof(f_93_4,plain,
( ! [U_242,U_244] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_242),c_Int_OBit1(U_244))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_242,U_244) )
& ! [U_243,U_241] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_241,U_243)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_241),c_Int_OBit1(U_243)) ) ),
inference(definitional_conversion,[status(esa)],[f_93_3]) ).
cnf(f_93_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_241,U_243)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_241),c_Int_OBit1(U_243)) ),
inference(clausify,[status(thm)],[f_93_4]) ).
cnf(f_93_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_242),c_Int_OBit1(U_244))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_242,U_244) ),
inference(clausify,[status(thm)],[f_93_4]) ).
fof(f_94_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_94_2,plain,
! [U_245] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_245))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_245) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_245)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_245)) ) ),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
( ! [U_247] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_247))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_247) )
& ! [U_246] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_246)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_246)) ) ),
inference(miniscope,[status(thm)],[f_94_2]) ).
fof(f_94_4,plain,
( ! [U_247] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_247))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_247) )
& ! [U_246] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_246)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_246)) ) ),
inference(definitional_conversion,[status(esa)],[f_94_3]) ).
cnf(f_94_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_246)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_246)) ),
inference(clausify,[status(thm)],[f_94_4]) ).
cnf(f_94_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_247))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_247) ),
inference(clausify,[status(thm)],[f_94_4]) ).
fof(f_95_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_95_2,plain,
! [U_248] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_248),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_248,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_248,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_248),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
( ! [U_250] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_250),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_250,c_Int_OPls) )
& ! [U_249] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_249,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_249),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_95_2]) ).
fof(f_95_4,plain,
( ! [U_250] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_250),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_250,c_Int_OPls) )
& ! [U_249] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_249,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_249),c_Int_OPls) ) ),
inference(definitional_conversion,[status(esa)],[f_95_3]) ).
cnf(f_95_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_249,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_249),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_95_4]) ).
cnf(f_95_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_250),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_250,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_95_4]) ).
fof(f_96_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(V_k_2),c_Int_OMin) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I30_J]) ).
fof(f_96_2,plain,
! [U_251] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_251),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_251,c_Int_OMin) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_251,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_251),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
( ! [U_253] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_253),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_253,c_Int_OMin) )
& ! [U_252] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_252,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_252),c_Int_OMin) ) ),
inference(miniscope,[status(thm)],[f_96_2]) ).
fof(f_96_4,plain,
( ! [U_253] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_253),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_253,c_Int_OMin) )
& ! [U_252] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_252,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_252),c_Int_OMin) ) ),
inference(definitional_conversion,[status(esa)],[f_96_3]) ).
cnf(f_96_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_252,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_252),c_Int_OMin) ),
inference(clausify,[status(thm)],[f_96_4]) ).
cnf(f_96_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit1(U_253),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_253,c_Int_OMin) ),
inference(clausify,[status(thm)],[f_96_4]) ).
fof(f_97_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,V_k_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,V_k_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I26_J]) ).
fof(f_97_2,plain,
! [U_254] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_254))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,U_254) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,U_254)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_254)) ) ),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
( ! [U_256] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_256))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,U_256) )
& ! [U_255] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,U_255)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_255)) ) ),
inference(miniscope,[status(thm)],[f_97_2]) ).
fof(f_97_4,plain,
( ! [U_256] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_256))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,U_256) )
& ! [U_255] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,U_255)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_255)) ) ),
inference(definitional_conversion,[status(esa)],[f_97_3]) ).
cnf(f_97_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,U_255)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_255)) ),
inference(clausify,[status(thm)],[f_97_4]) ).
cnf(f_97_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_256))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,U_256) ),
inference(clausify,[status(thm)],[f_97_4]) ).
fof(f_98_1,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I20_J]) ).
fof(f_98_2,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
inference(definitional_conversion,[status(esa)],[f_98_1]) ).
cnf(f_98_3,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,c_Int_OMin),
inference(clausify,[status(thm)],[f_98_2]) ).
fof(f_99_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I23_J]) ).
fof(f_99_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_99_1]) ).
cnf(f_99_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OMin,c_Int_OPls),
inference(clausify,[status(thm)],[f_99_2]) ).
fof(f_100_1,plain,
! [V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_k_2,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(V_k_2),c_Int_OMin) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I28_J]) ).
fof(f_100_2,plain,
! [U_257] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_257),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_257,c_Int_OMin) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_257,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_257),c_Int_OMin) ) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
( ! [U_259] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_259),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_259,c_Int_OMin) )
& ! [U_258] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_258,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_258),c_Int_OMin) ) ),
inference(miniscope,[status(thm)],[f_100_2]) ).
fof(f_100_4,plain,
( ! [U_259] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_259),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_259,c_Int_OMin) )
& ! [U_258] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_258,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_258),c_Int_OMin) ) ),
inference(definitional_conversion,[status(esa)],[f_100_3]) ).
cnf(f_100_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_258,c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_258),c_Int_OMin) ),
inference(clausify,[status(thm)],[f_100_4]) ).
cnf(f_100_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OBit0(U_259),c_Int_OMin)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_259,c_Int_OMin) ),
inference(clausify,[status(thm)],[f_100_4]) ).
fof(f_101_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_101_2,plain,
! [U_261,U_260] :
( c_Groups_Oplus__class_Oplus(U_260,c_Groups_Oone__class_Oone(U_260),c_Int_Onumber__class_Onumber__of(U_260,U_261)) = c_Int_Onumber__class_Onumber__of(U_260,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_261))
| ~ class_Int_Onumber__ring(U_260) ),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_260,U_261] :
( c_Groups_Oplus__class_Oplus(U_260,c_Groups_Oone__class_Oone(U_260),c_Int_Onumber__class_Onumber__of(U_260,U_261)) = c_Int_Onumber__class_Onumber__of(U_260,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_261))
| ~ class_Int_Onumber__ring(U_260) ),
inference(definitional_conversion,[status(esa)],[f_101_2]) ).
cnf(f_101_4,plain,
( c_Groups_Oplus__class_Oplus(U_260,c_Groups_Oone__class_Oone(U_260),c_Int_Onumber__class_Onumber__of(U_260,U_261)) = c_Int_Onumber__class_Onumber__of(U_260,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_261))
| ~ class_Int_Onumber__ring(U_260) ),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_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_102_2,plain,
! [U_263,U_262] :
( c_Groups_Oplus__class_Oplus(U_262,c_Int_Onumber__class_Onumber__of(U_262,U_263),c_Groups_Oone__class_Oone(U_262)) = c_Int_Onumber__class_Onumber__of(U_262,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_263,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_262) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_262,U_263] :
( c_Groups_Oplus__class_Oplus(U_262,c_Int_Onumber__class_Onumber__of(U_262,U_263),c_Groups_Oone__class_Oone(U_262)) = c_Int_Onumber__class_Onumber__of(U_262,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_263,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_262) ),
inference(definitional_conversion,[status(esa)],[f_102_2]) ).
cnf(f_102_4,plain,
( c_Groups_Oplus__class_Oplus(U_262,c_Int_Onumber__class_Onumber__of(U_262,U_263),c_Groups_Oone__class_Oone(U_262)) = c_Int_Onumber__class_Onumber__of(U_262,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_263,c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_262) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_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_103_2,plain,
! [U_265,U_264] :
( c_Int_Onumber__class_Onumber__of(U_264,c_Int_OBit1(U_265)) = c_Groups_Oplus__class_Oplus(U_264,c_Groups_Oplus__class_Oplus(U_264,c_Groups_Oone__class_Oone(U_264),c_Int_Onumber__class_Onumber__of(U_264,U_265)),c_Int_Onumber__class_Onumber__of(U_264,U_265))
| ~ class_Int_Onumber__ring(U_264) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_264,U_265] :
( c_Int_Onumber__class_Onumber__of(U_264,c_Int_OBit1(U_265)) = c_Groups_Oplus__class_Oplus(U_264,c_Groups_Oplus__class_Oplus(U_264,c_Groups_Oone__class_Oone(U_264),c_Int_Onumber__class_Onumber__of(U_264,U_265)),c_Int_Onumber__class_Onumber__of(U_264,U_265))
| ~ class_Int_Onumber__ring(U_264) ),
inference(definitional_conversion,[status(esa)],[f_103_2]) ).
cnf(f_103_4,plain,
( c_Int_Onumber__class_Onumber__of(U_264,c_Int_OBit1(U_265)) = c_Groups_Oplus__class_Oplus(U_264,c_Groups_Oplus__class_Oplus(U_264,c_Groups_Oone__class_Oone(U_264),c_Int_Onumber__class_Onumber__of(U_264,U_265)),c_Int_Onumber__class_Onumber__of(U_264,U_265))
| ~ class_Int_Onumber__ring(U_264) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_1,plain,
! [V_m,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_m,V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Oone__class_Oone(T_a))),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(f_104_2,plain,
! [U_267,U_266] :
( c_Groups_Oplus__class_Oplus(U_266,U_267,U_267) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_266),c_Groups_Oplus__class_Oplus(U_266,c_Groups_Oone__class_Oone(U_266),c_Groups_Oone__class_Oone(U_266))),U_267)
| ~ class_Rings_Ocomm__semiring__1(U_266) ),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_266,U_267] :
( c_Groups_Oplus__class_Oplus(U_266,U_267,U_267) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_266),c_Groups_Oplus__class_Oplus(U_266,c_Groups_Oone__class_Oone(U_266),c_Groups_Oone__class_Oone(U_266))),U_267)
| ~ class_Rings_Ocomm__semiring__1(U_266) ),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
( c_Groups_Oplus__class_Oplus(U_266,U_267,U_267) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_266),c_Groups_Oplus__class_Oplus(U_266,c_Groups_Oone__class_Oone(U_266),c_Groups_Oone__class_Oone(U_266))),U_267)
| ~ class_Rings_Ocomm__semiring__1(U_266) ),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_1,plain,
! [V_a,V_m,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J]) ).
fof(f_105_2,plain,
! [U_270,U_269,U_268] :
( c_Groups_Oplus__class_Oplus(U_268,U_269,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_268),U_270),U_269)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_268),c_Groups_Oplus__class_Oplus(U_268,U_270,c_Groups_Oone__class_Oone(U_268))),U_269)
| ~ class_Rings_Ocomm__semiring__1(U_268) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_268,U_269,U_270] :
( c_Groups_Oplus__class_Oplus(U_268,U_269,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_268),U_270),U_269)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_268),c_Groups_Oplus__class_Oplus(U_268,U_270,c_Groups_Oone__class_Oone(U_268))),U_269)
| ~ class_Rings_Ocomm__semiring__1(U_268) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( c_Groups_Oplus__class_Oplus(U_268,U_269,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_268),U_270),U_269)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_268),c_Groups_Oplus__class_Oplus(U_268,U_270,c_Groups_Oone__class_Oone(U_268))),U_269)
| ~ class_Rings_Ocomm__semiring__1(U_268) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_1,plain,
! [V_m,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_m),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oone__class_Oone(T_a))),V_m)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J]) ).
fof(f_106_2,plain,
! [U_273,U_272,U_271] :
( c_Groups_Oplus__class_Oplus(U_271,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_271),U_272),U_273),U_273) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_271),c_Groups_Oplus__class_Oplus(U_271,U_272,c_Groups_Oone__class_Oone(U_271))),U_273)
| ~ class_Rings_Ocomm__semiring__1(U_271) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_271,U_272,U_273] :
( c_Groups_Oplus__class_Oplus(U_271,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_271),U_272),U_273),U_273) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_271),c_Groups_Oplus__class_Oplus(U_271,U_272,c_Groups_Oone__class_Oone(U_271))),U_273)
| ~ class_Rings_Ocomm__semiring__1(U_271) ),
inference(definitional_conversion,[status(esa)],[f_106_2]) ).
cnf(f_106_4,plain,
( c_Groups_Oplus__class_Oplus(U_271,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_271),U_272),U_273),U_273) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_271),c_Groups_Oplus__class_Oplus(U_271,U_272,c_Groups_Oone__class_Oone(U_271))),U_273)
| ~ class_Rings_Ocomm__semiring__1(U_271) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_1,plain,
! [V_w,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,V_w)) = c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(V_w))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__number__of__Bit0]) ).
fof(f_107_2,plain,
! [U_275,U_274] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_274),c_Groups_Oplus__class_Oplus(U_274,c_Groups_Oone__class_Oone(U_274),c_Groups_Oone__class_Oone(U_274))),c_Int_Onumber__class_Onumber__of(U_274,U_275)) = c_Int_Onumber__class_Onumber__of(U_274,c_Int_OBit0(U_275))
| ~ class_Int_Onumber__ring(U_274) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_274,U_275] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_274),c_Groups_Oplus__class_Oplus(U_274,c_Groups_Oone__class_Oone(U_274),c_Groups_Oone__class_Oone(U_274))),c_Int_Onumber__class_Onumber__of(U_274,U_275)) = c_Int_Onumber__class_Onumber__of(U_274,c_Int_OBit0(U_275))
| ~ class_Int_Onumber__ring(U_274) ),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_274),c_Groups_Oplus__class_Oplus(U_274,c_Groups_Oone__class_Oone(U_274),c_Groups_Oone__class_Oone(U_274))),c_Int_Onumber__class_Onumber__of(U_274,U_275)) = c_Int_Onumber__class_Onumber__of(U_274,c_Int_OBit0(U_275))
| ~ class_Int_Onumber__ring(U_274) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_1,plain,
! [V_xa_2,V_w_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = V_xa_2
| V_xa_2 != c_Int_Onumber__class_Onumber__of(T_a,V_w_2) )
& ( V_xa_2 = c_Int_Onumber__class_Onumber__of(T_a,V_w_2)
| c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != V_xa_2 ) )
| ~ class_Int_Onumber(T_a) ),
inference(fof_nnf,[status(thm)],[fact_number__of__reorient]) ).
fof(f_108_2,plain,
! [U_278,U_277,U_276] :
( ( ( c_Int_Onumber__class_Onumber__of(U_276,U_277) = U_278
| U_278 != c_Int_Onumber__class_Onumber__of(U_276,U_277) )
& ( U_278 = c_Int_Onumber__class_Onumber__of(U_276,U_277)
| c_Int_Onumber__class_Onumber__of(U_276,U_277) != U_278 ) )
| ~ class_Int_Onumber(U_276) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
( ! [U_277,U_276,U_278] :
( c_Int_Onumber__class_Onumber__of(U_276,U_277) = U_278
| U_278 != c_Int_Onumber__class_Onumber__of(U_276,U_277)
| ~ sP7(U_277,U_276,U_278) )
& ! [U_277,U_276,U_278] :
( U_278 = c_Int_Onumber__class_Onumber__of(U_276,U_277)
| c_Int_Onumber__class_Onumber__of(U_276,U_277) != U_278
| ~ sP7(U_277,U_276,U_278) )
& ! [U_277,U_276,U_278] :
( sP7(U_277,U_276,U_278)
| ~ class_Int_Onumber(U_276) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_108_2]) ).
cnf(f_108_4,plain,
( sP7(U_277,U_276,U_278)
| ~ class_Int_Onumber(U_276) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_5,plain,
( U_278 = c_Int_Onumber__class_Onumber__of(U_276,U_277)
| c_Int_Onumber__class_Onumber__of(U_276,U_277) != U_278
| ~ sP7(U_277,U_276,U_278) ),
inference(clausify,[status(thm)],[f_108_3]) ).
cnf(f_108_6,plain,
( c_Int_Onumber__class_Onumber__of(U_276,U_277) = U_278
| U_278 != c_Int_Onumber__class_Onumber__of(U_276,U_277)
| ~ sP7(U_277,U_276,U_278) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_xa_2) = c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)
| V_xa_2 != V_ya_2 )
& ( V_xa_2 = V_ya_2
| c_Int_Onumber__class_Onumber__of(T_a,V_xa_2) != c_Int_Onumber__class_Onumber__of(T_a,V_ya_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_109_2,plain,
! [U_281,U_280,U_279] :
( ( ( c_Int_Onumber__class_Onumber__of(U_279,U_280) = c_Int_Onumber__class_Onumber__of(U_279,U_281)
| U_280 != U_281 )
& ( U_280 = U_281
| c_Int_Onumber__class_Onumber__of(U_279,U_280) != c_Int_Onumber__class_Onumber__of(U_279,U_281) ) )
| ~ class_Int_Oring__char__0(U_279)
| ~ class_Int_Onumber__ring(U_279) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
( ! [U_280,U_281,U_279] :
( c_Int_Onumber__class_Onumber__of(U_279,U_280) = c_Int_Onumber__class_Onumber__of(U_279,U_281)
| U_280 != U_281
| ~ sP8(U_280,U_281,U_279) )
& ! [U_280,U_281,U_279] :
( U_280 = U_281
| c_Int_Onumber__class_Onumber__of(U_279,U_280) != c_Int_Onumber__class_Onumber__of(U_279,U_281)
| ~ sP8(U_280,U_281,U_279) )
& ! [U_280,U_281,U_279] :
( sP8(U_280,U_281,U_279)
| ~ class_Int_Oring__char__0(U_279)
| ~ class_Int_Onumber__ring(U_279) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_109_2]) ).
cnf(f_109_4,plain,
( sP8(U_280,U_281,U_279)
| ~ class_Int_Oring__char__0(U_279)
| ~ class_Int_Onumber__ring(U_279) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_5,plain,
( U_280 = U_281
| c_Int_Onumber__class_Onumber__of(U_279,U_280) != c_Int_Onumber__class_Onumber__of(U_279,U_281)
| ~ sP8(U_280,U_281,U_279) ),
inference(clausify,[status(thm)],[f_109_3]) ).
cnf(f_109_6,plain,
( c_Int_Onumber__class_Onumber__of(U_279,U_280) = c_Int_Onumber__class_Onumber__of(U_279,U_281)
| U_280 != U_281
| ~ sP8(U_280,U_281,U_279) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_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_110_2,plain,
! [U_283,U_282] :
( ( c_Int_OBit1(U_282) = c_Int_OBit1(U_283)
| U_282 != U_283 )
& ( U_282 = U_283
| c_Int_OBit1(U_282) != c_Int_OBit1(U_283) ) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
( ! [U_287,U_285] :
( c_Int_OBit1(U_285) = c_Int_OBit1(U_287)
| U_285 != U_287 )
& ! [U_286,U_284] :
( U_284 = U_286
| c_Int_OBit1(U_284) != c_Int_OBit1(U_286) ) ),
inference(miniscope,[status(thm)],[f_110_2]) ).
fof(f_110_4,plain,
( ! [U_285,U_287] :
( c_Int_OBit1(U_285) = c_Int_OBit1(U_287)
| U_285 != U_287 )
& ! [U_284,U_286] :
( U_284 = U_286
| c_Int_OBit1(U_284) != c_Int_OBit1(U_286) ) ),
inference(definitional_conversion,[status(esa)],[f_110_3]) ).
cnf(f_110_5,plain,
( U_284 = U_286
| c_Int_OBit1(U_284) != c_Int_OBit1(U_286) ),
inference(clausify,[status(thm)],[f_110_4]) ).
cnf(f_110_6,plain,
( c_Int_OBit1(U_285) = c_Int_OBit1(U_287)
| U_285 != U_287 ),
inference(clausify,[status(thm)],[f_110_4]) ).
fof(f_111_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_111_2,plain,
! [U_289,U_288] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_288),U_289),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_289
| ~ class_Groups_Omonoid__mult(U_288) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_289,U_288] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_288),U_289),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_289
| ~ class_Groups_Omonoid__mult(U_288) ),
inference(definitional_conversion,[status(esa)],[f_111_2]) ).
cnf(f_111_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_288),U_289),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_289
| ~ class_Groups_Omonoid__mult(U_288) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_mult__Pls]) ).
fof(f_112_2,plain,
! [U_290] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_290) = c_Int_OPls,
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
! [U_290] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_290) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_112_2]) ).
cnf(f_112_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_290) = c_Int_OPls,
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_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_113_2,plain,
! [U_292,U_291] :
( ( c_Int_OBit0(U_291) = c_Int_OBit0(U_292)
| U_291 != U_292 )
& ( U_291 = U_292
| c_Int_OBit0(U_291) != c_Int_OBit0(U_292) ) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_296,U_294] :
( c_Int_OBit0(U_294) = c_Int_OBit0(U_296)
| U_294 != U_296 )
& ! [U_295,U_293] :
( U_293 = U_295
| c_Int_OBit0(U_293) != c_Int_OBit0(U_295) ) ),
inference(miniscope,[status(thm)],[f_113_2]) ).
fof(f_113_4,plain,
( ! [U_294,U_296] :
( c_Int_OBit0(U_294) = c_Int_OBit0(U_296)
| U_294 != U_296 )
& ! [U_295,U_293] :
( U_293 = U_295
| c_Int_OBit0(U_293) != c_Int_OBit0(U_295) ) ),
inference(definitional_conversion,[status(esa)],[f_113_3]) ).
cnf(f_113_5,plain,
( U_293 = U_295
| c_Int_OBit0(U_293) != c_Int_OBit0(U_295) ),
inference(clausify,[status(thm)],[f_113_4]) ).
cnf(f_113_6,plain,
( c_Int_OBit0(U_294) = c_Int_OBit0(U_296)
| U_294 != U_296 ),
inference(clausify,[status(thm)],[f_113_4]) ).
fof(f_114_1,plain,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),
inference(fof_nnf,[status(thm)],[fact_mult__Bit0]) ).
fof(f_114_2,plain,
! [U_298,U_297] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_297)),U_298) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_297),U_298)),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_297,U_298] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_297)),U_298) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_297),U_298)),
inference(definitional_conversion,[status(esa)],[f_114_2]) ).
cnf(f_114_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_297)),U_298) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_297),U_298)),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_1,plain,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),V_z) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_y),V_z)),
inference(fof_nnf,[status(thm)],[fact_zpower__zpower]) ).
fof(f_115_2,plain,
! [U_301,U_300,U_299] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_299),U_300)),U_301) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_300),U_301)),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_299,U_300,U_301] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_299),U_300)),U_301) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_300),U_301)),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_299),U_300)),U_301) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_299),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_300),U_301)),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_1,plain,
! [V_z,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__2__right]) ).
fof(f_116_2,plain,
! [U_303,U_302] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_302),U_303),c_Int_Onumber__class_Onumber__of(U_302,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_302,U_303,U_303)
| ~ class_Int_Onumber__ring(U_302) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_302,U_303] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_302),U_303),c_Int_Onumber__class_Onumber__of(U_302,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_302,U_303,U_303)
| ~ class_Int_Onumber__ring(U_302) ),
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_302),U_303),c_Int_Onumber__class_Onumber__of(U_302,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_302,U_303,U_303)
| ~ class_Int_Onumber__ring(U_302) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_1,plain,
! [V_z,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_z) = c_Groups_Oplus__class_Oplus(T_a,V_z,V_z)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__2]) ).
fof(f_117_2,plain,
! [U_305,U_304] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_304),c_Int_Onumber__class_Onumber__of(U_304,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_305) = c_Groups_Oplus__class_Oplus(U_304,U_305,U_305)
| ~ class_Int_Onumber__ring(U_304) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_304,U_305] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_304),c_Int_Onumber__class_Onumber__of(U_304,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_305) = c_Groups_Oplus__class_Oplus(U_304,U_305,U_305)
| ~ class_Int_Onumber__ring(U_304) ),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_304),c_Int_Onumber__class_Onumber__of(U_304,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_305) = c_Groups_Oplus__class_Oplus(U_304,U_305,U_305)
| ~ class_Int_Onumber__ring(U_304) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_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_118_2,plain,
! [U_306] :
( c_Groups_Oplus__class_Oplus(U_306,c_Groups_Oone__class_Oone(U_306),c_Groups_Oone__class_Oone(U_306)) = c_Int_Onumber__class_Onumber__of(U_306,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_306) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_306] :
( c_Groups_Oplus__class_Oplus(U_306,c_Groups_Oone__class_Oone(U_306),c_Groups_Oone__class_Oone(U_306)) = c_Int_Onumber__class_Onumber__of(U_306,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_306) ),
inference(definitional_conversion,[status(esa)],[f_118_2]) ).
cnf(f_118_4,plain,
( c_Groups_Oplus__class_Oplus(U_306,c_Groups_Oone__class_Oone(U_306),c_Groups_Oone__class_Oone(U_306)) = c_Int_Onumber__class_Onumber__of(U_306,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
| ~ class_Int_Onumber__ring(U_306) ),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_1,plain,
! [V_n,V_m] :
( V_m = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff__lemma]) ).
fof(f_119_2,plain,
! [U_308,U_307] :
( U_307 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| U_307 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_307),U_308) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_307,U_308] :
( U_307 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| U_307 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_307),U_308) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_119_2]) ).
cnf(f_119_4,plain,
( U_307 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| U_307 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_307),U_308) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( V_n_2 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| V_m_2 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) )
& ( V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( ( V_n_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
& V_m_2 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) )
| ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zmult__eq__1__iff]) ).
fof(f_120_2,plain,
! [U_310,U_309] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_309),U_310) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_310 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| U_309 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) )
& ( U_310 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_309 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( ( U_310 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
& U_309 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) )
| ( U_310 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_309 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_309),U_310) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_314,U_312] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_312),U_314) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ( ( U_314 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| U_312 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) )
& ( U_314 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_312 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ! [U_313,U_311] :
( ( U_313 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
& U_311 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin) )
| ( U_313 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_311 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_311),U_313) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_120_2]) ).
fof(f_120_4,plain,
( ! [U_312,U_314] :
( U_314 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| U_312 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| ~ sP11(U_312,U_314) )
& ! [U_312,U_314] :
( U_314 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_312 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP11(U_312,U_314) )
& ! [U_311,U_313] :
( U_313 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| ~ sP10(U_311,U_313) )
& ! [U_311,U_313] :
( U_311 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| ~ sP10(U_311,U_313) )
& ! [U_311,U_313] :
( U_313 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP9(U_311,U_313) )
& ! [U_311,U_313] :
( U_311 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP9(U_311,U_313) )
& ! [U_312,U_314] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_312),U_314) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| sP11(U_312,U_314) )
& ! [U_311,U_313] :
( sP10(U_311,U_313)
| sP9(U_311,U_313)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_311),U_313) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9,sP10,sP11])],[f_120_3]) ).
cnf(f_120_5,plain,
( sP10(U_311,U_313)
| sP9(U_311,U_313)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_311),U_313) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_312),U_314) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| sP11(U_312,U_314) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_7,plain,
( U_311 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP9(U_311,U_313) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_8,plain,
( U_313 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP9(U_311,U_313) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_9,plain,
( U_311 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| ~ sP10(U_311,U_313) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_10,plain,
( U_313 = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| ~ sP10(U_311,U_313) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_11,plain,
( U_314 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_312 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP11(U_312,U_314) ),
inference(clausify,[status(thm)],[f_120_4]) ).
cnf(f_120_12,plain,
( U_314 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| U_312 != c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OMin)
| ~ sP11(U_312,U_314) ),
inference(clausify,[status(thm)],[f_120_4]) ).
fof(f_121_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,V_ya_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__number__of]) ).
fof(f_121_2,plain,
! [U_317,U_316,U_315] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_315,c_Int_Onumber__class_Onumber__of(U_315,U_316),c_Int_Onumber__class_Onumber__of(U_315,U_317))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_316,U_317) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_316,U_317)
| ~ c_Orderings_Oord__class_Oless__eq(U_315,c_Int_Onumber__class_Onumber__of(U_315,U_316),c_Int_Onumber__class_Onumber__of(U_315,U_317)) ) )
| ~ class_Rings_Olinordered__idom(U_315)
| ~ class_Int_Onumber__ring(U_315) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
( ! [U_316,U_315,U_317] :
( c_Orderings_Oord__class_Oless__eq(U_315,c_Int_Onumber__class_Onumber__of(U_315,U_316),c_Int_Onumber__class_Onumber__of(U_315,U_317))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_316,U_317)
| ~ sP12(U_316,U_315,U_317) )
& ! [U_316,U_315,U_317] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_316,U_317)
| ~ c_Orderings_Oord__class_Oless__eq(U_315,c_Int_Onumber__class_Onumber__of(U_315,U_316),c_Int_Onumber__class_Onumber__of(U_315,U_317))
| ~ sP12(U_316,U_315,U_317) )
& ! [U_316,U_315,U_317] :
( sP12(U_316,U_315,U_317)
| ~ class_Rings_Olinordered__idom(U_315)
| ~ class_Int_Onumber__ring(U_315) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_121_2]) ).
cnf(f_121_4,plain,
( sP12(U_316,U_315,U_317)
| ~ class_Rings_Olinordered__idom(U_315)
| ~ class_Int_Onumber__ring(U_315) ),
inference(clausify,[status(thm)],[f_121_3]) ).
cnf(f_121_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_316,U_317)
| ~ c_Orderings_Oord__class_Oless__eq(U_315,c_Int_Onumber__class_Onumber__of(U_315,U_316),c_Int_Onumber__class_Onumber__of(U_315,U_317))
| ~ sP12(U_316,U_315,U_317) ),
inference(clausify,[status(thm)],[f_121_3]) ).
cnf(f_121_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_315,c_Int_Onumber__class_Onumber__of(U_315,U_316),c_Int_Onumber__class_Onumber__of(U_315,U_317))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_316,U_317)
| ~ sP12(U_316,U_315,U_317) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_1,plain,
! [V_w,V_v,T_a] :
( c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(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_122_2,plain,
! [U_320,U_319,U_318] :
( c_Int_Onumber__class_Onumber__of(U_318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_319),U_320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),c_Int_Onumber__class_Onumber__of(U_318,U_319)),c_Int_Onumber__class_Onumber__of(U_318,U_320))
| ~ class_Int_Onumber__ring(U_318) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_320,U_319,U_318] :
( c_Int_Onumber__class_Onumber__of(U_318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_319),U_320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),c_Int_Onumber__class_Onumber__of(U_318,U_319)),c_Int_Onumber__class_Onumber__of(U_318,U_320))
| ~ class_Int_Onumber__ring(U_318) ),
inference(definitional_conversion,[status(esa)],[f_122_2]) ).
cnf(f_122_4,plain,
( c_Int_Onumber__class_Onumber__of(U_318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_319),U_320)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),c_Int_Onumber__class_Onumber__of(U_318,U_319)),c_Int_Onumber__class_Onumber__of(U_318,U_320))
| ~ class_Int_Onumber__ring(U_318) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_1,plain,
! [V_w,V_v,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(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_123_2,plain,
! [U_323,U_322,U_321] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),c_Int_Onumber__class_Onumber__of(U_321,U_322)),c_Int_Onumber__class_Onumber__of(U_321,U_323)) = c_Int_Onumber__class_Onumber__of(U_321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_322),U_323))
| ~ class_Int_Onumber__ring(U_321) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_321,U_322,U_323] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),c_Int_Onumber__class_Onumber__of(U_321,U_322)),c_Int_Onumber__class_Onumber__of(U_321,U_323)) = c_Int_Onumber__class_Onumber__of(U_321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_322),U_323))
| ~ class_Int_Onumber__ring(U_321) ),
inference(definitional_conversion,[status(esa)],[f_123_2]) ).
cnf(f_123_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_321),c_Int_Onumber__class_Onumber__of(U_321,U_322)),c_Int_Onumber__class_Onumber__of(U_321,U_323)) = c_Int_Onumber__class_Onumber__of(U_321,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_322),U_323))
| ~ class_Int_Onumber__ring(U_321) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_1,plain,
! [V_z,V_w,V_v,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,hAPP(hAPP(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_124_2,plain,
! [U_327,U_326,U_325,U_324] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_324),c_Int_Onumber__class_Onumber__of(U_324,U_325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_324),c_Int_Onumber__class_Onumber__of(U_324,U_326)),U_327)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_324),c_Int_Onumber__class_Onumber__of(U_324,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_325),U_326))),U_327)
| ~ class_Int_Onumber__ring(U_324) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_324,U_325,U_326,U_327] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_324),c_Int_Onumber__class_Onumber__of(U_324,U_325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_324),c_Int_Onumber__class_Onumber__of(U_324,U_326)),U_327)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_324),c_Int_Onumber__class_Onumber__of(U_324,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_325),U_326))),U_327)
| ~ class_Int_Onumber__ring(U_324) ),
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_324),c_Int_Onumber__class_Onumber__of(U_324,U_325)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_324),c_Int_Onumber__class_Onumber__of(U_324,U_326)),U_327)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_324),c_Int_Onumber__class_Onumber__of(U_324,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_325),U_326))),U_327)
| ~ class_Int_Onumber__ring(U_324) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__commutes]) ).
fof(f_125_2,plain,
! [U_330,U_329,U_328] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_328),hAPP(hAPP(c_Power_Opower__class_Opower(U_328),U_329),U_330)),U_329) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_328),U_329),hAPP(hAPP(c_Power_Opower__class_Opower(U_328),U_329),U_330))
| ~ class_Groups_Omonoid__mult(U_328) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_328,U_329,U_330] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_328),hAPP(hAPP(c_Power_Opower__class_Opower(U_328),U_329),U_330)),U_329) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_328),U_329),hAPP(hAPP(c_Power_Opower__class_Opower(U_328),U_329),U_330))
| ~ class_Groups_Omonoid__mult(U_328) ),
inference(definitional_conversion,[status(esa)],[f_125_2]) ).
cnf(f_125_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_328),hAPP(hAPP(c_Power_Opower__class_Opower(U_328),U_329),U_330)),U_329) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_328),U_329),hAPP(hAPP(c_Power_Opower__class_Opower(U_328),U_329),U_330))
| ~ class_Groups_Omonoid__mult(U_328) ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_1,plain,
! [V_n,V_b,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))
| ~ class_Groups_Ocomm__monoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mult__distrib]) ).
fof(f_126_2,plain,
! [U_334,U_333,U_332,U_331] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_331),U_332),U_333)),U_334) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_331),hAPP(hAPP(c_Power_Opower__class_Opower(U_331),U_332),U_334)),hAPP(hAPP(c_Power_Opower__class_Opower(U_331),U_333),U_334))
| ~ class_Groups_Ocomm__monoid__mult(U_331) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_331,U_332,U_333,U_334] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_331),U_332),U_333)),U_334) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_331),hAPP(hAPP(c_Power_Opower__class_Opower(U_331),U_332),U_334)),hAPP(hAPP(c_Power_Opower__class_Opower(U_331),U_333),U_334))
| ~ class_Groups_Ocomm__monoid__mult(U_331) ),
inference(definitional_conversion,[status(esa)],[f_126_2]) ).
cnf(f_126_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_331),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_331),U_332),U_333)),U_334) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_331),hAPP(hAPP(c_Power_Opower__class_Opower(U_331),U_332),U_334)),hAPP(hAPP(c_Power_Opower__class_Opower(U_331),U_333),U_334))
| ~ class_Groups_Ocomm__monoid__mult(U_331) ),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_1,plain,
! [V_n,T_a] :
( hAPP(hAPP(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_127_2,plain,
! [U_336,U_335] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_335),c_Groups_Oone__class_Oone(U_335)),U_336) = c_Groups_Oone__class_Oone(U_335)
| ~ class_Groups_Omonoid__mult(U_335) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_336,U_335] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_335),c_Groups_Oone__class_Oone(U_335)),U_336) = c_Groups_Oone__class_Oone(U_335)
| ~ class_Groups_Omonoid__mult(U_335) ),
inference(definitional_conversion,[status(esa)],[f_127_2]) ).
cnf(f_127_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_335),c_Groups_Oone__class_Oone(U_335)),U_336) = c_Groups_Oone__class_Oone(U_335)
| ~ class_Groups_Omonoid__mult(U_335) ),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,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(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__sum]) ).
fof(f_128_2,plain,
! [U_339,U_338,U_337] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_337),c_Groups_Oplus__class_Oplus(U_337,U_338,U_339)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_337,c_Groups_Oplus__class_Oplus(U_337,hAPP(hAPP(c_Power_Opower__class_Opower(U_337),U_338),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_337),U_339),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_337),c_Int_Onumber__class_Onumber__of(U_337,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_338)),U_339))
| ~ class_Int_Onumber__ring(U_337) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_337,U_338,U_339] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_337),c_Groups_Oplus__class_Oplus(U_337,U_338,U_339)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_337,c_Groups_Oplus__class_Oplus(U_337,hAPP(hAPP(c_Power_Opower__class_Opower(U_337),U_338),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_337),U_339),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_337),c_Int_Onumber__class_Onumber__of(U_337,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_338)),U_339))
| ~ class_Int_Onumber__ring(U_337) ),
inference(definitional_conversion,[status(esa)],[f_128_2]) ).
cnf(f_128_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_337),c_Groups_Oplus__class_Oplus(U_337,U_338,U_339)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(U_337,c_Groups_Oplus__class_Oplus(U_337,hAPP(hAPP(c_Power_Opower__class_Opower(U_337),U_338),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_337),U_339),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_337),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_337),c_Int_Onumber__class_Onumber__of(U_337,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_338)),U_339))
| ~ class_Int_Onumber__ring(U_337) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_1,plain,
! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).
fof(f_129_2,plain,
! [U_340] : c_Int_OPls != c_Int_OBit1(U_340),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
! [U_340] : c_Int_OPls != c_Int_OBit1(U_340),
inference(definitional_conversion,[status(esa)],[f_129_2]) ).
cnf(f_129_4,plain,
c_Int_OPls != c_Int_OBit1(U_340),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).
fof(f_130_2,plain,
! [U_341] : c_Int_OBit1(U_341) != c_Int_OPls,
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
! [U_341] : c_Int_OBit1(U_341) != c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_130_2]) ).
cnf(f_130_4,plain,
c_Int_OBit1(U_341) != c_Int_OPls,
inference(clausify,[status(thm)],[f_130_3]) ).
fof(f_131_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]) ).
fof(f_131_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(definitional_conversion,[status(esa)],[f_131_1]) ).
cnf(f_131_3,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_131_2]) ).
fof(f_132_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_132_2,plain,
! [U_343,U_342] : c_Int_OBit0(U_342) != c_Int_OBit1(U_343),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_342,U_343] : c_Int_OBit0(U_342) != c_Int_OBit1(U_343),
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
c_Int_OBit0(U_342) != c_Int_OBit1(U_343),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_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_133_2,plain,
! [U_345,U_344] : c_Int_OBit1(U_344) != c_Int_OBit0(U_345),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_344,U_345] : c_Int_OBit1(U_344) != c_Int_OBit0(U_345),
inference(definitional_conversion,[status(esa)],[f_133_2]) ).
cnf(f_133_4,plain,
c_Int_OBit1(U_344) != c_Int_OBit0(U_345),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_1,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).
fof(f_134_2,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_134_1]) ).
cnf(f_134_3,plain,
c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
inference(clausify,[status(thm)],[f_134_2]) ).
fof(f_135_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_135_2,plain,
! [U_346] :
( ( c_Int_OPls = c_Int_OBit0(U_346)
| c_Int_OPls != U_346 )
& ( c_Int_OPls = U_346
| c_Int_OPls != c_Int_OBit0(U_346) ) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
( ! [U_348] :
( c_Int_OPls = c_Int_OBit0(U_348)
| c_Int_OPls != U_348 )
& ! [U_347] :
( c_Int_OPls = U_347
| c_Int_OPls != c_Int_OBit0(U_347) ) ),
inference(miniscope,[status(thm)],[f_135_2]) ).
fof(f_135_4,plain,
( ! [U_348] :
( c_Int_OPls = c_Int_OBit0(U_348)
| c_Int_OPls != U_348 )
& ! [U_347] :
( c_Int_OPls = U_347
| c_Int_OPls != c_Int_OBit0(U_347) ) ),
inference(definitional_conversion,[status(esa)],[f_135_3]) ).
cnf(f_135_5,plain,
( c_Int_OPls = U_347
| c_Int_OPls != c_Int_OBit0(U_347) ),
inference(clausify,[status(thm)],[f_135_4]) ).
cnf(f_135_6,plain,
( c_Int_OPls = c_Int_OBit0(U_348)
| c_Int_OPls != U_348 ),
inference(clausify,[status(thm)],[f_135_4]) ).
fof(f_136_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_136_2,plain,
! [U_349] :
( ( c_Int_OBit0(U_349) = c_Int_OPls
| U_349 != c_Int_OPls )
& ( U_349 = c_Int_OPls
| c_Int_OBit0(U_349) != c_Int_OPls ) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
( ! [U_351] :
( c_Int_OBit0(U_351) = c_Int_OPls
| U_351 != c_Int_OPls )
& ! [U_350] :
( U_350 = c_Int_OPls
| c_Int_OBit0(U_350) != c_Int_OPls ) ),
inference(miniscope,[status(thm)],[f_136_2]) ).
fof(f_136_4,plain,
( ! [U_351] :
( c_Int_OBit0(U_351) = c_Int_OPls
| U_351 != c_Int_OPls )
& ! [U_350] :
( U_350 = c_Int_OPls
| c_Int_OBit0(U_350) != c_Int_OPls ) ),
inference(definitional_conversion,[status(esa)],[f_136_3]) ).
cnf(f_136_5,plain,
( U_350 = c_Int_OPls
| c_Int_OBit0(U_350) != c_Int_OPls ),
inference(clausify,[status(thm)],[f_136_4]) ).
cnf(f_136_6,plain,
( c_Int_OBit0(U_351) = c_Int_OPls
| U_351 != c_Int_OPls ),
inference(clausify,[status(thm)],[f_136_4]) ).
fof(f_137_1,plain,
! [V_n,V_m,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_n)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__mult]) ).
fof(f_137_2,plain,
! [U_355,U_354,U_353,U_352] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_352),U_353),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_354),U_355)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_352),hAPP(hAPP(c_Power_Opower__class_Opower(U_352),U_353),U_354)),U_355)
| ~ class_Groups_Omonoid__mult(U_352) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_352,U_353,U_354,U_355] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_352),U_353),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_354),U_355)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_352),hAPP(hAPP(c_Power_Opower__class_Opower(U_352),U_353),U_354)),U_355)
| ~ class_Groups_Omonoid__mult(U_352) ),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_352),U_353),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_354),U_355)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_352),hAPP(hAPP(c_Power_Opower__class_Opower(U_352),U_353),U_354)),U_355)
| ~ class_Groups_Omonoid__mult(U_352) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_1,plain,
! [V_n,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(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_138_2,plain,
! [U_358,U_357,U_356] :
( c_Groups_Oabs__class_Oabs(U_356,hAPP(hAPP(c_Power_Opower__class_Opower(U_356),U_357),U_358)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_356),c_Groups_Oabs__class_Oabs(U_356,U_357)),U_358)
| ~ class_Rings_Olinordered__idom(U_356) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
! [U_356,U_357,U_358] :
( c_Groups_Oabs__class_Oabs(U_356,hAPP(hAPP(c_Power_Opower__class_Opower(U_356),U_357),U_358)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_356),c_Groups_Oabs__class_Oabs(U_356,U_357)),U_358)
| ~ class_Rings_Olinordered__idom(U_356) ),
inference(definitional_conversion,[status(esa)],[f_138_2]) ).
cnf(f_138_4,plain,
( c_Groups_Oabs__class_Oabs(U_356,hAPP(hAPP(c_Power_Opower__class_Opower(U_356),U_357),U_358)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_356),c_Groups_Oabs__class_Oabs(U_356,U_357)),U_358)
| ~ class_Rings_Olinordered__idom(U_356) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_1,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).
fof(f_139_2,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_139_1]) ).
cnf(f_139_3,plain,
c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
inference(clausify,[status(thm)],[f_139_2]) ).
fof(f_140_1,plain,
! [V_l_2] :
( ( c_Int_OMin = c_Int_OBit1(V_l_2)
| c_Int_OMin != V_l_2 )
& ( c_Int_OMin = V_l_2
| c_Int_OMin != c_Int_OBit1(V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I43_J]) ).
fof(f_140_2,plain,
! [U_359] :
( ( c_Int_OMin = c_Int_OBit1(U_359)
| c_Int_OMin != U_359 )
& ( c_Int_OMin = U_359
| c_Int_OMin != c_Int_OBit1(U_359) ) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
( ! [U_361] :
( c_Int_OMin = c_Int_OBit1(U_361)
| c_Int_OMin != U_361 )
& ! [U_360] :
( c_Int_OMin = U_360
| c_Int_OMin != c_Int_OBit1(U_360) ) ),
inference(miniscope,[status(thm)],[f_140_2]) ).
fof(f_140_4,plain,
( ! [U_361] :
( c_Int_OMin = c_Int_OBit1(U_361)
| c_Int_OMin != U_361 )
& ! [U_360] :
( c_Int_OMin = U_360
| c_Int_OMin != c_Int_OBit1(U_360) ) ),
inference(definitional_conversion,[status(esa)],[f_140_3]) ).
cnf(f_140_5,plain,
( c_Int_OMin = U_360
| c_Int_OMin != c_Int_OBit1(U_360) ),
inference(clausify,[status(thm)],[f_140_4]) ).
cnf(f_140_6,plain,
( c_Int_OMin = c_Int_OBit1(U_361)
| c_Int_OMin != U_361 ),
inference(clausify,[status(thm)],[f_140_4]) ).
fof(f_141_1,plain,
! [V_k_2] :
( ( c_Int_OBit1(V_k_2) = c_Int_OMin
| V_k_2 != c_Int_OMin )
& ( V_k_2 = c_Int_OMin
| c_Int_OBit1(V_k_2) != c_Int_OMin ) ),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I47_J]) ).
fof(f_141_2,plain,
! [U_362] :
( ( c_Int_OBit1(U_362) = c_Int_OMin
| U_362 != c_Int_OMin )
& ( U_362 = c_Int_OMin
| c_Int_OBit1(U_362) != c_Int_OMin ) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
( ! [U_364] :
( c_Int_OBit1(U_364) = c_Int_OMin
| U_364 != c_Int_OMin )
& ! [U_363] :
( U_363 = c_Int_OMin
| c_Int_OBit1(U_363) != c_Int_OMin ) ),
inference(miniscope,[status(thm)],[f_141_2]) ).
fof(f_141_4,plain,
( ! [U_364] :
( c_Int_OBit1(U_364) = c_Int_OMin
| U_364 != c_Int_OMin )
& ! [U_363] :
( U_363 = c_Int_OMin
| c_Int_OBit1(U_363) != c_Int_OMin ) ),
inference(definitional_conversion,[status(esa)],[f_141_3]) ).
cnf(f_141_5,plain,
( U_363 = c_Int_OMin
| c_Int_OBit1(U_363) != c_Int_OMin ),
inference(clausify,[status(thm)],[f_141_4]) ).
cnf(f_141_6,plain,
( c_Int_OBit1(U_364) = c_Int_OMin
| U_364 != c_Int_OMin ),
inference(clausify,[status(thm)],[f_141_4]) ).
fof(f_142_1,plain,
c_Int_OMin != c_Int_OPls,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).
fof(f_142_2,plain,
c_Int_OMin != c_Int_OPls,
inference(definitional_conversion,[status(esa)],[f_142_1]) ).
cnf(f_142_3,plain,
c_Int_OMin != c_Int_OPls,
inference(clausify,[status(thm)],[f_142_2]) ).
fof(f_143_1,plain,
c_Int_OPls != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).
fof(f_143_2,plain,
c_Int_OPls != c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_143_1]) ).
cnf(f_143_3,plain,
c_Int_OPls != c_Int_OMin,
inference(clausify,[status(thm)],[f_143_2]) ).
fof(f_144_1,plain,
! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).
fof(f_144_2,plain,
! [U_365] : c_Int_OMin != c_Int_OBit0(U_365),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_365] : c_Int_OMin != c_Int_OBit0(U_365),
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
c_Int_OMin != c_Int_OBit0(U_365),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_1,plain,
! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).
fof(f_145_2,plain,
! [U_366] : c_Int_OBit0(U_366) != c_Int_OMin,
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_366] : c_Int_OBit0(U_366) != c_Int_OMin,
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
c_Int_OBit0(U_366) != c_Int_OMin,
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_1,plain,
! [V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y)),
inference(fof_nnf,[status(thm)],[fact_real__sum__squared__expand]) ).
fof(f_146_2,plain,
! [U_368,U_367] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_367,U_368)),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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_367),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_368),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_367)),U_368)),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_367,U_368] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_367,U_368)),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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_367),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_368),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_367)),U_368)),
inference(definitional_conversion,[status(esa)],[f_146_2]) ).
cnf(f_146_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_367,U_368)),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_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_367),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_368),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_367)),U_368)),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_1,plain,
? [B_x,B_y] : v_z = c_Complex_Ocomplex_OComplex(B_x,B_y),
inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Az_A_061_AComplex_Ax_Ay_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(f_147_2,plain,
? [U_370,U_369] : v_z = c_Complex_Ocomplex_OComplex(U_370,U_369),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
? [U_369] : v_z = c_Complex_Ocomplex_OComplex(sK2,U_369),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_370,sK2)],[f_147_2]) ).
fof(f_147_4,plain,
v_z = c_Complex_Ocomplex_OComplex(sK2,sK3),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_369,sK3)],[f_147_3]) ).
fof(f_147_5,plain,
v_z = c_Complex_Ocomplex_OComplex(sK2,sK3),
inference(definitional_conversion,[status(esa)],[f_147_4]) ).
cnf(f_147_6,plain,
v_z = c_Complex_Ocomplex_OComplex(sK2,sK3),
inference(clausify,[status(thm)],[f_147_5]) ).
fof(f_148_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_148_2,plain,
! [U_373,U_372,U_371] :
( c_Orderings_Oord__class_Oless__eq(U_371,c_Groups_Oabs__class_Oabs(U_371,c_Groups_Oplus__class_Oplus(U_371,U_372,U_373)),c_Groups_Oplus__class_Oplus(U_371,c_Groups_Oabs__class_Oabs(U_371,U_372),c_Groups_Oabs__class_Oabs(U_371,U_373)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_371) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
! [U_371,U_372,U_373] :
( c_Orderings_Oord__class_Oless__eq(U_371,c_Groups_Oabs__class_Oabs(U_371,c_Groups_Oplus__class_Oplus(U_371,U_372,U_373)),c_Groups_Oplus__class_Oplus(U_371,c_Groups_Oabs__class_Oabs(U_371,U_372),c_Groups_Oabs__class_Oabs(U_371,U_373)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_371) ),
inference(definitional_conversion,[status(esa)],[f_148_2]) ).
cnf(f_148_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_371,c_Groups_Oabs__class_Oabs(U_371,c_Groups_Oplus__class_Oplus(U_371,U_372,U_373)),c_Groups_Oplus__class_Oplus(U_371,c_Groups_Oabs__class_Oabs(U_371,U_372),c_Groups_Oabs__class_Oabs(U_371,U_373)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_371) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_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_149_2,plain,
! [U_375,U_374] :
( c_Orderings_Oord__class_Oless__eq(U_374,U_375,U_375)
| ~ class_Orderings_Opreorder(U_374) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
! [U_374,U_375] :
( c_Orderings_Oord__class_Oless__eq(U_374,U_375,U_375)
| ~ class_Orderings_Opreorder(U_374) ),
inference(definitional_conversion,[status(esa)],[f_149_2]) ).
cnf(f_149_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_374,U_375,U_375)
| ~ class_Orderings_Opreorder(U_374) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_1,plain,
! [V_n,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)),c_Nat_OSuc(hAPP(hAPP(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_Int_Onumber__class_Onumber__of(T_a,c_Int_OMin)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__m1__odd]) ).
fof(f_150_2,plain,
! [U_377,U_376] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_376),c_Int_Onumber__class_Onumber__of(U_376,c_Int_OMin)),c_Nat_OSuc(hAPP(hAPP(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_377))) = c_Int_Onumber__class_Onumber__of(U_376,c_Int_OMin)
| ~ class_Int_Onumber__ring(U_376) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_376,U_377] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_376),c_Int_Onumber__class_Onumber__of(U_376,c_Int_OMin)),c_Nat_OSuc(hAPP(hAPP(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_377))) = c_Int_Onumber__class_Onumber__of(U_376,c_Int_OMin)
| ~ class_Int_Onumber__ring(U_376) ),
inference(definitional_conversion,[status(esa)],[f_150_2]) ).
cnf(f_150_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_376),c_Int_Onumber__class_Onumber__of(U_376,c_Int_OMin)),c_Nat_OSuc(hAPP(hAPP(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_377))) = c_Int_Onumber__class_Onumber__of(U_376,c_Int_OMin)
| ~ class_Int_Onumber__ring(U_376) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_1,plain,
! [T_a] :
( c_Power_Opower__class_Opower(T_a) = c_Power_Opower_Opower(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Otimes__class_Otimes(T_a))
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__power__power]) ).
fof(f_151_2,plain,
! [U_378] :
( c_Power_Opower__class_Opower(U_378) = c_Power_Opower_Opower(U_378,c_Groups_Oone__class_Oone(U_378),c_Groups_Otimes__class_Otimes(U_378))
| ~ class_Power_Opower(U_378) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_378] :
( c_Power_Opower__class_Opower(U_378) = c_Power_Opower_Opower(U_378,c_Groups_Oone__class_Oone(U_378),c_Groups_Otimes__class_Otimes(U_378))
| ~ class_Power_Opower(U_378) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( c_Power_Opower__class_Opower(U_378) = c_Power_Opower_Opower(U_378,c_Groups_Oone__class_Oone(U_378),c_Groups_Otimes__class_Otimes(U_378))
| ~ class_Power_Opower(U_378) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x)),V_y))
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power2__diff]) ).
fof(f_152_2,plain,
! [U_381,U_380,U_379] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_379),c_Groups_Ominus__class_Ominus(U_379,U_380,U_381)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(U_379,c_Groups_Oplus__class_Oplus(U_379,hAPP(hAPP(c_Power_Opower__class_Opower(U_379),U_380),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_379),U_381),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_379),c_Int_Onumber__class_Onumber__of(U_379,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_380)),U_381))
| ~ class_Int_Onumber__ring(U_379) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_379,U_380,U_381] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_379),c_Groups_Ominus__class_Ominus(U_379,U_380,U_381)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(U_379,c_Groups_Oplus__class_Oplus(U_379,hAPP(hAPP(c_Power_Opower__class_Opower(U_379),U_380),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_379),U_381),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_379),c_Int_Onumber__class_Onumber__of(U_379,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_380)),U_381))
| ~ class_Int_Onumber__ring(U_379) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_379),c_Groups_Ominus__class_Ominus(U_379,U_380,U_381)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ominus__class_Ominus(U_379,c_Groups_Oplus__class_Oplus(U_379,hAPP(hAPP(c_Power_Opower__class_Opower(U_379),U_380),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_379),U_381),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_379),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_379),c_Int_Onumber__class_Onumber__of(U_379,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_380)),U_381))
| ~ class_Int_Onumber__ring(U_379) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__le__even__power_H]) ).
fof(f_153_2,plain,
! [U_384,U_383,U_382] :
( c_Orderings_Oord__class_Oless__eq(U_382,c_Groups_Ozero__class_Ozero(U_382),hAPP(hAPP(c_Power_Opower__class_Opower(U_382),U_383),hAPP(hAPP(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_384)))
| ~ class_Rings_Olinordered__idom(U_382) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_382,U_383,U_384] :
( c_Orderings_Oord__class_Oless__eq(U_382,c_Groups_Ozero__class_Ozero(U_382),hAPP(hAPP(c_Power_Opower__class_Opower(U_382),U_383),hAPP(hAPP(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_384)))
| ~ class_Rings_Olinordered__idom(U_382) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_382,c_Groups_Ozero__class_Ozero(U_382),hAPP(hAPP(c_Power_Opower__class_Opower(U_382),U_383),hAPP(hAPP(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_384)))
| ~ class_Rings_Olinordered__idom(U_382) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_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,hAPP(hAPP(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)))),hAPP(hAPP(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_154_2,plain,
! [U_386,U_385] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_385),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_385),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_386),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_385,U_386] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_385),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_385),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_386),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(definitional_conversion,[status(esa)],[f_154_2]) ).
cnf(f_154_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_385),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_385),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_386),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_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,hAPP(hAPP(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)))),hAPP(hAPP(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_155_2,plain,
! [U_388,U_387] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_387),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_388),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_387),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_387,U_388] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_387),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_388),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_387),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(definitional_conversion,[status(esa)],[f_155_2]) ).
cnf(f_155_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_387),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_388),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_387),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_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,hAPP(hAPP(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)))),hAPP(hAPP(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_156_2,plain,
! [U_391,U_390,U_389] :
( c_Orderings_Oord__class_Oless__eq(U_389,c_Groups_Ozero__class_Ozero(U_389),c_Groups_Oplus__class_Oplus(U_389,hAPP(hAPP(c_Power_Opower__class_Opower(U_389),U_390),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_389),U_391),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_389) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_389,U_390,U_391] :
( c_Orderings_Oord__class_Oless__eq(U_389,c_Groups_Ozero__class_Ozero(U_389),c_Groups_Oplus__class_Oplus(U_389,hAPP(hAPP(c_Power_Opower__class_Opower(U_389),U_390),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_389),U_391),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_389) ),
inference(definitional_conversion,[status(esa)],[f_156_2]) ).
cnf(f_156_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_389,c_Groups_Ozero__class_Ozero(U_389),c_Groups_Oplus__class_Oplus(U_389,hAPP(hAPP(c_Power_Opower__class_Opower(U_389),U_390),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_389),U_391),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ class_Rings_Olinordered__idom(U_389) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
inference(fof_nnf,[status(thm)],[fact_C_I2_J]) ).
fof(f_157_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
inference(definitional_conversion,[status(esa)],[f_157_1]) ).
cnf(f_157_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
inference(clausify,[status(thm)],[f_157_2]) ).
fof(f_158_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
inference(fof_nnf,[status(thm)],[fact_C_I1_J]) ).
fof(f_158_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
inference(definitional_conversion,[status(esa)],[f_158_1]) ).
cnf(f_158_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)))),
inference(clausify,[status(thm)],[f_158_2]) ).
fof(f_159_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))),
inference(fof_nnf,[status(thm)],[fact_C_I4_J]) ).
fof(f_159_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))),
inference(definitional_conversion,[status(esa)],[f_159_1]) ).
cnf(f_159_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))),
inference(clausify,[status(thm)],[f_159_2]) ).
fof(f_160_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))),
inference(fof_nnf,[status(thm)],[fact_C_I3_J]) ).
fof(f_160_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))),
inference(definitional_conversion,[status(esa)],[f_160_1]) ).
cnf(f_160_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,v_z,c_Complex_Oii))),
inference(clausify,[status(thm)],[f_160_2]) ).
fof(f_161_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]) ).
fof(f_161_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_161_1]) ).
cnf(f_161_3,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_161_2]) ).
fof(f_162_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_162_2,plain,
! [U_392] : 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_392),U_392) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_392] : 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_392),U_392) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,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_392),U_392) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_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_163_2,plain,
! [U_395,U_394,U_393] :
( c_Int_Onumber__class_Onumber__of(U_393,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_394,U_395)) = c_Groups_Ominus__class_Ominus(U_393,c_Int_Onumber__class_Onumber__of(U_393,U_394),c_Int_Onumber__class_Onumber__of(U_393,U_395))
| ~ class_Int_Onumber__ring(U_393) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_393,U_394,U_395] :
( c_Int_Onumber__class_Onumber__of(U_393,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_394,U_395)) = c_Groups_Ominus__class_Ominus(U_393,c_Int_Onumber__class_Onumber__of(U_393,U_394),c_Int_Onumber__class_Onumber__of(U_393,U_395))
| ~ class_Int_Onumber__ring(U_393) ),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
( c_Int_Onumber__class_Onumber__of(U_393,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_394,U_395)) = c_Groups_Ominus__class_Ominus(U_393,c_Int_Onumber__class_Onumber__of(U_393,U_394),c_Int_Onumber__class_Onumber__of(U_393,U_395))
| ~ class_Int_Onumber__ring(U_393) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z,
inference(fof_nnf,[status(thm)],[fact_zmult__1]) ).
fof(f_164_2,plain,
! [U_396] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_396) = U_396,
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_396] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_396) = U_396,
inference(definitional_conversion,[status(esa)],[f_164_2]) ).
cnf(f_164_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_396) = U_396,
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zmult__1__right]) ).
fof(f_165_2,plain,
! [U_397] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_397),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_397,
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_397] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_397),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_397,
inference(definitional_conversion,[status(esa)],[f_165_2]) ).
cnf(f_165_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_397),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_397,
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_1,plain,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z),
inference(fof_nnf,[status(thm)],[fact_zmult__commute]) ).
fof(f_166_2,plain,
! [U_399,U_398] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_398),U_399) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_399),U_398),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_399,U_398] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_398),U_399) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_399),U_398),
inference(definitional_conversion,[status(esa)],[f_166_2]) ).
cnf(f_166_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_398),U_399) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_399),U_398),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_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_167_2,plain,
! [U_401,U_400] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_400,U_401) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_400,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_401))
| U_400 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_400,U_401) = U_401
| U_400 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
( ! [U_405,U_403] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_403,U_405) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_403,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_405))
| U_403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_404,U_402] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_402,U_404) = U_404
| U_402 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_167_2]) ).
fof(f_167_4,plain,
( ! [U_405,U_403] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_403,U_405) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_403,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_405))
| U_403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_402,U_404] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_402,U_404) = U_404
| U_402 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_167_3]) ).
cnf(f_167_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_402,U_404) = U_404
| U_402 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_167_4]) ).
cnf(f_167_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_403,U_405) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_403,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_405))
| U_403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_167_4]) ).
fof(f_168_1,plain,
! [V_z,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_y)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_z)),
inference(fof_nnf,[status(thm)],[fact_zpower__zadd__distrib]) ).
fof(f_168_2,plain,
! [U_408,U_407,U_406] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_406),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_407,U_408)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_406),U_407)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_406),U_408)),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
! [U_406,U_407,U_408] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_406),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_407,U_408)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_406),U_407)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_406),U_408)),
inference(definitional_conversion,[status(esa)],[f_168_2]) ).
cnf(f_168_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_406),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_407,U_408)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_406),U_407)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_406),U_408)),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_1,plain,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib2]) ).
fof(f_169_2,plain,
! [U_411,U_410,U_409] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_409),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_410,U_411)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_409),U_410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_409),U_411)),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_409,U_410,U_411] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_409),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_410,U_411)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_409),U_410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_409),U_411)),
inference(definitional_conversion,[status(esa)],[f_169_2]) ).
cnf(f_169_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_409),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_410,U_411)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_409),U_410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_409),U_411)),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_1,plain,
! [V_z2,V_z1,V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_w),V_z2)),
inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib2]) ).
fof(f_170_2,plain,
! [U_414,U_413,U_412] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_412),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_413,U_414)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_412),U_413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_412),U_414)),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_412,U_413,U_414] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_412),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_413,U_414)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_412),U_413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_412),U_414)),
inference(definitional_conversion,[status(esa)],[f_170_2]) ).
cnf(f_170_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_412),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_413,U_414)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_412),U_413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_412),U_414)),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_1,plain,
! [V_n] : hAPP(hAPP(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_171_2,plain,
! [U_415] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_415) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_415] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_415) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_171_2]) ).
cnf(f_171_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_415) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_1,plain,
! [V_z3,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_z2)),V_z3) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_z3)),
inference(fof_nnf,[status(thm)],[fact_zmult__assoc]) ).
fof(f_172_2,plain,
! [U_418,U_417,U_416] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_416),U_417)),U_418) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_417),U_418)),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_416,U_417,U_418] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_416),U_417)),U_418) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_417),U_418)),
inference(definitional_conversion,[status(esa)],[f_172_2]) ).
cnf(f_172_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_416),U_417)),U_418) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_417),U_418)),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_1,plain,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
inference(fof_nnf,[status(thm)],[fact_zadd__zmult__distrib]) ).
fof(f_173_2,plain,
! [U_421,U_420,U_419] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_419,U_420)),U_421) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_419),U_421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_420),U_421)),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_419,U_420,U_421] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_419,U_420)),U_421) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_419),U_421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_420),U_421)),
inference(definitional_conversion,[status(esa)],[f_173_2]) ).
cnf(f_173_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_419,U_420)),U_421) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_419),U_421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_420),U_421)),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_1,plain,
! [V_w,V_z2,V_z1] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z1,V_z2)),V_w) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z1),V_w),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z2),V_w)),
inference(fof_nnf,[status(thm)],[fact_zdiff__zmult__distrib]) ).
fof(f_174_2,plain,
! [U_424,U_423,U_422] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_422,U_423)),U_424) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_422),U_424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_423),U_424)),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_422,U_423,U_424] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_422,U_423)),U_424) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_422),U_424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_423),U_424)),
inference(definitional_conversion,[status(esa)],[f_174_2]) ).
cnf(f_174_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_422,U_423)),U_424) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_422),U_424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_423),U_424)),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_1,plain,
! [V_m_2,V_xa_2] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_2),V_m_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( V_xa_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_xa_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_xa_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_175_2,plain,
! [U_426,U_425] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_425),U_426) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_425 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_426 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_425 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_426 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_425),U_426) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
( ! [U_430,U_428] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_428),U_430) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_428 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_430 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_429,U_427] :
( U_427 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_427),U_429) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_175_2]) ).
fof(f_175_4,plain,
( ! [U_430,U_428] :
( U_428 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP13(U_430,U_428) )
& ! [U_430,U_428] :
( U_430 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP13(U_430,U_428) )
& ! [U_430,U_428] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_428),U_430) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP13(U_430,U_428) )
& ! [U_429,U_427] :
( U_427 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_427),U_429) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_175_3]) ).
cnf(f_175_5,plain,
( U_427 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_429 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_427),U_429) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_175_4]) ).
cnf(f_175_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_428),U_430) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP13(U_430,U_428) ),
inference(clausify,[status(thm)],[f_175_4]) ).
cnf(f_175_7,plain,
( U_430 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP13(U_430,U_428) ),
inference(clausify,[status(thm)],[f_175_4]) ).
cnf(f_175_8,plain,
( U_428 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP13(U_430,U_428) ),
inference(clausify,[status(thm)],[f_175_4]) ).
fof(f_176_1,plain,
! [V_n,V_m] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_abs__zmult__eq__1]) ).
fof(f_176_2,plain,
! [U_432,U_431] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_431) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_431),U_432)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_432,U_431] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_431) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_431),U_432)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_176_2]) ).
cnf(f_176_4,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_431) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_431),U_432)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [V_n_2,V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Nat_OSuc(V_n_2)) = hAPP(hAPP(V_times_2,V_a_2),hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),V_n_2)),
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__Suc]) ).
fof(f_177_2,plain,
! [U_437,U_436,U_435,U_434,U_433] : hAPP(hAPP(c_Power_Opower_Opower(U_433,U_434,U_435),U_436),c_Nat_OSuc(U_437)) = hAPP(hAPP(U_435,U_436),hAPP(hAPP(c_Power_Opower_Opower(U_433,U_434,U_435),U_436),U_437)),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_434,U_433,U_435,U_436,U_437] : hAPP(hAPP(c_Power_Opower_Opower(U_433,U_434,U_435),U_436),c_Nat_OSuc(U_437)) = hAPP(hAPP(U_435,U_436),hAPP(hAPP(c_Power_Opower_Opower(U_433,U_434,U_435),U_436),U_437)),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_433,U_434,U_435),U_436),c_Nat_OSuc(U_437)) = hAPP(hAPP(U_435,U_436),hAPP(hAPP(c_Power_Opower_Opower(U_433,U_434,U_435),U_436),U_437)),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_1,plain,
! [V_a_2,V_times_2,V_one_2,T_a] : hAPP(hAPP(c_Power_Opower_Opower(T_a,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2,
inference(fof_nnf,[status(thm)],[fact_power_Opower_Opower__0]) ).
fof(f_178_2,plain,
! [U_441,U_440,U_439,U_438] : hAPP(hAPP(c_Power_Opower_Opower(U_438,U_439,U_440),U_441),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_439,
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_438,U_439,U_440,U_441] : hAPP(hAPP(c_Power_Opower_Opower(U_438,U_439,U_440),U_441),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_439,
inference(definitional_conversion,[status(esa)],[f_178_2]) ).
cnf(f_178_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_438,U_439,U_440),U_441),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_439,
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_1,plain,
! [V_d,V_c,V_b,V_a] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_b,V_d)),
inference(fof_nnf,[status(thm)],[fact_complex__diff]) ).
fof(f_179_2,plain,
! [U_445,U_444,U_443,U_442] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_442,U_443),c_Complex_Ocomplex_OComplex(U_444,U_445)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_442,U_444),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_443,U_445)),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_442,U_443,U_444,U_445] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_442,U_443),c_Complex_Ocomplex_OComplex(U_444,U_445)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_442,U_444),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_443,U_445)),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_442,U_443),c_Complex_Ocomplex_OComplex(U_444,U_445)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_442,U_444),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_443,U_445)),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_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_180_2,plain,
! [U_448,U_447,U_446] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_446,U_447),U_448) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_446,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_447,U_448)),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
! [U_447,U_446,U_448] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_446,U_447),U_448) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_446,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_447,U_448)),
inference(definitional_conversion,[status(esa)],[f_180_2]) ).
cnf(f_180_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_446,U_447),U_448) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_446,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_447,U_448)),
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_1,plain,
! [V_b_2,V_a_2] :
( ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| V_b_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_a_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(fof_nnf,[status(thm)],[fact_Complex__eq__0]) ).
fof(f_181_2,plain,
! [U_450,U_449] :
( ( c_Complex_Ocomplex_OComplex(U_449,U_450) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| U_450 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_449 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_450 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_449 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_449,U_450) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
( ! [U_454,U_452] :
( c_Complex_Ocomplex_OComplex(U_452,U_454) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| U_454 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_452 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_453,U_451] :
( ( U_453 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_451 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_451,U_453) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(miniscope,[status(thm)],[f_181_2]) ).
fof(f_181_4,plain,
( ! [U_453,U_451] :
( U_453 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP14(U_453,U_451) )
& ! [U_453,U_451] :
( U_451 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP14(U_453,U_451) )
& ! [U_452,U_454] :
( c_Complex_Ocomplex_OComplex(U_452,U_454) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| U_454 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_452 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_453,U_451] :
( sP14(U_453,U_451)
| c_Complex_Ocomplex_OComplex(U_451,U_453) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_181_3]) ).
cnf(f_181_5,plain,
( sP14(U_453,U_451)
| c_Complex_Ocomplex_OComplex(U_451,U_453) != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_6,plain,
( c_Complex_Ocomplex_OComplex(U_452,U_454) = c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex)
| U_454 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_452 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_7,plain,
( U_451 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP14(U_453,U_451) ),
inference(clausify,[status(thm)],[f_181_4]) ).
cnf(f_181_8,plain,
( U_453 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP14(U_453,U_451) ),
inference(clausify,[status(thm)],[f_181_4]) ).
fof(f_182_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_182_2,plain,
! [U_456,U_455] : 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_455,U_456)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_455)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_456)),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_456,U_455] : 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_455,U_456)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_455)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_456)),
inference(definitional_conversion,[status(esa)],[f_182_2]) ).
cnf(f_182_4,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_455,U_456)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_455)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_456)),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_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_183_2,plain,
! [U_459,U_458,U_457] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_457,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_458,U_459)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_458,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_457,U_459)),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_457,U_458,U_459] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_457,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_458,U_459)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_458,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_457,U_459)),
inference(definitional_conversion,[status(esa)],[f_183_2]) ).
cnf(f_183_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_457,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_458,U_459)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_458,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_457,U_459)),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_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_184_2,plain,
! [U_462,U_461,U_460] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_460,U_461,U_462)
| ~ c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ominus__class_Ominus(U_460,U_461,U_462),c_Groups_Ozero__class_Ozero(U_460)) )
& ( c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ominus__class_Ominus(U_460,U_461,U_462),c_Groups_Ozero__class_Ozero(U_460))
| ~ c_Orderings_Oord__class_Oless__eq(U_460,U_461,U_462) ) )
| ~ class_Groups_Oordered__ab__group__add(U_460) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
( ! [U_460,U_461,U_462] :
( c_Orderings_Oord__class_Oless__eq(U_460,U_461,U_462)
| ~ c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ominus__class_Ominus(U_460,U_461,U_462),c_Groups_Ozero__class_Ozero(U_460))
| ~ sP15(U_460,U_461,U_462) )
& ! [U_460,U_461,U_462] :
( c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ominus__class_Ominus(U_460,U_461,U_462),c_Groups_Ozero__class_Ozero(U_460))
| ~ c_Orderings_Oord__class_Oless__eq(U_460,U_461,U_462)
| ~ sP15(U_460,U_461,U_462) )
& ! [U_460,U_461,U_462] :
( sP15(U_460,U_461,U_462)
| ~ class_Groups_Oordered__ab__group__add(U_460) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_184_2]) ).
cnf(f_184_4,plain,
( sP15(U_460,U_461,U_462)
| ~ class_Groups_Oordered__ab__group__add(U_460) ),
inference(clausify,[status(thm)],[f_184_3]) ).
cnf(f_184_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ominus__class_Ominus(U_460,U_461,U_462),c_Groups_Ozero__class_Ozero(U_460))
| ~ c_Orderings_Oord__class_Oless__eq(U_460,U_461,U_462)
| ~ sP15(U_460,U_461,U_462) ),
inference(clausify,[status(thm)],[f_184_3]) ).
cnf(f_184_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_460,U_461,U_462)
| ~ c_Orderings_Oord__class_Oless__eq(U_460,c_Groups_Ominus__class_Ominus(U_460,U_461,U_462),c_Groups_Ozero__class_Ozero(U_460))
| ~ sP15(U_460,U_461,U_462) ),
inference(clausify,[status(thm)],[f_184_3]) ).
fof(f_185_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_185_2,plain,
! [U_464,U_463] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_463,U_464) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_464,U_463),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
! [U_464,U_463] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_463,U_464) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_464,U_463),
inference(definitional_conversion,[status(esa)],[f_185_2]) ).
cnf(f_185_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_463,U_464) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_464,U_463),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_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_186_2,plain,
! [U_465] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_465,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_465,
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_465] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_465,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_465,
inference(definitional_conversion,[status(esa)],[f_186_2]) ).
cnf(f_186_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_465,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_465,
inference(clausify,[status(thm)],[f_186_3]) ).
fof(f_187_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_187_2,plain,
! [U_466] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_466) = U_466,
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_466] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_466) = U_466,
inference(definitional_conversion,[status(esa)],[f_187_2]) ).
cnf(f_187_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_466) = U_466,
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_1,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_complex__zero__def]) ).
fof(f_188_2,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_188_1]) ).
cnf(f_188_3,plain,
c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_188_2]) ).
fof(f_189_1,plain,
! [V_xa_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = V_xa_2
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) != V_xa_2 ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).
fof(f_189_2,plain,
! [U_468,U_467] :
( ( ( c_Groups_Ozero__class_Ozero(U_467) = U_468
| U_468 != c_Groups_Ozero__class_Ozero(U_467) )
& ( U_468 = c_Groups_Ozero__class_Ozero(U_467)
| c_Groups_Ozero__class_Ozero(U_467) != U_468 ) )
| ~ class_Groups_Ozero(U_467) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
( ! [U_467,U_468] :
( c_Groups_Ozero__class_Ozero(U_467) = U_468
| U_468 != c_Groups_Ozero__class_Ozero(U_467)
| ~ sP16(U_467,U_468) )
& ! [U_467,U_468] :
( U_468 = c_Groups_Ozero__class_Ozero(U_467)
| c_Groups_Ozero__class_Ozero(U_467) != U_468
| ~ sP16(U_467,U_468) )
& ! [U_467,U_468] :
( sP16(U_467,U_468)
| ~ class_Groups_Ozero(U_467) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_189_2]) ).
cnf(f_189_4,plain,
( sP16(U_467,U_468)
| ~ class_Groups_Ozero(U_467) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_5,plain,
( U_468 = c_Groups_Ozero__class_Ozero(U_467)
| c_Groups_Ozero__class_Ozero(U_467) != U_468
| ~ sP16(U_467,U_468) ),
inference(clausify,[status(thm)],[f_189_3]) ).
cnf(f_189_6,plain,
( c_Groups_Ozero__class_Ozero(U_467) = U_468
| U_468 != c_Groups_Ozero__class_Ozero(U_467)
| ~ sP16(U_467,U_468) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_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_190_2,plain,
! [U_470,U_469] :
( c_Groups_Ominus__class_Ominus(U_469,U_470,c_Groups_Ozero__class_Ozero(U_469)) = U_470
| ~ class_Groups_Ogroup__add(U_469) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
! [U_470,U_469] :
( c_Groups_Ominus__class_Ominus(U_469,U_470,c_Groups_Ozero__class_Ozero(U_469)) = U_470
| ~ class_Groups_Ogroup__add(U_469) ),
inference(definitional_conversion,[status(esa)],[f_190_2]) ).
cnf(f_190_4,plain,
( c_Groups_Ominus__class_Ominus(U_469,U_470,c_Groups_Ozero__class_Ozero(U_469)) = U_470
| ~ class_Groups_Ogroup__add(U_469) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_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_191_2,plain,
! [U_472,U_471] :
( c_Groups_Ominus__class_Ominus(U_471,U_472,U_472) = c_Groups_Ozero__class_Ozero(U_471)
| ~ class_Groups_Ogroup__add(U_471) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
! [U_471,U_472] :
( c_Groups_Ominus__class_Ominus(U_471,U_472,U_472) = c_Groups_Ozero__class_Ozero(U_471)
| ~ class_Groups_Ogroup__add(U_471) ),
inference(definitional_conversion,[status(esa)],[f_191_2]) ).
cnf(f_191_4,plain,
( c_Groups_Ominus__class_Ominus(U_471,U_472,U_472) = c_Groups_Ozero__class_Ozero(U_471)
| ~ class_Groups_Ogroup__add(U_471) ),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_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_192_2,plain,
! [U_475,U_474,U_473] :
( ( ( U_474 = U_475
| c_Groups_Ominus__class_Ominus(U_473,U_474,U_475) != c_Groups_Ozero__class_Ozero(U_473) )
& ( c_Groups_Ominus__class_Ominus(U_473,U_474,U_475) = c_Groups_Ozero__class_Ozero(U_473)
| U_474 != U_475 ) )
| ~ class_Groups_Oab__group__add(U_473) ),
inference(variable_rename,[status(thm)],[f_192_1]) ).
fof(f_192_3,plain,
( ! [U_473,U_474,U_475] :
( U_474 = U_475
| c_Groups_Ominus__class_Ominus(U_473,U_474,U_475) != c_Groups_Ozero__class_Ozero(U_473)
| ~ sP17(U_473,U_474,U_475) )
& ! [U_473,U_474,U_475] :
( c_Groups_Ominus__class_Ominus(U_473,U_474,U_475) = c_Groups_Ozero__class_Ozero(U_473)
| U_474 != U_475
| ~ sP17(U_473,U_474,U_475) )
& ! [U_473,U_474,U_475] :
( sP17(U_473,U_474,U_475)
| ~ class_Groups_Oab__group__add(U_473) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17])],[f_192_2]) ).
cnf(f_192_4,plain,
( sP17(U_473,U_474,U_475)
| ~ class_Groups_Oab__group__add(U_473) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_5,plain,
( c_Groups_Ominus__class_Ominus(U_473,U_474,U_475) = c_Groups_Ozero__class_Ozero(U_473)
| U_474 != U_475
| ~ sP17(U_473,U_474,U_475) ),
inference(clausify,[status(thm)],[f_192_3]) ).
cnf(f_192_6,plain,
( U_474 = U_475
| c_Groups_Ominus__class_Ominus(U_473,U_474,U_475) != c_Groups_Ozero__class_Ozero(U_473)
| ~ sP17(U_473,U_474,U_475) ),
inference(clausify,[status(thm)],[f_192_3]) ).
fof(f_193_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_193_2,plain,
! [U_478,U_477,U_476] :
( ( ( c_Groups_Ominus__class_Ominus(U_476,U_477,U_478) = c_Groups_Ozero__class_Ozero(U_476)
| U_477 != U_478 )
& ( U_477 = U_478
| c_Groups_Ominus__class_Ominus(U_476,U_477,U_478) != c_Groups_Ozero__class_Ozero(U_476) ) )
| ~ class_Groups_Ogroup__add(U_476) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
( ! [U_477,U_478,U_476] :
( c_Groups_Ominus__class_Ominus(U_476,U_477,U_478) = c_Groups_Ozero__class_Ozero(U_476)
| U_477 != U_478
| ~ sP18(U_477,U_478,U_476) )
& ! [U_477,U_478,U_476] :
( U_477 = U_478
| c_Groups_Ominus__class_Ominus(U_476,U_477,U_478) != c_Groups_Ozero__class_Ozero(U_476)
| ~ sP18(U_477,U_478,U_476) )
& ! [U_477,U_478,U_476] :
( sP18(U_477,U_478,U_476)
| ~ class_Groups_Ogroup__add(U_476) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_193_2]) ).
cnf(f_193_4,plain,
( sP18(U_477,U_478,U_476)
| ~ class_Groups_Ogroup__add(U_476) ),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_193_5,plain,
( U_477 = U_478
| c_Groups_Ominus__class_Ominus(U_476,U_477,U_478) != c_Groups_Ozero__class_Ozero(U_476)
| ~ sP18(U_477,U_478,U_476) ),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_193_6,plain,
( c_Groups_Ominus__class_Ominus(U_476,U_477,U_478) = c_Groups_Ozero__class_Ozero(U_476)
| U_477 != U_478
| ~ sP18(U_477,U_478,U_476) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_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_194_2,plain,
! [U_483,U_482,U_481,U_480,U_479] :
( ( ( U_480 = U_481
| U_482 != U_483 )
& ( U_482 = U_483
| U_480 != U_481 ) )
| c_Groups_Ominus__class_Ominus(U_479,U_480,U_481) != c_Groups_Ominus__class_Ominus(U_479,U_482,U_483)
| ~ class_Groups_Oab__group__add(U_479) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
( ! [U_483,U_481,U_482,U_480] :
( U_480 = U_481
| U_482 != U_483
| ~ sP19(U_483,U_481,U_482,U_480) )
& ! [U_483,U_481,U_482,U_480] :
( U_482 = U_483
| U_480 != U_481
| ~ sP19(U_483,U_481,U_482,U_480) )
& ! [U_483,U_481,U_479,U_482,U_480] :
( sP19(U_483,U_481,U_482,U_480)
| c_Groups_Ominus__class_Ominus(U_479,U_480,U_481) != c_Groups_Ominus__class_Ominus(U_479,U_482,U_483)
| ~ class_Groups_Oab__group__add(U_479) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_194_2]) ).
cnf(f_194_4,plain,
( sP19(U_483,U_481,U_482,U_480)
| c_Groups_Ominus__class_Ominus(U_479,U_480,U_481) != c_Groups_Ominus__class_Ominus(U_479,U_482,U_483)
| ~ class_Groups_Oab__group__add(U_479) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_5,plain,
( U_482 = U_483
| U_480 != U_481
| ~ sP19(U_483,U_481,U_482,U_480) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_6,plain,
( U_480 = U_481
| U_482 != U_483
| ~ sP19(U_483,U_481,U_482,U_480) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_1,plain,
! [V_ya_2,V_xa_2] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_NthRoot_Osqrt(V_ya_2)
| V_xa_2 != V_ya_2 )
& ( V_xa_2 = V_ya_2
| c_NthRoot_Osqrt(V_xa_2) != c_NthRoot_Osqrt(V_ya_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__iff]) ).
fof(f_195_2,plain,
! [U_485,U_484] :
( ( c_NthRoot_Osqrt(U_484) = c_NthRoot_Osqrt(U_485)
| U_484 != U_485 )
& ( U_484 = U_485
| c_NthRoot_Osqrt(U_484) != c_NthRoot_Osqrt(U_485) ) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
( ! [U_489,U_487] :
( c_NthRoot_Osqrt(U_487) = c_NthRoot_Osqrt(U_489)
| U_487 != U_489 )
& ! [U_488,U_486] :
( U_486 = U_488
| c_NthRoot_Osqrt(U_486) != c_NthRoot_Osqrt(U_488) ) ),
inference(miniscope,[status(thm)],[f_195_2]) ).
fof(f_195_4,plain,
( ! [U_487,U_489] :
( c_NthRoot_Osqrt(U_487) = c_NthRoot_Osqrt(U_489)
| U_487 != U_489 )
& ! [U_488,U_486] :
( U_486 = U_488
| c_NthRoot_Osqrt(U_486) != c_NthRoot_Osqrt(U_488) ) ),
inference(definitional_conversion,[status(esa)],[f_195_3]) ).
cnf(f_195_5,plain,
( U_486 = U_488
| c_NthRoot_Osqrt(U_486) != c_NthRoot_Osqrt(U_488) ),
inference(clausify,[status(thm)],[f_195_4]) ).
cnf(f_195_6,plain,
( c_NthRoot_Osqrt(U_487) = c_NthRoot_Osqrt(U_489)
| U_487 != U_489 ),
inference(clausify,[status(thm)],[f_195_4]) ).
fof(f_196_1,plain,
! [V_xa_2] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_xa_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(V_xa_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__0__iff]) ).
fof(f_196_2,plain,
! [U_490] :
( ( c_NthRoot_Osqrt(U_490) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_490 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_490 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_490) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
( ! [U_492] :
( c_NthRoot_Osqrt(U_492) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_492 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_491] :
( U_491 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_491) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_196_2]) ).
fof(f_196_4,plain,
( ! [U_492] :
( c_NthRoot_Osqrt(U_492) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_492 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_491] :
( U_491 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_491) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa)],[f_196_3]) ).
cnf(f_196_5,plain,
( U_491 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_491) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_196_4]) ).
cnf(f_196_6,plain,
( c_NthRoot_Osqrt(U_492) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_492 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_196_4]) ).
fof(f_197_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]) ).
fof(f_197_2,plain,
c_NthRoot_Osqrt(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_197_1]) ).
cnf(f_197_3,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_197_2]) ).
fof(f_198_1,plain,
! [V_ya_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__0__iff]) ).
fof(f_198_2,plain,
! [U_493] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_493))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_493) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_493)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_493)) ) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
( ! [U_495] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_495))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_495) )
& ! [U_494] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_494)) ) ),
inference(miniscope,[status(thm)],[f_198_2]) ).
fof(f_198_4,plain,
( ! [U_495] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_495))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_495) )
& ! [U_494] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_494)) ) ),
inference(definitional_conversion,[status(esa)],[f_198_3]) ).
cnf(f_198_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_494)) ),
inference(clausify,[status(thm)],[f_198_4]) ).
cnf(f_198_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_495))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_495) ),
inference(clausify,[status(thm)],[f_198_4]) ).
fof(f_199_1,plain,
! [V_xa_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__0__iff]) ).
fof(f_199_2,plain,
! [U_496] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_496),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_496,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_496,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_496),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
( ! [U_498] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_498),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_498,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_497] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_497,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_497),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_199_2]) ).
fof(f_199_4,plain,
( ! [U_498] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_498),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_498,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_497] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_497,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_497),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_199_3]) ).
cnf(f_199_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_497,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_497),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_199_4]) ).
cnf(f_199_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_498),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_498,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_199_4]) ).
fof(f_200_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_200_2,plain,
! [U_499] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_499))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_499) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
! [U_499] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_499))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_499) ),
inference(definitional_conversion,[status(esa)],[f_200_2]) ).
cnf(f_200_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_499))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_499) ),
inference(clausify,[status(thm)],[f_200_3]) ).
fof(f_201_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_201_2,plain,
! [U_500] :
( U_500 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_500) != 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_500) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
! [U_500] :
( U_500 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_500) != 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_500) ),
inference(definitional_conversion,[status(esa)],[f_201_2]) ).
cnf(f_201_4,plain,
( U_500 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_500) != 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_500) ),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_1,plain,
! [V_ya_2,V_xa_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_xa_2,V_ya_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_xa_2,V_ya_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff]) ).
fof(f_202_2,plain,
! [U_502,U_501] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_501,U_502)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_501,U_502),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_501,U_502),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_501,U_502) ) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
( ! [U_506,U_504] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_504,U_506)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_504,U_506),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_505,U_503] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_503,U_505),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_503,U_505) ) ),
inference(miniscope,[status(thm)],[f_202_2]) ).
fof(f_202_4,plain,
( ! [U_506,U_504] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_504,U_506)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_504,U_506),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_503,U_505] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_503,U_505),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_503,U_505) ) ),
inference(definitional_conversion,[status(esa)],[f_202_3]) ).
cnf(f_202_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_503,U_505),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_503,U_505) ),
inference(clausify,[status(thm)],[f_202_4]) ).
cnf(f_202_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_504,U_506)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_504,U_506),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_202_4]) ).
fof(f_203_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_203_2,plain,
! [U_508,U_507] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_507,c_Nat_OSuc(U_508)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_507,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_508),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_508,U_507] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_507,c_Nat_OSuc(U_508)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_507,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_508),
inference(definitional_conversion,[status(esa)],[f_203_2]) ).
cnf(f_203_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_507,c_Nat_OSuc(U_508)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_507,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_508),
inference(clausify,[status(thm)],[f_203_3]) ).
fof(f_204_1,plain,
! [V_n,T_a] :
( hAPP(hAPP(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_204_2,plain,
! [U_510,U_509] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_509),c_Groups_Ozero__class_Ozero(U_509)),c_Nat_OSuc(U_510)) = c_Groups_Ozero__class_Ozero(U_509)
| ~ class_Rings_Osemiring__0(U_509)
| ~ class_Power_Opower(U_509) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_509,U_510] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_509),c_Groups_Ozero__class_Ozero(U_509)),c_Nat_OSuc(U_510)) = c_Groups_Ozero__class_Ozero(U_509)
| ~ class_Rings_Osemiring__0(U_509)
| ~ class_Power_Opower(U_509) ),
inference(definitional_conversion,[status(esa)],[f_204_2]) ).
cnf(f_204_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_509),c_Groups_Ozero__class_Ozero(U_509)),c_Nat_OSuc(U_510)) = c_Groups_Ozero__class_Ozero(U_509)
| ~ class_Rings_Osemiring__0(U_509)
| ~ class_Power_Opower(U_509) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_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_205_2,plain,
! [U_511] : c_Nat_OSuc(U_511) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_511,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_511] : c_Nat_OSuc(U_511) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_511,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
c_Nat_OSuc(U_511) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_511,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_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_206_2,plain,
! [U_512] : c_Nat_OSuc(U_512) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_512),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_512] : c_Nat_OSuc(U_512) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_512),
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
c_Nat_OSuc(U_512) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_512),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_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)),hAPP(hAPP(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_207_2,plain,
! [U_514,U_513] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_513),U_514))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_513) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_513,U_514] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_513),U_514))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_513) ),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_513),U_514))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_513) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_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_208_2,plain,
! [U_519,U_518,U_517,U_516,U_515] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_515,U_516,U_517)
| ~ c_Orderings_Oord__class_Oless__eq(U_515,U_518,U_519) )
& ( c_Orderings_Oord__class_Oless__eq(U_515,U_518,U_519)
| ~ c_Orderings_Oord__class_Oless__eq(U_515,U_516,U_517) ) )
| c_Groups_Ominus__class_Ominus(U_515,U_516,U_517) != c_Groups_Ominus__class_Ominus(U_515,U_518,U_519)
| ~ class_Groups_Oordered__ab__group__add(U_515) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
( ! [U_515,U_516,U_517,U_518,U_519] :
( c_Orderings_Oord__class_Oless__eq(U_515,U_516,U_517)
| ~ c_Orderings_Oord__class_Oless__eq(U_515,U_518,U_519)
| ~ sP20(U_515,U_516,U_517,U_518,U_519) )
& ! [U_515,U_516,U_517,U_518,U_519] :
( c_Orderings_Oord__class_Oless__eq(U_515,U_518,U_519)
| ~ c_Orderings_Oord__class_Oless__eq(U_515,U_516,U_517)
| ~ sP20(U_515,U_516,U_517,U_518,U_519) )
& ! [U_515,U_516,U_517,U_518,U_519] :
( sP20(U_515,U_516,U_517,U_518,U_519)
| c_Groups_Ominus__class_Ominus(U_515,U_516,U_517) != c_Groups_Ominus__class_Ominus(U_515,U_518,U_519)
| ~ class_Groups_Oordered__ab__group__add(U_515) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_208_2]) ).
cnf(f_208_4,plain,
( sP20(U_515,U_516,U_517,U_518,U_519)
| c_Groups_Ominus__class_Ominus(U_515,U_516,U_517) != c_Groups_Ominus__class_Ominus(U_515,U_518,U_519)
| ~ class_Groups_Oordered__ab__group__add(U_515) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_515,U_518,U_519)
| ~ c_Orderings_Oord__class_Oless__eq(U_515,U_516,U_517)
| ~ sP20(U_515,U_516,U_517,U_518,U_519) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_515,U_516,U_517)
| ~ c_Orderings_Oord__class_Oless__eq(U_515,U_518,U_519)
| ~ sP20(U_515,U_516,U_517,U_518,U_519) ),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_1,plain,
! [V_n_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(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) )
| hAPP(hAPP(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_209_2,plain,
! [U_522,U_521,U_520] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_520),U_521),U_522) = c_Groups_Ozero__class_Ozero(U_520)
| U_522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_521 != c_Groups_Ozero__class_Ozero(U_520) )
& ( ( U_522 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_521 = c_Groups_Ozero__class_Ozero(U_520) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_520),U_521),U_522) != c_Groups_Ozero__class_Ozero(U_520) ) )
| ~ class_Rings_Ozero__neq__one(U_520)
| ~ class_Rings_Ono__zero__divisors(U_520)
| ~ class_Rings_Omult__zero(U_520)
| ~ class_Power_Opower(U_520) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
( ! [U_520,U_522,U_521] :
( U_522 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP21(U_520,U_522,U_521) )
& ! [U_520,U_522,U_521] :
( U_521 = c_Groups_Ozero__class_Ozero(U_520)
| ~ sP21(U_520,U_522,U_521) )
& ! [U_520,U_522,U_521] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_520),U_521),U_522) = c_Groups_Ozero__class_Ozero(U_520)
| U_522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_521 != c_Groups_Ozero__class_Ozero(U_520)
| ~ sP22(U_520,U_522,U_521) )
& ! [U_520,U_522,U_521] :
( sP21(U_520,U_522,U_521)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_520),U_521),U_522) != c_Groups_Ozero__class_Ozero(U_520)
| ~ sP22(U_520,U_522,U_521) )
& ! [U_520,U_522,U_521] :
( sP22(U_520,U_522,U_521)
| ~ class_Rings_Ozero__neq__one(U_520)
| ~ class_Rings_Ono__zero__divisors(U_520)
| ~ class_Rings_Omult__zero(U_520)
| ~ class_Power_Opower(U_520) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21,sP22])],[f_209_2]) ).
cnf(f_209_4,plain,
( sP22(U_520,U_522,U_521)
| ~ class_Rings_Ozero__neq__one(U_520)
| ~ class_Rings_Ono__zero__divisors(U_520)
| ~ class_Rings_Omult__zero(U_520)
| ~ class_Power_Opower(U_520) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_5,plain,
( sP21(U_520,U_522,U_521)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_520),U_521),U_522) != c_Groups_Ozero__class_Ozero(U_520)
| ~ sP22(U_520,U_522,U_521) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_520),U_521),U_522) = c_Groups_Ozero__class_Ozero(U_520)
| U_522 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_521 != c_Groups_Ozero__class_Ozero(U_520)
| ~ sP22(U_520,U_522,U_521) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_7,plain,
( U_521 = c_Groups_Ozero__class_Ozero(U_520)
| ~ sP21(U_520,U_522,U_521) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_8,plain,
( U_522 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP21(U_520,U_522,U_521) ),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_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_210_2,plain,
! [U_525,U_524,U_523] :
( c_Groups_Oplus__class_Oplus(U_523,c_Groups_Ominus__class_Ominus(U_523,U_524,U_525),U_525) = U_524
| ~ class_Groups_Ogroup__add(U_523) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_525,U_523,U_524] :
( c_Groups_Oplus__class_Oplus(U_523,c_Groups_Ominus__class_Ominus(U_523,U_524,U_525),U_525) = U_524
| ~ class_Groups_Ogroup__add(U_523) ),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
( c_Groups_Oplus__class_Oplus(U_523,c_Groups_Ominus__class_Ominus(U_523,U_524,U_525),U_525) = U_524
| ~ class_Groups_Ogroup__add(U_523) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_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_211_2,plain,
! [U_528,U_527,U_526] :
( c_Groups_Ominus__class_Ominus(U_526,c_Groups_Oplus__class_Oplus(U_526,U_527,U_528),U_528) = U_527
| ~ class_Groups_Ogroup__add(U_526) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_526,U_527,U_528] :
( c_Groups_Ominus__class_Ominus(U_526,c_Groups_Oplus__class_Oplus(U_526,U_527,U_528),U_528) = U_527
| ~ class_Groups_Ogroup__add(U_526) ),
inference(definitional_conversion,[status(esa)],[f_211_2]) ).
cnf(f_211_4,plain,
( c_Groups_Ominus__class_Ominus(U_526,c_Groups_Oplus__class_Oplus(U_526,U_527,U_528),U_528) = U_527
| ~ class_Groups_Ogroup__add(U_526) ),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_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_212_2,plain,
! [U_531,U_530,U_529] :
( c_Groups_Oabs__class_Oabs(U_529,c_Groups_Ominus__class_Ominus(U_529,U_530,U_531)) = c_Groups_Oabs__class_Oabs(U_529,c_Groups_Ominus__class_Ominus(U_529,U_531,U_530))
| ~ class_Groups_Oordered__ab__group__add__abs(U_529) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_529,U_531,U_530] :
( c_Groups_Oabs__class_Oabs(U_529,c_Groups_Ominus__class_Ominus(U_529,U_530,U_531)) = c_Groups_Oabs__class_Oabs(U_529,c_Groups_Ominus__class_Ominus(U_529,U_531,U_530))
| ~ class_Groups_Oordered__ab__group__add__abs(U_529) ),
inference(definitional_conversion,[status(esa)],[f_212_2]) ).
cnf(f_212_4,plain,
( c_Groups_Oabs__class_Oabs(U_529,c_Groups_Ominus__class_Ominus(U_529,U_530,U_531)) = c_Groups_Oabs__class_Oabs(U_529,c_Groups_Ominus__class_Ominus(U_529,U_531,U_530))
| ~ class_Groups_Oordered__ab__group__add__abs(U_529) ),
inference(clausify,[status(thm)],[f_212_3]) ).
fof(f_213_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_213_2,plain,
! [U_533,U_532] :
( c_Groups_Oplus__class_Oplus(U_532,c_Groups_Ozero__class_Ozero(U_532),U_533) = U_533
| ~ class_Groups_Omonoid__add(U_532) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_533,U_532] :
( c_Groups_Oplus__class_Oplus(U_532,c_Groups_Ozero__class_Ozero(U_532),U_533) = U_533
| ~ class_Groups_Omonoid__add(U_532) ),
inference(definitional_conversion,[status(esa)],[f_213_2]) ).
cnf(f_213_4,plain,
( c_Groups_Oplus__class_Oplus(U_532,c_Groups_Ozero__class_Ozero(U_532),U_533) = U_533
| ~ class_Groups_Omonoid__add(U_532) ),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_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_214_2,plain,
! [U_535,U_534] :
( c_Groups_Oplus__class_Oplus(U_534,c_Groups_Ozero__class_Ozero(U_534),U_535) = U_535
| ~ class_Groups_Ocomm__monoid__add(U_534) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
! [U_534,U_535] :
( c_Groups_Oplus__class_Oplus(U_534,c_Groups_Ozero__class_Ozero(U_534),U_535) = U_535
| ~ class_Groups_Ocomm__monoid__add(U_534) ),
inference(definitional_conversion,[status(esa)],[f_214_2]) ).
cnf(f_214_4,plain,
( c_Groups_Oplus__class_Oplus(U_534,c_Groups_Ozero__class_Ozero(U_534),U_535) = U_535
| ~ class_Groups_Ocomm__monoid__add(U_534) ),
inference(clausify,[status(thm)],[f_214_3]) ).
fof(f_215_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_215_2,plain,
! [U_537,U_536] :
( ( ( c_Groups_Ozero__class_Ozero(U_536) = c_Groups_Oplus__class_Oplus(U_536,U_537,U_537)
| U_537 != c_Groups_Ozero__class_Ozero(U_536) )
& ( U_537 = c_Groups_Ozero__class_Ozero(U_536)
| c_Groups_Ozero__class_Ozero(U_536) != c_Groups_Oplus__class_Oplus(U_536,U_537,U_537) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_536) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
( ! [U_536,U_537] :
( c_Groups_Ozero__class_Ozero(U_536) = c_Groups_Oplus__class_Oplus(U_536,U_537,U_537)
| U_537 != c_Groups_Ozero__class_Ozero(U_536)
| ~ sP23(U_536,U_537) )
& ! [U_536,U_537] :
( U_537 = c_Groups_Ozero__class_Ozero(U_536)
| c_Groups_Ozero__class_Ozero(U_536) != c_Groups_Oplus__class_Oplus(U_536,U_537,U_537)
| ~ sP23(U_536,U_537) )
& ! [U_536,U_537] :
( sP23(U_536,U_537)
| ~ class_Groups_Olinordered__ab__group__add(U_536) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23])],[f_215_2]) ).
cnf(f_215_4,plain,
( sP23(U_536,U_537)
| ~ class_Groups_Olinordered__ab__group__add(U_536) ),
inference(clausify,[status(thm)],[f_215_3]) ).
cnf(f_215_5,plain,
( U_537 = c_Groups_Ozero__class_Ozero(U_536)
| c_Groups_Ozero__class_Ozero(U_536) != c_Groups_Oplus__class_Oplus(U_536,U_537,U_537)
| ~ sP23(U_536,U_537) ),
inference(clausify,[status(thm)],[f_215_3]) ).
cnf(f_215_6,plain,
( c_Groups_Ozero__class_Ozero(U_536) = c_Groups_Oplus__class_Oplus(U_536,U_537,U_537)
| U_537 != c_Groups_Ozero__class_Ozero(U_536)
| ~ sP23(U_536,U_537) ),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_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_216_2,plain,
! [U_539,U_538] :
( c_Groups_Oplus__class_Oplus(U_538,U_539,c_Groups_Ozero__class_Ozero(U_538)) = U_539
| ~ class_Groups_Omonoid__add(U_538) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_539,U_538] :
( c_Groups_Oplus__class_Oplus(U_538,U_539,c_Groups_Ozero__class_Ozero(U_538)) = U_539
| ~ class_Groups_Omonoid__add(U_538) ),
inference(definitional_conversion,[status(esa)],[f_216_2]) ).
cnf(f_216_4,plain,
( c_Groups_Oplus__class_Oplus(U_538,U_539,c_Groups_Ozero__class_Ozero(U_538)) = U_539
| ~ class_Groups_Omonoid__add(U_538) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_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_217_2,plain,
! [U_541,U_540] :
( c_Groups_Oplus__class_Oplus(U_540,U_541,c_Groups_Ozero__class_Ozero(U_540)) = U_541
| ~ class_Groups_Ocomm__monoid__add(U_540) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_540,U_541] :
( c_Groups_Oplus__class_Oplus(U_540,U_541,c_Groups_Ozero__class_Ozero(U_540)) = U_541
| ~ class_Groups_Ocomm__monoid__add(U_540) ),
inference(definitional_conversion,[status(esa)],[f_217_2]) ).
cnf(f_217_4,plain,
( c_Groups_Oplus__class_Oplus(U_540,U_541,c_Groups_Ozero__class_Ozero(U_540)) = U_541
| ~ class_Groups_Ocomm__monoid__add(U_540) ),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_1,plain,
! [V_n,V_m] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(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) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__if]) ).
fof(f_218_2,plain,
! [U_543,U_542] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_542),U_543) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_543,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_542,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_543))
| U_542 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_542),U_543) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_542 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
( ! [U_547,U_545] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_545),U_547) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_545,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_547))
| U_545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_546,U_544] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_544),U_546) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_544 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_218_2]) ).
fof(f_218_4,plain,
( ! [U_547,U_545] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_545),U_547) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_545,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_547))
| U_545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_544,U_546] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_544),U_546) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_544 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_218_3]) ).
cnf(f_218_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_544),U_546) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_544 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_218_4]) ).
cnf(f_218_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_545),U_547) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_545,c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_547))
| U_545 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_218_4]) ).
fof(f_219_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_219_2,plain,
! [U_549,U_548] :
( ( ( c_Groups_Oabs__class_Oabs(U_548,U_549) = c_Groups_Ozero__class_Ozero(U_548)
| U_549 != c_Groups_Ozero__class_Ozero(U_548) )
& ( U_549 = c_Groups_Ozero__class_Ozero(U_548)
| c_Groups_Oabs__class_Oabs(U_548,U_549) != c_Groups_Ozero__class_Ozero(U_548) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_548) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
( ! [U_548,U_549] :
( c_Groups_Oabs__class_Oabs(U_548,U_549) = c_Groups_Ozero__class_Ozero(U_548)
| U_549 != c_Groups_Ozero__class_Ozero(U_548)
| ~ sP24(U_548,U_549) )
& ! [U_548,U_549] :
( U_549 = c_Groups_Ozero__class_Ozero(U_548)
| c_Groups_Oabs__class_Oabs(U_548,U_549) != c_Groups_Ozero__class_Ozero(U_548)
| ~ sP24(U_548,U_549) )
& ! [U_548,U_549] :
( sP24(U_548,U_549)
| ~ class_Groups_Oordered__ab__group__add__abs(U_548) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP24])],[f_219_2]) ).
cnf(f_219_4,plain,
( sP24(U_548,U_549)
| ~ class_Groups_Oordered__ab__group__add__abs(U_548) ),
inference(clausify,[status(thm)],[f_219_3]) ).
cnf(f_219_5,plain,
( U_549 = c_Groups_Ozero__class_Ozero(U_548)
| c_Groups_Oabs__class_Oabs(U_548,U_549) != c_Groups_Ozero__class_Ozero(U_548)
| ~ sP24(U_548,U_549) ),
inference(clausify,[status(thm)],[f_219_3]) ).
cnf(f_219_6,plain,
( c_Groups_Oabs__class_Oabs(U_548,U_549) = c_Groups_Ozero__class_Ozero(U_548)
| U_549 != c_Groups_Ozero__class_Ozero(U_548)
| ~ sP24(U_548,U_549) ),
inference(clausify,[status(thm)],[f_219_3]) ).
fof(f_220_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_220_2,plain,
! [U_550] :
( c_Groups_Oabs__class_Oabs(U_550,c_Groups_Ozero__class_Ozero(U_550)) = c_Groups_Ozero__class_Ozero(U_550)
| ~ class_Groups_Oordered__ab__group__add__abs(U_550) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_550] :
( c_Groups_Oabs__class_Oabs(U_550,c_Groups_Ozero__class_Ozero(U_550)) = c_Groups_Ozero__class_Ozero(U_550)
| ~ class_Groups_Oordered__ab__group__add__abs(U_550) ),
inference(definitional_conversion,[status(esa)],[f_220_2]) ).
cnf(f_220_4,plain,
( c_Groups_Oabs__class_Oabs(U_550,c_Groups_Ozero__class_Ozero(U_550)) = c_Groups_Ozero__class_Ozero(U_550)
| ~ class_Groups_Oordered__ab__group__add__abs(U_550) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_y)),c_Groups_Oplus__class_Oplus(T_a,V_x,V_y))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__two__diff]) ).
fof(f_221_2,plain,
! [U_553,U_552,U_551] :
( c_Groups_Ominus__class_Ominus(U_551,hAPP(hAPP(c_Power_Opower__class_Opower(U_551),U_552),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_551),U_553),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_551),c_Groups_Ominus__class_Ominus(U_551,U_552,U_553)),c_Groups_Oplus__class_Oplus(U_551,U_552,U_553))
| ~ class_Rings_Ocomm__ring__1(U_551) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_551,U_552,U_553] :
( c_Groups_Ominus__class_Ominus(U_551,hAPP(hAPP(c_Power_Opower__class_Opower(U_551),U_552),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_551),U_553),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_551),c_Groups_Ominus__class_Ominus(U_551,U_552,U_553)),c_Groups_Oplus__class_Oplus(U_551,U_552,U_553))
| ~ class_Rings_Ocomm__ring__1(U_551) ),
inference(definitional_conversion,[status(esa)],[f_221_2]) ).
cnf(f_221_4,plain,
( c_Groups_Ominus__class_Ominus(U_551,hAPP(hAPP(c_Power_Opower__class_Opower(U_551),U_552),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_551),U_553),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_551),c_Groups_Ominus__class_Ominus(U_551,U_552,U_553)),c_Groups_Oplus__class_Oplus(U_551,U_552,U_553))
| ~ class_Rings_Ocomm__ring__1(U_551) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_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_222_2,plain,
! [U_555,U_554] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_554),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_554,U_555)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_555))),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
! [U_554,U_555] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_554),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_554,U_555)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_555))),
inference(definitional_conversion,[status(esa)],[f_222_2]) ).
cnf(f_222_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_554),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_554,U_555)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_555))),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_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)
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) != hAPP(hAPP(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_223_2,plain,
! [U_559,U_558,U_557,U_556] :
( U_557 = U_559
| ~ c_Orderings_Oord__class_Oless__eq(U_556,c_Groups_Ozero__class_Ozero(U_556),U_559)
| ~ c_Orderings_Oord__class_Oless__eq(U_556,c_Groups_Ozero__class_Ozero(U_556),U_557)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_556),U_557),c_Nat_OSuc(U_558)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_556),U_559),c_Nat_OSuc(U_558))
| ~ class_Rings_Olinordered__semidom(U_556) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
! [U_556,U_557,U_558,U_559] :
( U_557 = U_559
| ~ c_Orderings_Oord__class_Oless__eq(U_556,c_Groups_Ozero__class_Ozero(U_556),U_559)
| ~ c_Orderings_Oord__class_Oless__eq(U_556,c_Groups_Ozero__class_Ozero(U_556),U_557)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_556),U_557),c_Nat_OSuc(U_558)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_556),U_559),c_Nat_OSuc(U_558))
| ~ class_Rings_Olinordered__semidom(U_556) ),
inference(definitional_conversion,[status(esa)],[f_223_2]) ).
cnf(f_223_4,plain,
( U_557 = U_559
| ~ c_Orderings_Oord__class_Oless__eq(U_556,c_Groups_Ozero__class_Ozero(U_556),U_559)
| ~ c_Orderings_Oord__class_Oless__eq(U_556,c_Groups_Ozero__class_Ozero(U_556),U_557)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_556),U_557),c_Nat_OSuc(U_558)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_556),U_559),c_Nat_OSuc(U_558))
| ~ class_Rings_Olinordered__semidom(U_556) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)),hAPP(hAPP(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_224_2,plain,
! [U_563,U_562,U_561,U_560] :
( c_Orderings_Oord__class_Oless__eq(U_560,U_561,U_563)
| ~ c_Orderings_Oord__class_Oless__eq(U_560,c_Groups_Ozero__class_Ozero(U_560),U_563)
| ~ c_Orderings_Oord__class_Oless__eq(U_560,hAPP(hAPP(c_Power_Opower__class_Opower(U_560),U_561),c_Nat_OSuc(U_562)),hAPP(hAPP(c_Power_Opower__class_Opower(U_560),U_563),c_Nat_OSuc(U_562)))
| ~ class_Rings_Olinordered__semidom(U_560) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_560,U_561,U_562,U_563] :
( c_Orderings_Oord__class_Oless__eq(U_560,U_561,U_563)
| ~ c_Orderings_Oord__class_Oless__eq(U_560,c_Groups_Ozero__class_Ozero(U_560),U_563)
| ~ c_Orderings_Oord__class_Oless__eq(U_560,hAPP(hAPP(c_Power_Opower__class_Opower(U_560),U_561),c_Nat_OSuc(U_562)),hAPP(hAPP(c_Power_Opower__class_Opower(U_560),U_563),c_Nat_OSuc(U_562)))
| ~ class_Rings_Olinordered__semidom(U_560) ),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_560,U_561,U_563)
| ~ c_Orderings_Oord__class_Oless__eq(U_560,c_Groups_Ozero__class_Ozero(U_560),U_563)
| ~ c_Orderings_Oord__class_Oless__eq(U_560,hAPP(hAPP(c_Power_Opower__class_Opower(U_560),U_561),c_Nat_OSuc(U_562)),hAPP(hAPP(c_Power_Opower__class_Opower(U_560),U_563),c_Nat_OSuc(U_562)))
| ~ class_Rings_Olinordered__semidom(U_560) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_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_225_2,plain,
! [U_565,U_564] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_564),c_NthRoot_Osqrt(U_565))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_564,U_565) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
! [U_564,U_565] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_564),c_NthRoot_Osqrt(U_565))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_564,U_565) ),
inference(definitional_conversion,[status(esa)],[f_225_2]) ).
cnf(f_225_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_564),c_NthRoot_Osqrt(U_565))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_564,U_565) ),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_1,plain,
! [V_ya_2,V_xa_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__iff]) ).
fof(f_226_2,plain,
! [U_567,U_566] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_566),c_NthRoot_Osqrt(U_567))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_566,U_567) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_566,U_567)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_566),c_NthRoot_Osqrt(U_567)) ) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
( ! [U_571,U_569] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_569),c_NthRoot_Osqrt(U_571))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_569,U_571) )
& ! [U_570,U_568] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_568,U_570)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_568),c_NthRoot_Osqrt(U_570)) ) ),
inference(miniscope,[status(thm)],[f_226_2]) ).
fof(f_226_4,plain,
( ! [U_571,U_569] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_569),c_NthRoot_Osqrt(U_571))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_569,U_571) )
& ! [U_570,U_568] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_568,U_570)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_568),c_NthRoot_Osqrt(U_570)) ) ),
inference(definitional_conversion,[status(esa)],[f_226_3]) ).
cnf(f_226_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_568,U_570)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_568),c_NthRoot_Osqrt(U_570)) ),
inference(clausify,[status(thm)],[f_226_4]) ).
cnf(f_226_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_569),c_NthRoot_Osqrt(U_571))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_569,U_571) ),
inference(clausify,[status(thm)],[f_226_4]) ).
fof(f_227_1,plain,
! [V_n,T_a] :
( ( ( hAPP(hAPP(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) )
& ( hAPP(hAPP(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_227_2,plain,
! [U_573,U_572] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_572),c_Groups_Ozero__class_Ozero(U_572)),U_573) = c_Groups_Ozero__class_Ozero(U_572)
| U_573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_572),c_Groups_Ozero__class_Ozero(U_572)),U_573) = c_Groups_Oone__class_Oone(U_572)
| U_573 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_572)
| ~ class_Power_Opower(U_572) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
( ! [U_573,U_572] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_572),c_Groups_Ozero__class_Ozero(U_572)),U_573) = c_Groups_Ozero__class_Ozero(U_572)
| U_573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP25(U_573,U_572) )
& ! [U_573,U_572] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_572),c_Groups_Ozero__class_Ozero(U_572)),U_573) = c_Groups_Oone__class_Oone(U_572)
| U_573 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP25(U_573,U_572) )
& ! [U_573,U_572] :
( sP25(U_573,U_572)
| ~ class_Rings_Osemiring__0(U_572)
| ~ class_Power_Opower(U_572) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_227_2]) ).
cnf(f_227_4,plain,
( sP25(U_573,U_572)
| ~ class_Rings_Osemiring__0(U_572)
| ~ class_Power_Opower(U_572) ),
inference(clausify,[status(thm)],[f_227_3]) ).
cnf(f_227_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_572),c_Groups_Ozero__class_Ozero(U_572)),U_573) = c_Groups_Oone__class_Oone(U_572)
| U_573 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP25(U_573,U_572) ),
inference(clausify,[status(thm)],[f_227_3]) ).
cnf(f_227_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_572),c_Groups_Ozero__class_Ozero(U_572)),U_573) = c_Groups_Ozero__class_Ozero(U_572)
| U_573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP25(U_573,U_572) ),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_1,plain,
! [V_p,V_m] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_p),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_power__eq__if]) ).
fof(f_228_2,plain,
! [U_575,U_574] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_575),U_574) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_575),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_575),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_574,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_574 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_575),U_574) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_574 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
( ! [U_579,U_577] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_579),U_577) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_579),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_579),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_577,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_578,U_576] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_578),U_576) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_576 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_228_2]) ).
fof(f_228_4,plain,
( ! [U_579,U_577] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_579),U_577) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_579),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_579),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_577,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_576,U_578] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_578),U_576) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_576 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_228_3]) ).
cnf(f_228_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_578),U_576) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_576 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_228_4]) ).
cnf(f_228_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_579),U_577) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_579),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_579),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_577,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_577 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_228_4]) ).
fof(f_229_1,plain,
! [V_y,V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y)) = hAPP(hAPP(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_229_2,plain,
! [U_581,U_580] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_580),U_581)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_580)),c_NthRoot_Osqrt(U_581)),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_580,U_581] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_580),U_581)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_580)),c_NthRoot_Osqrt(U_581)),
inference(definitional_conversion,[status(esa)],[f_229_2]) ).
cnf(f_229_4,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_580),U_581)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_580)),c_NthRoot_Osqrt(U_581)),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_1,plain,
! [V_k,V_x] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_k)) = hAPP(hAPP(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_230_2,plain,
! [U_583,U_582] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_582),U_583)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_582)),U_583),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_582,U_583] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_582),U_583)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_582)),U_583),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_582),U_583)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_582)),U_583),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_1,plain,
! [V_xa_2] :
( ( c_NthRoot_Osqrt(V_xa_2) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| V_xa_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( V_xa_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(V_xa_2) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__eq__1__iff]) ).
fof(f_231_2,plain,
! [U_584] :
( ( c_NthRoot_Osqrt(U_584) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_584 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( U_584 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_584) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
( ! [U_586] :
( c_NthRoot_Osqrt(U_586) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_586 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ! [U_585] :
( U_585 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_585) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_231_2]) ).
fof(f_231_4,plain,
( ! [U_586] :
( c_NthRoot_Osqrt(U_586) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_586 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ! [U_585] :
( U_585 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_585) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa)],[f_231_3]) ).
cnf(f_231_5,plain,
( U_585 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(U_585) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_231_4]) ).
cnf(f_231_6,plain,
( c_NthRoot_Osqrt(U_586) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_586 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_231_4]) ).
fof(f_232_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]) ).
fof(f_232_2,plain,
c_NthRoot_Osqrt(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_232_1]) ).
cnf(f_232_3,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_232_2]) ).
fof(f_233_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_233_2,plain,
! [U_587] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_587,c_Int_OPls) = U_587,
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
! [U_587] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_587,c_Int_OPls) = U_587,
inference(definitional_conversion,[status(esa)],[f_233_2]) ).
cnf(f_233_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_587,c_Int_OPls) = U_587,
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_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_234_2,plain,
! [U_589,U_588] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(U_588),c_Int_OBit0(U_589)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_588,U_589)),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_588,U_589] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(U_588),c_Int_OBit0(U_589)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_588,U_589)),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit0(U_588),c_Int_OBit0(U_589)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_588,U_589)),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_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_235_2,plain,
! [U_590] : c_Int_OBit1(U_590) = 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_590),U_590),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_590] : c_Int_OBit1(U_590) = 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_590),U_590),
inference(definitional_conversion,[status(esa)],[f_235_2]) ).
cnf(f_235_4,plain,
c_Int_OBit1(U_590) = 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_590),U_590),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_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_236_2,plain,
! [U_591] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_591,c_Int_OPls) = U_591,
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_591] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_591,c_Int_OPls) = U_591,
inference(definitional_conversion,[status(esa)],[f_236_2]) ).
cnf(f_236_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_591,c_Int_OPls) = U_591,
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_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_237_2,plain,
! [U_592] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_592) = U_592,
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_592] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_592) = U_592,
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OPls,U_592) = U_592,
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_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_238_2,plain,
! [U_594,U_593] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_593),c_Int_OBit0(U_594)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_593,U_594)),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_593,U_594] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_593),c_Int_OBit0(U_594)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_593,U_594)),
inference(definitional_conversion,[status(esa)],[f_238_2]) ).
cnf(f_238_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_593),c_Int_OBit0(U_594)) = c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_593,U_594)),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_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_239_2,plain,
! [U_595] : c_Int_OBit0(U_595) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_595,U_595),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
! [U_595] : c_Int_OBit0(U_595) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_595,U_595),
inference(definitional_conversion,[status(esa)],[f_239_2]) ).
cnf(f_239_4,plain,
c_Int_OBit0(U_595) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_595,U_595),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_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_240_2,plain,
! [U_598,U_597,U_596] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_598,U_596),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_598,U_597))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_596,U_597) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_597,U_596,U_598] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_598,U_596),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_598,U_597))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_596,U_597) ),
inference(definitional_conversion,[status(esa)],[f_240_2]) ).
cnf(f_240_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_598,U_596),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_598,U_597))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_596,U_597) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_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_241_2,plain,
! [U_600,U_599] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_599),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_600)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_599,U_600)),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
! [U_599,U_600] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_599),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_600)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_599,U_600)),
inference(definitional_conversion,[status(esa)],[f_241_2]) ).
cnf(f_241_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_599),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_600)) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_599,U_600)),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_242_2,plain,
! [U_602,U_601] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_601),U_602),c_Groups_Ozero__class_Ozero(U_601)) = c_Groups_Ozero__class_Ozero(U_601)
| ~ class_Rings_Ocomm__semiring__1(U_601) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_601,U_602] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_601),U_602),c_Groups_Ozero__class_Ozero(U_601)) = c_Groups_Ozero__class_Ozero(U_601)
| ~ class_Rings_Ocomm__semiring__1(U_601) ),
inference(definitional_conversion,[status(esa)],[f_242_2]) ).
cnf(f_242_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_601),U_602),c_Groups_Ozero__class_Ozero(U_601)) = c_Groups_Ozero__class_Ozero(U_601)
| ~ class_Rings_Ocomm__semiring__1(U_601) ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_243_2,plain,
! [U_604,U_603] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_603),c_Groups_Ozero__class_Ozero(U_603)),U_604) = c_Groups_Ozero__class_Ozero(U_603)
| ~ class_Rings_Ocomm__semiring__1(U_603) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_603,U_604] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_603),c_Groups_Ozero__class_Ozero(U_603)),U_604) = c_Groups_Ozero__class_Ozero(U_603)
| ~ class_Rings_Ocomm__semiring__1(U_603) ),
inference(definitional_conversion,[status(esa)],[f_243_2]) ).
cnf(f_243_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_603),c_Groups_Ozero__class_Ozero(U_603)),U_604) = c_Groups_Ozero__class_Ozero(U_603)
| ~ class_Rings_Ocomm__semiring__1(U_603) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_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_244_2,plain,
! [U_606,U_605] :
( ( ( c_Groups_Oplus__class_Oplus(U_605,U_606,U_606) = c_Groups_Ozero__class_Ozero(U_605)
| U_606 != c_Groups_Ozero__class_Ozero(U_605) )
& ( U_606 = c_Groups_Ozero__class_Ozero(U_605)
| c_Groups_Oplus__class_Oplus(U_605,U_606,U_606) != c_Groups_Ozero__class_Ozero(U_605) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_605) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
( ! [U_605,U_606] :
( c_Groups_Oplus__class_Oplus(U_605,U_606,U_606) = c_Groups_Ozero__class_Ozero(U_605)
| U_606 != c_Groups_Ozero__class_Ozero(U_605)
| ~ sP26(U_605,U_606) )
& ! [U_605,U_606] :
( U_606 = c_Groups_Ozero__class_Ozero(U_605)
| c_Groups_Oplus__class_Oplus(U_605,U_606,U_606) != c_Groups_Ozero__class_Ozero(U_605)
| ~ sP26(U_605,U_606) )
& ! [U_605,U_606] :
( sP26(U_605,U_606)
| ~ class_Groups_Olinordered__ab__group__add(U_605) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_244_2]) ).
cnf(f_244_4,plain,
( sP26(U_605,U_606)
| ~ class_Groups_Olinordered__ab__group__add(U_605) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_5,plain,
( U_606 = c_Groups_Ozero__class_Ozero(U_605)
| c_Groups_Oplus__class_Oplus(U_605,U_606,U_606) != c_Groups_Ozero__class_Ozero(U_605)
| ~ sP26(U_605,U_606) ),
inference(clausify,[status(thm)],[f_244_3]) ).
cnf(f_244_6,plain,
( c_Groups_Oplus__class_Oplus(U_605,U_606,U_606) = c_Groups_Ozero__class_Ozero(U_605)
| U_606 != c_Groups_Ozero__class_Ozero(U_605)
| ~ sP26(U_605,U_606) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_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_245_2,plain,
! [U_609,U_608,U_607] :
( ( ( U_608 = c_Groups_Oplus__class_Oplus(U_607,U_608,U_609)
| U_609 != c_Groups_Ozero__class_Ozero(U_607) )
& ( U_609 = c_Groups_Ozero__class_Ozero(U_607)
| U_608 != c_Groups_Oplus__class_Oplus(U_607,U_608,U_609) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_607) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
( ! [U_608,U_609,U_607] :
( U_608 = c_Groups_Oplus__class_Oplus(U_607,U_608,U_609)
| U_609 != c_Groups_Ozero__class_Ozero(U_607)
| ~ sP27(U_608,U_609,U_607) )
& ! [U_608,U_609,U_607] :
( U_609 = c_Groups_Ozero__class_Ozero(U_607)
| U_608 != c_Groups_Oplus__class_Oplus(U_607,U_608,U_609)
| ~ sP27(U_608,U_609,U_607) )
& ! [U_608,U_609,U_607] :
( sP27(U_608,U_609,U_607)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_607) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_245_2]) ).
cnf(f_245_4,plain,
( sP27(U_608,U_609,U_607)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_607) ),
inference(clausify,[status(thm)],[f_245_3]) ).
cnf(f_245_5,plain,
( U_609 = c_Groups_Ozero__class_Ozero(U_607)
| U_608 != c_Groups_Oplus__class_Oplus(U_607,U_608,U_609)
| ~ sP27(U_608,U_609,U_607) ),
inference(clausify,[status(thm)],[f_245_3]) ).
cnf(f_245_6,plain,
( U_608 = c_Groups_Oplus__class_Oplus(U_607,U_608,U_609)
| U_609 != c_Groups_Ozero__class_Ozero(U_607)
| ~ sP27(U_608,U_609,U_607) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_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_246_2,plain,
! [U_611,U_610] :
( c_Groups_Oplus__class_Oplus(U_610,U_611,c_Groups_Ozero__class_Ozero(U_610)) = U_611
| ~ class_Rings_Ocomm__semiring__1(U_610) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_611,U_610] :
( c_Groups_Oplus__class_Oplus(U_610,U_611,c_Groups_Ozero__class_Ozero(U_610)) = U_611
| ~ class_Rings_Ocomm__semiring__1(U_610) ),
inference(definitional_conversion,[status(esa)],[f_246_2]) ).
cnf(f_246_4,plain,
( c_Groups_Oplus__class_Oplus(U_610,U_611,c_Groups_Ozero__class_Ozero(U_610)) = U_611
| ~ class_Rings_Ocomm__semiring__1(U_610) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_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_247_2,plain,
! [U_613,U_612] :
( c_Groups_Oplus__class_Oplus(U_612,c_Groups_Ozero__class_Ozero(U_612),U_613) = U_613
| ~ class_Rings_Ocomm__semiring__1(U_612) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_613,U_612] :
( c_Groups_Oplus__class_Oplus(U_612,c_Groups_Ozero__class_Ozero(U_612),U_613) = U_613
| ~ class_Rings_Ocomm__semiring__1(U_612) ),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
( c_Groups_Oplus__class_Oplus(U_612,c_Groups_Ozero__class_Ozero(U_612),U_613) = U_613
| ~ class_Rings_Ocomm__semiring__1(U_612) ),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(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_248_2,plain,
! [U_616,U_615,U_614] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_614),U_615),U_616) != c_Groups_Ozero__class_Ozero(U_614)
| U_615 = c_Groups_Ozero__class_Ozero(U_614)
| ~ class_Rings_Oring__1__no__zero__divisors(U_614) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_614,U_615,U_616] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_614),U_615),U_616) != c_Groups_Ozero__class_Ozero(U_614)
| U_615 = c_Groups_Ozero__class_Ozero(U_614)
| ~ class_Rings_Oring__1__no__zero__divisors(U_614) ),
inference(definitional_conversion,[status(esa)],[f_248_2]) ).
cnf(f_248_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_614),U_615),U_616) != c_Groups_Ozero__class_Ozero(U_614)
| U_615 = c_Groups_Ozero__class_Ozero(U_614)
| ~ class_Rings_Oring__1__no__zero__divisors(U_614) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_1,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).
fof(f_249_2,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_249_1]) ).
cnf(f_249_3,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_249_2]) ).
fof(f_250_1,plain,
! [V_n,V_x] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(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_250_2,plain,
! [U_618,U_617] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_617)),U_618)),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_617,U_618] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_617)),U_618)),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_617)),U_618)),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_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_251_2,plain,
! [U_621,U_620,U_619] :
( c_Orderings_Oord__class_Oless__eq(U_619,c_Groups_Ominus__class_Ominus(U_619,c_Groups_Oabs__class_Oabs(U_619,U_620),c_Groups_Oabs__class_Oabs(U_619,U_621)),c_Groups_Oabs__class_Oabs(U_619,c_Groups_Ominus__class_Ominus(U_619,U_621,U_620)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_619) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
! [U_619,U_620,U_621] :
( c_Orderings_Oord__class_Oless__eq(U_619,c_Groups_Ominus__class_Ominus(U_619,c_Groups_Oabs__class_Oabs(U_619,U_620),c_Groups_Oabs__class_Oabs(U_619,U_621)),c_Groups_Oabs__class_Oabs(U_619,c_Groups_Ominus__class_Ominus(U_619,U_621,U_620)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_619) ),
inference(definitional_conversion,[status(esa)],[f_251_2]) ).
cnf(f_251_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_619,c_Groups_Ominus__class_Ominus(U_619,c_Groups_Oabs__class_Oabs(U_619,U_620),c_Groups_Oabs__class_Oabs(U_619,U_621)),c_Groups_Oabs__class_Oabs(U_619,c_Groups_Ominus__class_Ominus(U_619,U_621,U_620)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_619) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_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_252_2,plain,
! [U_624,U_623,U_622] :
( c_Orderings_Oord__class_Oless__eq(U_622,c_Groups_Ominus__class_Ominus(U_622,c_Groups_Oabs__class_Oabs(U_622,U_623),c_Groups_Oabs__class_Oabs(U_622,U_624)),c_Groups_Oabs__class_Oabs(U_622,c_Groups_Ominus__class_Ominus(U_622,U_623,U_624)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_622) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
! [U_622,U_623,U_624] :
( c_Orderings_Oord__class_Oless__eq(U_622,c_Groups_Ominus__class_Ominus(U_622,c_Groups_Oabs__class_Oabs(U_622,U_623),c_Groups_Oabs__class_Oabs(U_622,U_624)),c_Groups_Oabs__class_Oabs(U_622,c_Groups_Ominus__class_Ominus(U_622,U_623,U_624)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_622) ),
inference(definitional_conversion,[status(esa)],[f_252_2]) ).
cnf(f_252_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_622,c_Groups_Ominus__class_Ominus(U_622,c_Groups_Oabs__class_Oabs(U_622,U_623),c_Groups_Oabs__class_Oabs(U_622,U_624)),c_Groups_Oabs__class_Oabs(U_622,c_Groups_Ominus__class_Ominus(U_622,U_623,U_624)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_622) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_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_253_2,plain,
! [U_627,U_626,U_625] :
( c_Orderings_Oord__class_Oless__eq(U_625,c_Groups_Oabs__class_Oabs(U_625,c_Groups_Ominus__class_Ominus(U_625,c_Groups_Oabs__class_Oabs(U_625,U_626),c_Groups_Oabs__class_Oabs(U_625,U_627))),c_Groups_Oabs__class_Oabs(U_625,c_Groups_Ominus__class_Ominus(U_625,U_626,U_627)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_625) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
! [U_625,U_626,U_627] :
( c_Orderings_Oord__class_Oless__eq(U_625,c_Groups_Oabs__class_Oabs(U_625,c_Groups_Ominus__class_Ominus(U_625,c_Groups_Oabs__class_Oabs(U_625,U_626),c_Groups_Oabs__class_Oabs(U_625,U_627))),c_Groups_Oabs__class_Oabs(U_625,c_Groups_Ominus__class_Ominus(U_625,U_626,U_627)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_625) ),
inference(definitional_conversion,[status(esa)],[f_253_2]) ).
cnf(f_253_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_625,c_Groups_Oabs__class_Oabs(U_625,c_Groups_Ominus__class_Ominus(U_625,c_Groups_Oabs__class_Oabs(U_625,U_626),c_Groups_Oabs__class_Oabs(U_625,U_627))),c_Groups_Oabs__class_Oabs(U_625,c_Groups_Ominus__class_Ominus(U_625,U_626,U_627)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_625) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_1,plain,
! [V_b_2,V_a_2,V_c_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) = hAPP(hAPP(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
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c_2),V_a_2) != hAPP(hAPP(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_254_2,plain,
! [U_630,U_629,U_628] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_629) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_630)
| U_629 != U_630 )
& ( U_629 = U_630
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_629) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_630) ) )
| U_628 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
( ! [U_628,U_629,U_630] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_629) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_630)
| U_629 != U_630
| ~ sP28(U_628,U_629,U_630) )
& ! [U_628,U_629,U_630] :
( U_629 = U_630
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_629) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_630)
| ~ sP28(U_628,U_629,U_630) )
& ! [U_628,U_629,U_630] :
( sP28(U_628,U_629,U_630)
| U_628 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_254_2]) ).
cnf(f_254_4,plain,
( sP28(U_628,U_629,U_630)
| U_628 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_254_3]) ).
cnf(f_254_5,plain,
( U_629 = U_630
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_629) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_630)
| ~ sP28(U_628,U_629,U_630) ),
inference(clausify,[status(thm)],[f_254_3]) ).
cnf(f_254_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_629) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_628),U_630)
| U_629 != U_630
| ~ sP28(U_628,U_629,U_630) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_1,plain,
! [V_b_2,V_a_2,V_c_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) = hAPP(hAPP(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
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_c_2) != hAPP(hAPP(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_255_2,plain,
! [U_633,U_632,U_631] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_632),U_631) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_633),U_631)
| U_632 != U_633 )
& ( U_632 = U_633
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_632),U_631) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_633),U_631) ) )
| U_631 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
( ! [U_633,U_632,U_631] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_632),U_631) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_633),U_631)
| U_632 != U_633
| ~ sP29(U_633,U_632,U_631) )
& ! [U_633,U_632,U_631] :
( U_632 = U_633
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_632),U_631) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_633),U_631)
| ~ sP29(U_633,U_632,U_631) )
& ! [U_633,U_632,U_631] :
( sP29(U_633,U_632,U_631)
| U_631 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_255_2]) ).
cnf(f_255_4,plain,
( sP29(U_633,U_632,U_631)
| U_631 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_5,plain,
( U_632 = U_633
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_632),U_631) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_633),U_631)
| ~ sP29(U_633,U_632,U_631) ),
inference(clausify,[status(thm)],[f_255_3]) ).
cnf(f_255_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_632),U_631) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_633),U_631)
| U_632 != U_633
| ~ sP29(U_633,U_632,U_631) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_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]) ).
fof(f_256_2,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_256_1]) ).
cnf(f_256_3,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_256_2]) ).
fof(f_257_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_257_2,plain,
! [U_635,U_634] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),c_Groups_Oplus__class_Oplus(U_634,U_635,U_635))
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635) )
& ( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635)
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),c_Groups_Oplus__class_Oplus(U_634,U_635,U_635)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_634) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
( ! [U_634,U_635] :
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),c_Groups_Oplus__class_Oplus(U_634,U_635,U_635))
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635)
| ~ sP30(U_634,U_635) )
& ! [U_634,U_635] :
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635)
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),c_Groups_Oplus__class_Oplus(U_634,U_635,U_635))
| ~ sP30(U_634,U_635) )
& ! [U_634,U_635] :
( sP30(U_634,U_635)
| ~ class_Groups_Olinordered__ab__group__add(U_634) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_257_2]) ).
cnf(f_257_4,plain,
( sP30(U_634,U_635)
| ~ class_Groups_Olinordered__ab__group__add(U_634) ),
inference(clausify,[status(thm)],[f_257_3]) ).
cnf(f_257_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635)
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),c_Groups_Oplus__class_Oplus(U_634,U_635,U_635))
| ~ sP30(U_634,U_635) ),
inference(clausify,[status(thm)],[f_257_3]) ).
cnf(f_257_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),c_Groups_Oplus__class_Oplus(U_634,U_635,U_635))
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635)
| ~ sP30(U_634,U_635) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_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_258_2,plain,
! [U_637,U_636] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_636,c_Groups_Oplus__class_Oplus(U_636,U_637,U_637),c_Groups_Ozero__class_Ozero(U_636))
| ~ c_Orderings_Oord__class_Oless__eq(U_636,U_637,c_Groups_Ozero__class_Ozero(U_636)) )
& ( c_Orderings_Oord__class_Oless__eq(U_636,U_637,c_Groups_Ozero__class_Ozero(U_636))
| ~ c_Orderings_Oord__class_Oless__eq(U_636,c_Groups_Oplus__class_Oplus(U_636,U_637,U_637),c_Groups_Ozero__class_Ozero(U_636)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_636) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
( ! [U_637,U_636] :
( c_Orderings_Oord__class_Oless__eq(U_636,c_Groups_Oplus__class_Oplus(U_636,U_637,U_637),c_Groups_Ozero__class_Ozero(U_636))
| ~ c_Orderings_Oord__class_Oless__eq(U_636,U_637,c_Groups_Ozero__class_Ozero(U_636))
| ~ sP31(U_637,U_636) )
& ! [U_637,U_636] :
( c_Orderings_Oord__class_Oless__eq(U_636,U_637,c_Groups_Ozero__class_Ozero(U_636))
| ~ c_Orderings_Oord__class_Oless__eq(U_636,c_Groups_Oplus__class_Oplus(U_636,U_637,U_637),c_Groups_Ozero__class_Ozero(U_636))
| ~ sP31(U_637,U_636) )
& ! [U_637,U_636] :
( sP31(U_637,U_636)
| ~ class_Groups_Olinordered__ab__group__add(U_636) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_258_2]) ).
cnf(f_258_4,plain,
( sP31(U_637,U_636)
| ~ class_Groups_Olinordered__ab__group__add(U_636) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_636,U_637,c_Groups_Ozero__class_Ozero(U_636))
| ~ c_Orderings_Oord__class_Oless__eq(U_636,c_Groups_Oplus__class_Oplus(U_636,U_637,U_637),c_Groups_Ozero__class_Ozero(U_636))
| ~ sP31(U_637,U_636) ),
inference(clausify,[status(thm)],[f_258_3]) ).
cnf(f_258_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_636,c_Groups_Oplus__class_Oplus(U_636,U_637,U_637),c_Groups_Ozero__class_Ozero(U_636))
| ~ c_Orderings_Oord__class_Oless__eq(U_636,U_637,c_Groups_Ozero__class_Ozero(U_636))
| ~ sP31(U_637,U_636) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_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_259_2,plain,
! [U_640,U_639,U_638] :
( c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),c_Groups_Oplus__class_Oplus(U_638,U_639,U_640))
| ~ c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),U_640)
| ~ c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),U_639)
| ~ class_Groups_Oordered__comm__monoid__add(U_638) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_639,U_640,U_638] :
( c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),c_Groups_Oplus__class_Oplus(U_638,U_639,U_640))
| ~ c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),U_640)
| ~ c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),U_639)
| ~ class_Groups_Oordered__comm__monoid__add(U_638) ),
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),c_Groups_Oplus__class_Oplus(U_638,U_639,U_640))
| ~ c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),U_640)
| ~ c_Orderings_Oord__class_Oless__eq(U_638,c_Groups_Ozero__class_Ozero(U_638),U_639)
| ~ class_Groups_Oordered__comm__monoid__add(U_638) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,V_xa_2,V_ya_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_xa_2)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).
fof(f_260_2,plain,
! [U_643,U_642,U_641] :
( ( ( c_Groups_Oplus__class_Oplus(U_641,U_642,U_643) = c_Groups_Ozero__class_Ozero(U_641)
| U_643 != c_Groups_Ozero__class_Ozero(U_641)
| U_642 != c_Groups_Ozero__class_Ozero(U_641) )
& ( ( U_643 = c_Groups_Ozero__class_Ozero(U_641)
& U_642 = c_Groups_Ozero__class_Ozero(U_641) )
| c_Groups_Oplus__class_Oplus(U_641,U_642,U_643) != c_Groups_Ozero__class_Ozero(U_641) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_641,c_Groups_Ozero__class_Ozero(U_641),U_643)
| ~ c_Orderings_Oord__class_Oless__eq(U_641,c_Groups_Ozero__class_Ozero(U_641),U_642)
| ~ class_Groups_Oordered__comm__monoid__add(U_641) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
( ! [U_641,U_642,U_643] :
( U_643 = c_Groups_Ozero__class_Ozero(U_641)
| ~ sP32(U_641,U_642,U_643) )
& ! [U_641,U_642,U_643] :
( U_642 = c_Groups_Ozero__class_Ozero(U_641)
| ~ sP32(U_641,U_642,U_643) )
& ! [U_641,U_642,U_643] :
( c_Groups_Oplus__class_Oplus(U_641,U_642,U_643) = c_Groups_Ozero__class_Ozero(U_641)
| U_643 != c_Groups_Ozero__class_Ozero(U_641)
| U_642 != c_Groups_Ozero__class_Ozero(U_641)
| ~ sP33(U_641,U_642,U_643) )
& ! [U_641,U_642,U_643] :
( sP32(U_641,U_642,U_643)
| c_Groups_Oplus__class_Oplus(U_641,U_642,U_643) != c_Groups_Ozero__class_Ozero(U_641)
| ~ sP33(U_641,U_642,U_643) )
& ! [U_641,U_642,U_643] :
( sP33(U_641,U_642,U_643)
| ~ c_Orderings_Oord__class_Oless__eq(U_641,c_Groups_Ozero__class_Ozero(U_641),U_643)
| ~ c_Orderings_Oord__class_Oless__eq(U_641,c_Groups_Ozero__class_Ozero(U_641),U_642)
| ~ class_Groups_Oordered__comm__monoid__add(U_641) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32,sP33])],[f_260_2]) ).
cnf(f_260_4,plain,
( sP33(U_641,U_642,U_643)
| ~ c_Orderings_Oord__class_Oless__eq(U_641,c_Groups_Ozero__class_Ozero(U_641),U_643)
| ~ c_Orderings_Oord__class_Oless__eq(U_641,c_Groups_Ozero__class_Ozero(U_641),U_642)
| ~ class_Groups_Oordered__comm__monoid__add(U_641) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_5,plain,
( sP32(U_641,U_642,U_643)
| c_Groups_Oplus__class_Oplus(U_641,U_642,U_643) != c_Groups_Ozero__class_Ozero(U_641)
| ~ sP33(U_641,U_642,U_643) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_6,plain,
( c_Groups_Oplus__class_Oplus(U_641,U_642,U_643) = c_Groups_Ozero__class_Ozero(U_641)
| U_643 != c_Groups_Ozero__class_Ozero(U_641)
| U_642 != c_Groups_Ozero__class_Ozero(U_641)
| ~ sP33(U_641,U_642,U_643) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_7,plain,
( U_642 = c_Groups_Ozero__class_Ozero(U_641)
| ~ sP32(U_641,U_642,U_643) ),
inference(clausify,[status(thm)],[f_260_3]) ).
cnf(f_260_8,plain,
( U_643 = c_Groups_Ozero__class_Ozero(U_641)
| ~ sP32(U_641,U_642,U_643) ),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_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_261_2,plain,
! [U_647,U_646,U_645,U_644] :
( c_Orderings_Oord__class_Oless__eq(U_644,U_646,c_Groups_Oplus__class_Oplus(U_644,U_645,U_647))
| ~ c_Orderings_Oord__class_Oless__eq(U_644,U_646,U_647)
| ~ c_Orderings_Oord__class_Oless__eq(U_644,c_Groups_Ozero__class_Ozero(U_644),U_645)
| ~ class_Groups_Oordered__comm__monoid__add(U_644) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
! [U_647,U_645,U_646,U_644] :
( c_Orderings_Oord__class_Oless__eq(U_644,U_646,c_Groups_Oplus__class_Oplus(U_644,U_645,U_647))
| ~ c_Orderings_Oord__class_Oless__eq(U_644,U_646,U_647)
| ~ c_Orderings_Oord__class_Oless__eq(U_644,c_Groups_Ozero__class_Ozero(U_644),U_645)
| ~ class_Groups_Oordered__comm__monoid__add(U_644) ),
inference(definitional_conversion,[status(esa)],[f_261_2]) ).
cnf(f_261_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_644,U_646,c_Groups_Oplus__class_Oplus(U_644,U_645,U_647))
| ~ c_Orderings_Oord__class_Oless__eq(U_644,U_646,U_647)
| ~ c_Orderings_Oord__class_Oless__eq(U_644,c_Groups_Ozero__class_Ozero(U_644),U_645)
| ~ class_Groups_Oordered__comm__monoid__add(U_644) ),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_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_262_2,plain,
! [U_651,U_650,U_649,U_648] :
( c_Orderings_Oord__class_Oless__eq(U_648,U_650,c_Groups_Oplus__class_Oplus(U_648,U_651,U_649))
| ~ c_Orderings_Oord__class_Oless__eq(U_648,U_650,U_651)
| ~ c_Orderings_Oord__class_Oless__eq(U_648,c_Groups_Ozero__class_Ozero(U_648),U_649)
| ~ class_Groups_Oordered__comm__monoid__add(U_648) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_651,U_650,U_648,U_649] :
( c_Orderings_Oord__class_Oless__eq(U_648,U_650,c_Groups_Oplus__class_Oplus(U_648,U_651,U_649))
| ~ c_Orderings_Oord__class_Oless__eq(U_648,U_650,U_651)
| ~ c_Orderings_Oord__class_Oless__eq(U_648,c_Groups_Ozero__class_Ozero(U_648),U_649)
| ~ class_Groups_Oordered__comm__monoid__add(U_648) ),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_648,U_650,c_Groups_Oplus__class_Oplus(U_648,U_651,U_649))
| ~ c_Orderings_Oord__class_Oless__eq(U_648,U_650,U_651)
| ~ c_Orderings_Oord__class_Oless__eq(U_648,c_Groups_Ozero__class_Ozero(U_648),U_649)
| ~ class_Groups_Oordered__comm__monoid__add(U_648) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_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_263_2,plain,
! [U_654,U_653,U_652] :
( c_Orderings_Oord__class_Oless__eq(U_652,c_Groups_Oplus__class_Oplus(U_652,U_653,U_654),c_Groups_Ozero__class_Ozero(U_652))
| ~ c_Orderings_Oord__class_Oless__eq(U_652,U_654,c_Groups_Ozero__class_Ozero(U_652))
| ~ c_Orderings_Oord__class_Oless__eq(U_652,U_653,c_Groups_Ozero__class_Ozero(U_652))
| ~ class_Groups_Oordered__comm__monoid__add(U_652) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_653,U_654,U_652] :
( c_Orderings_Oord__class_Oless__eq(U_652,c_Groups_Oplus__class_Oplus(U_652,U_653,U_654),c_Groups_Ozero__class_Ozero(U_652))
| ~ c_Orderings_Oord__class_Oless__eq(U_652,U_654,c_Groups_Ozero__class_Ozero(U_652))
| ~ c_Orderings_Oord__class_Oless__eq(U_652,U_653,c_Groups_Ozero__class_Ozero(U_652))
| ~ class_Groups_Oordered__comm__monoid__add(U_652) ),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_652,c_Groups_Oplus__class_Oplus(U_652,U_653,U_654),c_Groups_Ozero__class_Ozero(U_652))
| ~ c_Orderings_Oord__class_Oless__eq(U_652,U_654,c_Groups_Ozero__class_Ozero(U_652))
| ~ c_Orderings_Oord__class_Oless__eq(U_652,U_653,c_Groups_Ozero__class_Ozero(U_652))
| ~ class_Groups_Oordered__comm__monoid__add(U_652) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_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_264_2,plain,
! [U_656,U_655] :
( c_Groups_Oabs__class_Oabs(U_655,U_656) = U_656
| ~ c_Orderings_Oord__class_Oless__eq(U_655,c_Groups_Ozero__class_Ozero(U_655),U_656)
| ~ class_Groups_Oordered__ab__group__add__abs(U_655) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
! [U_656,U_655] :
( c_Groups_Oabs__class_Oabs(U_655,U_656) = U_656
| ~ c_Orderings_Oord__class_Oless__eq(U_655,c_Groups_Ozero__class_Ozero(U_655),U_656)
| ~ class_Groups_Oordered__ab__group__add__abs(U_655) ),
inference(definitional_conversion,[status(esa)],[f_264_2]) ).
cnf(f_264_4,plain,
( c_Groups_Oabs__class_Oabs(U_655,U_656) = U_656
| ~ c_Orderings_Oord__class_Oless__eq(U_655,c_Groups_Ozero__class_Ozero(U_655),U_656)
| ~ class_Groups_Oordered__ab__group__add__abs(U_655) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_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_265_2,plain,
! [U_658,U_657] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_657,c_Groups_Oabs__class_Oabs(U_657,U_658),c_Groups_Ozero__class_Ozero(U_657))
| U_658 != c_Groups_Ozero__class_Ozero(U_657) )
& ( U_658 = c_Groups_Ozero__class_Ozero(U_657)
| ~ c_Orderings_Oord__class_Oless__eq(U_657,c_Groups_Oabs__class_Oabs(U_657,U_658),c_Groups_Ozero__class_Ozero(U_657)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_657) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
( ! [U_657,U_658] :
( c_Orderings_Oord__class_Oless__eq(U_657,c_Groups_Oabs__class_Oabs(U_657,U_658),c_Groups_Ozero__class_Ozero(U_657))
| U_658 != c_Groups_Ozero__class_Ozero(U_657)
| ~ sP34(U_657,U_658) )
& ! [U_657,U_658] :
( U_658 = c_Groups_Ozero__class_Ozero(U_657)
| ~ c_Orderings_Oord__class_Oless__eq(U_657,c_Groups_Oabs__class_Oabs(U_657,U_658),c_Groups_Ozero__class_Ozero(U_657))
| ~ sP34(U_657,U_658) )
& ! [U_657,U_658] :
( sP34(U_657,U_658)
| ~ class_Groups_Oordered__ab__group__add__abs(U_657) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34])],[f_265_2]) ).
cnf(f_265_4,plain,
( sP34(U_657,U_658)
| ~ class_Groups_Oordered__ab__group__add__abs(U_657) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_5,plain,
( U_658 = c_Groups_Ozero__class_Ozero(U_657)
| ~ c_Orderings_Oord__class_Oless__eq(U_657,c_Groups_Oabs__class_Oabs(U_657,U_658),c_Groups_Ozero__class_Ozero(U_657))
| ~ sP34(U_657,U_658) ),
inference(clausify,[status(thm)],[f_265_3]) ).
cnf(f_265_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_657,c_Groups_Oabs__class_Oabs(U_657,U_658),c_Groups_Ozero__class_Ozero(U_657))
| U_658 != c_Groups_Ozero__class_Ozero(U_657)
| ~ sP34(U_657,U_658) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_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_266_2,plain,
! [U_660,U_659] :
( c_Orderings_Oord__class_Oless__eq(U_659,c_Groups_Ozero__class_Ozero(U_659),c_Groups_Oabs__class_Oabs(U_659,U_660))
| ~ class_Groups_Oordered__ab__group__add__abs(U_659) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_660,U_659] :
( c_Orderings_Oord__class_Oless__eq(U_659,c_Groups_Ozero__class_Ozero(U_659),c_Groups_Oabs__class_Oabs(U_659,U_660))
| ~ class_Groups_Oordered__ab__group__add__abs(U_659) ),
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_659,c_Groups_Ozero__class_Ozero(U_659),c_Groups_Oabs__class_Oabs(U_659,U_660))
| ~ class_Groups_Oordered__ab__group__add__abs(U_659) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [V_d,V_c,V_b,V_a] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_a,V_b),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_a,V_c),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_b,V_d)),
inference(fof_nnf,[status(thm)],[fact_complex__add]) ).
fof(f_267_2,plain,
! [U_664,U_663,U_662,U_661] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_661,U_662),c_Complex_Ocomplex_OComplex(U_663,U_664)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_661,U_663),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_662,U_664)),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_661,U_662,U_663,U_664] : c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_661,U_662),c_Complex_Ocomplex_OComplex(U_663,U_664)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_661,U_663),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_662,U_664)),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_661,U_662),c_Complex_Ocomplex_OComplex(U_663,U_664)) = c_Complex_Ocomplex_OComplex(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_661,U_663),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_662,U_664)),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_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_268_2,plain,
! [U_665] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(U_665))) = 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_665),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
! [U_665] : c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(U_665))) = 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_665),
inference(definitional_conversion,[status(esa)],[f_268_2]) ).
cnf(f_268_4,plain,
c_Nat_OSuc(c_Nat_OSuc(c_Nat_OSuc(U_665))) = 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_665),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),V_y)))),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__mult__self__sum__ge__zero]) ).
fof(f_269_2,plain,
! [U_667,U_666] : 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_666),U_666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_667),U_667)))),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
! [U_666,U_667] : 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_666),U_666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_667),U_667)))),
inference(definitional_conversion,[status(esa)],[f_269_2]) ).
cnf(f_269_4,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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_666),U_666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_667),U_667)))),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_1,plain,
! [V_n,V_r,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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_270_2,plain,
! [U_670,U_669,U_668] :
( c_Orderings_Oord__class_Oless__eq(U_668,hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),c_Nat_OSuc(U_670)),U_669)
| ~ c_Orderings_Oord__class_Oless__eq(U_668,U_669,c_Groups_Oone__class_Oone(U_668))
| ~ c_Orderings_Oord__class_Oless__eq(U_668,c_Groups_Ozero__class_Ozero(U_668),U_669)
| ~ class_Rings_Olinordered__semidom(U_668) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_668,U_669,U_670] :
( c_Orderings_Oord__class_Oless__eq(U_668,hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),c_Nat_OSuc(U_670)),U_669)
| ~ c_Orderings_Oord__class_Oless__eq(U_668,U_669,c_Groups_Oone__class_Oone(U_668))
| ~ c_Orderings_Oord__class_Oless__eq(U_668,c_Groups_Ozero__class_Ozero(U_668),U_669)
| ~ class_Rings_Olinordered__semidom(U_668) ),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_668,hAPP(hAPP(c_Power_Opower__class_Opower(U_668),U_669),c_Nat_OSuc(U_670)),U_669)
| ~ c_Orderings_Oord__class_Oless__eq(U_668,U_669,c_Groups_Oone__class_Oone(U_668))
| ~ c_Orderings_Oord__class_Oless__eq(U_668,c_Groups_Ozero__class_Ozero(U_668),U_669)
| ~ class_Rings_Olinordered__semidom(U_668) ),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_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]) ).
fof(f_271_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(definitional_conversion,[status(esa)],[f_271_1]) ).
cnf(f_271_3,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_271_2]) ).
fof(f_272_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]) ).
fof(f_272_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(definitional_conversion,[status(esa)],[f_272_1]) ).
cnf(f_272_3,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_272_2]) ).
fof(f_273_1,plain,
! [V_w_2,V_b_2,V_a_2] :
( ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w_2)
| V_b_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_a_2 != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w_2) )
& ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,V_w_2) )
| c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Complex__eq__number__of]) ).
fof(f_273_2,plain,
! [U_673,U_672,U_671] :
( ( c_Complex_Ocomplex_OComplex(U_671,U_672) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_673)
| U_672 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_671 != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_673) )
& ( ( U_672 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_671 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_673) )
| c_Complex_Ocomplex_OComplex(U_671,U_672) != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_673) ) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
( ! [U_679,U_677,U_675] :
( c_Complex_Ocomplex_OComplex(U_675,U_677) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_679)
| U_677 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_675 != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_679) )
& ! [U_678,U_676,U_674] :
( ( U_676 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_674 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_678) )
| c_Complex_Ocomplex_OComplex(U_674,U_676) != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_678) ) ),
inference(miniscope,[status(thm)],[f_273_2]) ).
fof(f_273_4,plain,
( ! [U_674,U_676,U_678] :
( U_676 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP35(U_674,U_676,U_678) )
& ! [U_674,U_676,U_678] :
( U_674 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_678)
| ~ sP35(U_674,U_676,U_678) )
& ! [U_675,U_679,U_677] :
( c_Complex_Ocomplex_OComplex(U_675,U_677) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_679)
| U_677 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_675 != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_679) )
& ! [U_674,U_676,U_678] :
( sP35(U_674,U_676,U_678)
| c_Complex_Ocomplex_OComplex(U_674,U_676) != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_678) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_273_3]) ).
cnf(f_273_5,plain,
( sP35(U_674,U_676,U_678)
| c_Complex_Ocomplex_OComplex(U_674,U_676) != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_678) ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_6,plain,
( c_Complex_Ocomplex_OComplex(U_675,U_677) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_679)
| U_677 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_675 != c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_679) ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_7,plain,
( U_674 = c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_678)
| ~ sP35(U_674,U_676,U_678) ),
inference(clausify,[status(thm)],[f_273_4]) ).
cnf(f_273_8,plain,
( U_676 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP35(U_674,U_676,U_678) ),
inference(clausify,[status(thm)],[f_273_4]) ).
fof(f_274_1,plain,
! [V_b_2,V_a_2] :
( ( c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| V_b_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_a_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( ( V_b_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_a_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(V_a_2,V_b_2) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(fof_nnf,[status(thm)],[fact_Complex__eq__1]) ).
fof(f_274_2,plain,
! [U_681,U_680] :
( ( c_Complex_Ocomplex_OComplex(U_680,U_681) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| U_681 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_680 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( ( U_681 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_680 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_680,U_681) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
( ! [U_685,U_683] :
( c_Complex_Ocomplex_OComplex(U_683,U_685) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| U_685 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_683 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ! [U_684,U_682] :
( ( U_684 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_682 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_682,U_684) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(miniscope,[status(thm)],[f_274_2]) ).
fof(f_274_4,plain,
( ! [U_684,U_682] :
( U_684 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP36(U_684,U_682) )
& ! [U_684,U_682] :
( U_682 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ sP36(U_684,U_682) )
& ! [U_685,U_683] :
( c_Complex_Ocomplex_OComplex(U_683,U_685) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| U_685 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_683 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ! [U_684,U_682] :
( sP36(U_684,U_682)
| c_Complex_Ocomplex_OComplex(U_682,U_684) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36])],[f_274_3]) ).
cnf(f_274_5,plain,
( sP36(U_684,U_682)
| c_Complex_Ocomplex_OComplex(U_682,U_684) != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) ),
inference(clausify,[status(thm)],[f_274_4]) ).
cnf(f_274_6,plain,
( c_Complex_Ocomplex_OComplex(U_683,U_685) = c_Groups_Oone__class_Oone(tc_Complex_Ocomplex)
| U_685 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_683 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_274_4]) ).
cnf(f_274_7,plain,
( U_682 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ sP36(U_684,U_682) ),
inference(clausify,[status(thm)],[f_274_4]) ).
cnf(f_274_8,plain,
( U_684 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP36(U_684,U_682) ),
inference(clausify,[status(thm)],[f_274_4]) ).
fof(f_275_1,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_complex__one__def]) ).
fof(f_275_2,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_275_1]) ).
cnf(f_275_3,plain,
c_Groups_Oone__class_Oone(tc_Complex_Ocomplex) = c_Complex_Ocomplex_OComplex(c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_275_2]) ).
fof(f_276_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_276_2,plain,
! [U_686] : 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_686) = c_Nat_OSuc(c_Nat_OSuc(U_686)),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
! [U_686] : 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_686) = c_Nat_OSuc(c_Nat_OSuc(U_686)),
inference(definitional_conversion,[status(esa)],[f_276_2]) ).
cnf(f_276_4,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_686) = c_Nat_OSuc(c_Nat_OSuc(U_686)),
inference(clausify,[status(thm)],[f_276_3]) ).
fof(f_277_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_277_2,plain,
! [U_687] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_687,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_687)),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
! [U_687] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_687,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_687)),
inference(definitional_conversion,[status(esa)],[f_277_2]) ).
cnf(f_277_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_687,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_687)),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_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_278_2,plain,
! [U_688] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_688))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_688) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
! [U_688] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_688))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_688) ),
inference(definitional_conversion,[status(esa)],[f_278_2]) ).
cnf(f_278_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_688))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_688) ),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_1,plain,
! [V_xa_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__le__1__iff]) ).
fof(f_279_2,plain,
! [U_689] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_689),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_689,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_689,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_689),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
( ! [U_691] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_691),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_691,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_690] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_690,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_690),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_279_2]) ).
fof(f_279_4,plain,
( ! [U_691] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_691),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_691,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_690] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_690,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_690),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_279_3]) ).
cnf(f_279_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_690,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_690),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_279_4]) ).
cnf(f_279_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_691),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_691,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_279_4]) ).
fof(f_280_1,plain,
! [V_ya_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__ge__1__iff]) ).
fof(f_280_2,plain,
! [U_692] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_692))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_692) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_692)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_692)) ) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
( ! [U_694] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_694))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_694) )
& ! [U_693] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_693)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_693)) ) ),
inference(miniscope,[status(thm)],[f_280_2]) ).
fof(f_280_4,plain,
( ! [U_694] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_694))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_694) )
& ! [U_693] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_693)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_693)) ) ),
inference(definitional_conversion,[status(esa)],[f_280_3]) ).
cnf(f_280_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_693)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_693)) ),
inference(clausify,[status(thm)],[f_280_4]) ).
cnf(f_280_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_694))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_694) ),
inference(clausify,[status(thm)],[f_280_4]) ).
fof(f_281_1,plain,
! [V_b,V_a,V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),c_Groups_Ominus__class_Ominus(T_a,V_y,V_b)),hAPP(hAPP(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_281_2,plain,
! [U_699,U_698,U_697,U_696,U_695] :
( c_Groups_Ominus__class_Ominus(U_695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),U_696),U_697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),U_698),U_699)) = c_Groups_Oplus__class_Oplus(U_695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),U_696),c_Groups_Ominus__class_Ominus(U_695,U_697,U_699)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),c_Groups_Ominus__class_Ominus(U_695,U_696,U_698)),U_699))
| ~ class_Rings_Oring(U_695) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
! [U_698,U_699,U_695,U_696,U_697] :
( c_Groups_Ominus__class_Ominus(U_695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),U_696),U_697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),U_698),U_699)) = c_Groups_Oplus__class_Oplus(U_695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),U_696),c_Groups_Ominus__class_Ominus(U_695,U_697,U_699)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),c_Groups_Ominus__class_Ominus(U_695,U_696,U_698)),U_699))
| ~ class_Rings_Oring(U_695) ),
inference(definitional_conversion,[status(esa)],[f_281_2]) ).
cnf(f_281_4,plain,
( c_Groups_Ominus__class_Ominus(U_695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),U_696),U_697),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),U_698),U_699)) = c_Groups_Oplus__class_Oplus(U_695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),U_696),c_Groups_Ominus__class_Ominus(U_695,U_697,U_699)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_695),c_Groups_Ominus__class_Ominus(U_695,U_696,U_698)),U_699))
| ~ class_Rings_Oring(U_695) ),
inference(clausify,[status(thm)],[f_281_3]) ).
fof(f_282_1,plain,
! [V_v,V_b,V_a,T_b] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a),c_Int_Onumber__class_Onumber__of(T_b,V_v)),hAPP(hAPP(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_282_2,plain,
! [U_703,U_702,U_701,U_700] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),c_Groups_Ominus__class_Ominus(U_700,U_701,U_702)),c_Int_Onumber__class_Onumber__of(U_700,U_703)) = c_Groups_Ominus__class_Ominus(U_700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),U_701),c_Int_Onumber__class_Onumber__of(U_700,U_703)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),U_702),c_Int_Onumber__class_Onumber__of(U_700,U_703)))
| ~ class_Rings_Oring(U_700)
| ~ class_Int_Onumber(U_700) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
! [U_700,U_701,U_702,U_703] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),c_Groups_Ominus__class_Ominus(U_700,U_701,U_702)),c_Int_Onumber__class_Onumber__of(U_700,U_703)) = c_Groups_Ominus__class_Ominus(U_700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),U_701),c_Int_Onumber__class_Onumber__of(U_700,U_703)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),U_702),c_Int_Onumber__class_Onumber__of(U_700,U_703)))
| ~ class_Rings_Oring(U_700)
| ~ class_Int_Onumber(U_700) ),
inference(definitional_conversion,[status(esa)],[f_282_2]) ).
cnf(f_282_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),c_Groups_Ominus__class_Ominus(U_700,U_701,U_702)),c_Int_Onumber__class_Onumber__of(U_700,U_703)) = c_Groups_Ominus__class_Ominus(U_700,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),U_701),c_Int_Onumber__class_Onumber__of(U_700,U_703)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_700),U_702),c_Int_Onumber__class_Onumber__of(U_700,U_703)))
| ~ class_Rings_Oring(U_700)
| ~ class_Int_Onumber(U_700) ),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_1,plain,
! [V_c,V_b,V_v,T_b] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),c_Int_Onumber__class_Onumber__of(T_b,V_v)),V_b),hAPP(hAPP(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_283_2,plain,
! [U_707,U_706,U_705,U_704] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_704),c_Int_Onumber__class_Onumber__of(U_704,U_705)),c_Groups_Ominus__class_Ominus(U_704,U_706,U_707)) = c_Groups_Ominus__class_Ominus(U_704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_704),c_Int_Onumber__class_Onumber__of(U_704,U_705)),U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_704),c_Int_Onumber__class_Onumber__of(U_704,U_705)),U_707))
| ~ class_Rings_Oring(U_704)
| ~ class_Int_Onumber(U_704) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_704,U_705,U_706,U_707] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_704),c_Int_Onumber__class_Onumber__of(U_704,U_705)),c_Groups_Ominus__class_Ominus(U_704,U_706,U_707)) = c_Groups_Ominus__class_Ominus(U_704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_704),c_Int_Onumber__class_Onumber__of(U_704,U_705)),U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_704),c_Int_Onumber__class_Onumber__of(U_704,U_705)),U_707))
| ~ class_Rings_Oring(U_704)
| ~ class_Int_Onumber(U_704) ),
inference(definitional_conversion,[status(esa)],[f_283_2]) ).
cnf(f_283_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_704),c_Int_Onumber__class_Onumber__of(U_704,U_705)),c_Groups_Ominus__class_Ominus(U_704,U_706,U_707)) = c_Groups_Ominus__class_Ominus(U_704,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_704),c_Int_Onumber__class_Onumber__of(U_704,U_705)),U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_704),c_Int_Onumber__class_Onumber__of(U_704,U_705)),U_707))
| ~ class_Rings_Oring(U_704)
| ~ class_Int_Onumber(U_704) ),
inference(clausify,[status(thm)],[f_283_3]) ).
fof(f_284_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_284_2,plain,
! [U_711,U_710,U_709,U_708] :
( c_Groups_Oplus__class_Oplus(U_708,c_Int_Onumber__class_Onumber__of(U_708,U_709),c_Groups_Ominus__class_Ominus(U_708,c_Int_Onumber__class_Onumber__of(U_708,U_710),U_711)) = c_Groups_Ominus__class_Ominus(U_708,c_Int_Onumber__class_Onumber__of(U_708,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_709,U_710)),U_711)
| ~ class_Int_Onumber__ring(U_708) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_708,U_709,U_710,U_711] :
( c_Groups_Oplus__class_Oplus(U_708,c_Int_Onumber__class_Onumber__of(U_708,U_709),c_Groups_Ominus__class_Ominus(U_708,c_Int_Onumber__class_Onumber__of(U_708,U_710),U_711)) = c_Groups_Ominus__class_Ominus(U_708,c_Int_Onumber__class_Onumber__of(U_708,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_709,U_710)),U_711)
| ~ class_Int_Onumber__ring(U_708) ),
inference(definitional_conversion,[status(esa)],[f_284_2]) ).
cnf(f_284_4,plain,
( c_Groups_Oplus__class_Oplus(U_708,c_Int_Onumber__class_Onumber__of(U_708,U_709),c_Groups_Ominus__class_Ominus(U_708,c_Int_Onumber__class_Onumber__of(U_708,U_710),U_711)) = c_Groups_Ominus__class_Ominus(U_708,c_Int_Onumber__class_Onumber__of(U_708,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_709,U_710)),U_711)
| ~ class_Int_Onumber__ring(U_708) ),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_285_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_285_2,plain,
! [U_716,U_715,U_714,U_713,U_712] :
( c_Orderings_Oord__class_Oless__eq(U_712,c_Groups_Oabs__class_Oabs(U_712,c_Groups_Ominus__class_Ominus(U_712,c_Groups_Oplus__class_Oplus(U_712,U_713,U_714),c_Groups_Oplus__class_Oplus(U_712,U_715,U_716))),c_Groups_Oplus__class_Oplus(U_712,c_Groups_Oabs__class_Oabs(U_712,c_Groups_Ominus__class_Ominus(U_712,U_713,U_715)),c_Groups_Oabs__class_Oabs(U_712,c_Groups_Ominus__class_Ominus(U_712,U_714,U_716))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_712) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_712,U_713,U_714,U_715,U_716] :
( c_Orderings_Oord__class_Oless__eq(U_712,c_Groups_Oabs__class_Oabs(U_712,c_Groups_Ominus__class_Ominus(U_712,c_Groups_Oplus__class_Oplus(U_712,U_713,U_714),c_Groups_Oplus__class_Oplus(U_712,U_715,U_716))),c_Groups_Oplus__class_Oplus(U_712,c_Groups_Oabs__class_Oabs(U_712,c_Groups_Ominus__class_Ominus(U_712,U_713,U_715)),c_Groups_Oabs__class_Oabs(U_712,c_Groups_Ominus__class_Ominus(U_712,U_714,U_716))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_712) ),
inference(definitional_conversion,[status(esa)],[f_285_2]) ).
cnf(f_285_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_712,c_Groups_Oabs__class_Oabs(U_712,c_Groups_Ominus__class_Ominus(U_712,c_Groups_Oplus__class_Oplus(U_712,U_713,U_714),c_Groups_Oplus__class_Oplus(U_712,U_715,U_716))),c_Groups_Oplus__class_Oplus(U_712,c_Groups_Oabs__class_Oabs(U_712,c_Groups_Ominus__class_Ominus(U_712,U_713,U_715)),c_Groups_Oabs__class_Oabs(U_712,c_Groups_Ominus__class_Ominus(U_712,U_714,U_716))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_712) ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_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_286_2,plain,
! [U_719,U_718,U_717] :
( c_Orderings_Oord__class_Oless__eq(U_717,c_Groups_Oabs__class_Oabs(U_717,c_Groups_Ominus__class_Ominus(U_717,U_718,U_719)),c_Groups_Oplus__class_Oplus(U_717,c_Groups_Oabs__class_Oabs(U_717,U_718),c_Groups_Oabs__class_Oabs(U_717,U_719)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_717) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_717,U_718,U_719] :
( c_Orderings_Oord__class_Oless__eq(U_717,c_Groups_Oabs__class_Oabs(U_717,c_Groups_Ominus__class_Ominus(U_717,U_718,U_719)),c_Groups_Oplus__class_Oplus(U_717,c_Groups_Oabs__class_Oabs(U_717,U_718),c_Groups_Oabs__class_Oabs(U_717,U_719)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_717) ),
inference(definitional_conversion,[status(esa)],[f_286_2]) ).
cnf(f_286_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_717,c_Groups_Oabs__class_Oabs(U_717,c_Groups_Ominus__class_Ominus(U_717,U_718,U_719)),c_Groups_Oplus__class_Oplus(U_717,c_Groups_Oabs__class_Oabs(U_717,U_718),c_Groups_Oabs__class_Oabs(U_717,U_719)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_717) ),
inference(clausify,[status(thm)],[f_286_3]) ).
fof(f_287_1,plain,
! [V_x] : c_NthRoot_Osqrt(hAPP(hAPP(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_287_2,plain,
! [U_720] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_720),U_720)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_720),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_720] : c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_720),U_720)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_720),
inference(definitional_conversion,[status(esa)],[f_287_2]) ).
cnf(f_287_4,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_720),U_720)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_720),
inference(clausify,[status(thm)],[f_287_3]) ).
fof(f_288_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]) ).
fof(f_288_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(definitional_conversion,[status(esa)],[f_288_1]) ).
cnf(f_288_3,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_288_2]) ).
fof(f_289_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]) ).
fof(f_289_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(definitional_conversion,[status(esa)],[f_289_1]) ).
cnf(f_289_3,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_289_2]) ).
fof(f_290_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_290_2,plain,
! [U_722,U_721] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_721),c_Int_OBit1(U_722)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_721,U_722)),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_721,U_722] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_721),c_Int_OBit1(U_722)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_721,U_722)),
inference(definitional_conversion,[status(esa)],[f_290_2]) ).
cnf(f_290_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_721),c_Int_OBit1(U_722)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_721,U_722)),
inference(clausify,[status(thm)],[f_290_3]) ).
fof(f_291_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_291_2,plain,
! [U_724,U_723] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_723),c_Int_OBit0(U_724)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_723,U_724)),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_723,U_724] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_723),c_Int_OBit0(U_724)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_723,U_724)),
inference(definitional_conversion,[status(esa)],[f_291_2]) ).
cnf(f_291_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OBit1(U_723),c_Int_OBit0(U_724)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_723,U_724)),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_292_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_292_2,plain,
! [U_725] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_725)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,U_725)),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_725] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_725)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,U_725)),
inference(definitional_conversion,[status(esa)],[f_292_2]) ).
cnf(f_292_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_725)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,U_725)),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_1,plain,
! [V_q,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)),V_x) = hAPP(hAPP(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_293_2,plain,
! [U_728,U_727,U_726] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_726),hAPP(hAPP(c_Power_Opower__class_Opower(U_726),U_727),U_728)),U_727) = hAPP(hAPP(c_Power_Opower__class_Opower(U_726),U_727),c_Nat_OSuc(U_728))
| ~ class_Rings_Ocomm__semiring__1(U_726) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_726,U_727,U_728] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_726),hAPP(hAPP(c_Power_Opower__class_Opower(U_726),U_727),U_728)),U_727) = hAPP(hAPP(c_Power_Opower__class_Opower(U_726),U_727),c_Nat_OSuc(U_728))
| ~ class_Rings_Ocomm__semiring__1(U_726) ),
inference(definitional_conversion,[status(esa)],[f_293_2]) ).
cnf(f_293_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_726),hAPP(hAPP(c_Power_Opower__class_Opower(U_726),U_727),U_728)),U_727) = hAPP(hAPP(c_Power_Opower__class_Opower(U_726),U_727),c_Nat_OSuc(U_728))
| ~ class_Rings_Ocomm__semiring__1(U_726) ),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_1,plain,
! [V_q,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(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_294_2,plain,
! [U_731,U_730,U_729] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_729),U_730),hAPP(hAPP(c_Power_Opower__class_Opower(U_729),U_730),U_731)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_729),U_730),c_Nat_OSuc(U_731))
| ~ class_Rings_Ocomm__semiring__1(U_729) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_729,U_730,U_731] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_729),U_730),hAPP(hAPP(c_Power_Opower__class_Opower(U_729),U_730),U_731)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_729),U_730),c_Nat_OSuc(U_731))
| ~ class_Rings_Ocomm__semiring__1(U_729) ),
inference(definitional_conversion,[status(esa)],[f_294_2]) ).
cnf(f_294_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_729),U_730),hAPP(hAPP(c_Power_Opower__class_Opower(U_729),U_730),U_731)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_729),U_730),c_Nat_OSuc(U_731))
| ~ class_Rings_Ocomm__semiring__1(U_729) ),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_1,plain,
! [V_q,V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(V_q)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(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_295_2,plain,
! [U_734,U_733,U_732] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_732),U_733),c_Nat_OSuc(U_734)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_732),U_733),hAPP(hAPP(c_Power_Opower__class_Opower(U_732),U_733),U_734))
| ~ class_Rings_Ocomm__semiring__1(U_732) ),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_732,U_733,U_734] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_732),U_733),c_Nat_OSuc(U_734)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_732),U_733),hAPP(hAPP(c_Power_Opower__class_Opower(U_732),U_733),U_734))
| ~ class_Rings_Ocomm__semiring__1(U_732) ),
inference(definitional_conversion,[status(esa)],[f_295_2]) ).
cnf(f_295_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_732),U_733),c_Nat_OSuc(U_734)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_732),U_733),hAPP(hAPP(c_Power_Opower__class_Opower(U_732),U_733),U_734))
| ~ class_Rings_Ocomm__semiring__1(U_732) ),
inference(clausify,[status(thm)],[f_295_3]) ).
fof(f_296_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(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_296_2,plain,
! [U_737,U_736,U_735] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_735),U_736),c_Nat_OSuc(U_737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_735),hAPP(hAPP(c_Power_Opower__class_Opower(U_735),U_736),U_737)),U_736)
| ~ class_Groups_Omonoid__mult(U_735) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_735,U_736,U_737] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_735),U_736),c_Nat_OSuc(U_737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_735),hAPP(hAPP(c_Power_Opower__class_Opower(U_735),U_736),U_737)),U_736)
| ~ class_Groups_Omonoid__mult(U_735) ),
inference(definitional_conversion,[status(esa)],[f_296_2]) ).
cnf(f_296_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_735),U_736),c_Nat_OSuc(U_737)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_735),hAPP(hAPP(c_Power_Opower__class_Opower(U_735),U_736),U_737)),U_736)
| ~ class_Groups_Omonoid__mult(U_735) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(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_297_2,plain,
! [U_740,U_739,U_738] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_738),U_739),c_Nat_OSuc(U_740)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_739),hAPP(hAPP(c_Power_Opower__class_Opower(U_738),U_739),U_740))
| ~ class_Power_Opower(U_738) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_738,U_739,U_740] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_738),U_739),c_Nat_OSuc(U_740)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_739),hAPP(hAPP(c_Power_Opower__class_Opower(U_738),U_739),U_740))
| ~ class_Power_Opower(U_738) ),
inference(definitional_conversion,[status(esa)],[f_297_2]) ).
cnf(f_297_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_738),U_739),c_Nat_OSuc(U_740)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_739),hAPP(hAPP(c_Power_Opower__class_Opower(U_738),U_739),U_740))
| ~ class_Power_Opower(U_738) ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_1,plain,
! [V_q,V_p,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_p)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_q)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_p,V_q))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J]) ).
fof(f_298_2,plain,
! [U_744,U_743,U_742,U_741] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_741),hAPP(hAPP(c_Power_Opower__class_Opower(U_741),U_742),U_743)),hAPP(hAPP(c_Power_Opower__class_Opower(U_741),U_742),U_744)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_741),U_742),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_743,U_744))
| ~ class_Rings_Ocomm__semiring__1(U_741) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_741,U_742,U_743,U_744] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_741),hAPP(hAPP(c_Power_Opower__class_Opower(U_741),U_742),U_743)),hAPP(hAPP(c_Power_Opower__class_Opower(U_741),U_742),U_744)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_741),U_742),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_743,U_744))
| ~ class_Rings_Ocomm__semiring__1(U_741) ),
inference(definitional_conversion,[status(esa)],[f_298_2]) ).
cnf(f_298_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_741),hAPP(hAPP(c_Power_Opower__class_Opower(U_741),U_742),U_743)),hAPP(hAPP(c_Power_Opower__class_Opower(U_741),U_742),U_744)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_741),U_742),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_743,U_744))
| ~ class_Rings_Ocomm__semiring__1(U_741) ),
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_1,plain,
! [V_n,V_m,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__add]) ).
fof(f_299_2,plain,
! [U_748,U_747,U_746,U_745] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_745),U_746),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_747,U_748)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_745),hAPP(hAPP(c_Power_Opower__class_Opower(U_745),U_746),U_747)),hAPP(hAPP(c_Power_Opower__class_Opower(U_745),U_746),U_748))
| ~ class_Groups_Omonoid__mult(U_745) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_745,U_746,U_747,U_748] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_745),U_746),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_747,U_748)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_745),hAPP(hAPP(c_Power_Opower__class_Opower(U_745),U_746),U_747)),hAPP(hAPP(c_Power_Opower__class_Opower(U_745),U_746),U_748))
| ~ class_Groups_Omonoid__mult(U_745) ),
inference(definitional_conversion,[status(esa)],[f_299_2]) ).
cnf(f_299_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_745),U_746),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_747,U_748)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_745),hAPP(hAPP(c_Power_Opower__class_Opower(U_745),U_746),U_747)),hAPP(hAPP(c_Power_Opower__class_Opower(U_745),U_746),U_748))
| ~ class_Groups_Omonoid__mult(U_745) ),
inference(clausify,[status(thm)],[f_299_3]) ).
fof(f_300_1,plain,
! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),V_l),
inference(fof_nnf,[status(thm)],[fact_mult__Bit1]) ).
fof(f_300_2,plain,
! [U_750,U_749] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_749)),U_750) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_749),U_750)),U_750),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_749,U_750] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_749)),U_750) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_749),U_750)),U_750),
inference(definitional_conversion,[status(esa)],[f_300_2]) ).
cnf(f_300_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_749)),U_750) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_749),U_750)),U_750),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_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_301_2,plain,
! [U_752,U_751] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(U_751),c_Int_OBit0(U_752)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_751,U_752)),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_751,U_752] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(U_751),c_Int_OBit0(U_752)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_751,U_752)),
inference(definitional_conversion,[status(esa)],[f_301_2]) ).
cnf(f_301_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit1(U_751),c_Int_OBit0(U_752)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_751,U_752)),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_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_302_2,plain,
! [U_754,U_753] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_753),c_Int_OBit1(U_754)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_753,U_754)),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_753,U_754] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_753),c_Int_OBit1(U_754)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_753,U_754)),
inference(definitional_conversion,[status(esa)],[f_302_2]) ).
cnf(f_302_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Int_OBit0(U_753),c_Int_OBit1(U_754)) = c_Int_OBit1(c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_753,U_754)),
inference(clausify,[status(thm)],[f_302_3]) ).
fof(f_303_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)) = c_Groups_Ozero__class_Ozero(T_a)
| V_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_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_303_2,plain,
! [U_757,U_756,U_755] :
( ( ( c_Groups_Oplus__class_Oplus(U_755,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_756),U_756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_757),U_757)) = c_Groups_Ozero__class_Ozero(U_755)
| U_757 != c_Groups_Ozero__class_Ozero(U_755)
| U_756 != c_Groups_Ozero__class_Ozero(U_755) )
& ( ( U_757 = c_Groups_Ozero__class_Ozero(U_755)
& U_756 = c_Groups_Ozero__class_Ozero(U_755) )
| c_Groups_Oplus__class_Oplus(U_755,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_756),U_756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_757),U_757)) != c_Groups_Ozero__class_Ozero(U_755) ) )
| ~ class_Rings_Olinordered__ring__strict(U_755) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
( ! [U_755,U_756,U_757] :
( U_757 = c_Groups_Ozero__class_Ozero(U_755)
| ~ sP37(U_755,U_756,U_757) )
& ! [U_755,U_756,U_757] :
( U_756 = c_Groups_Ozero__class_Ozero(U_755)
| ~ sP37(U_755,U_756,U_757) )
& ! [U_755,U_756,U_757] :
( c_Groups_Oplus__class_Oplus(U_755,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_756),U_756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_757),U_757)) = c_Groups_Ozero__class_Ozero(U_755)
| U_757 != c_Groups_Ozero__class_Ozero(U_755)
| U_756 != c_Groups_Ozero__class_Ozero(U_755)
| ~ sP38(U_755,U_756,U_757) )
& ! [U_755,U_756,U_757] :
( sP37(U_755,U_756,U_757)
| c_Groups_Oplus__class_Oplus(U_755,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_756),U_756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_757),U_757)) != c_Groups_Ozero__class_Ozero(U_755)
| ~ sP38(U_755,U_756,U_757) )
& ! [U_755,U_756,U_757] :
( sP38(U_755,U_756,U_757)
| ~ class_Rings_Olinordered__ring__strict(U_755) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37,sP38])],[f_303_2]) ).
cnf(f_303_4,plain,
( sP38(U_755,U_756,U_757)
| ~ class_Rings_Olinordered__ring__strict(U_755) ),
inference(clausify,[status(thm)],[f_303_3]) ).
cnf(f_303_5,plain,
( sP37(U_755,U_756,U_757)
| c_Groups_Oplus__class_Oplus(U_755,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_756),U_756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_757),U_757)) != c_Groups_Ozero__class_Ozero(U_755)
| ~ sP38(U_755,U_756,U_757) ),
inference(clausify,[status(thm)],[f_303_3]) ).
cnf(f_303_6,plain,
( c_Groups_Oplus__class_Oplus(U_755,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_756),U_756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_755),U_757),U_757)) = c_Groups_Ozero__class_Ozero(U_755)
| U_757 != c_Groups_Ozero__class_Ozero(U_755)
| U_756 != c_Groups_Ozero__class_Ozero(U_755)
| ~ sP38(U_755,U_756,U_757) ),
inference(clausify,[status(thm)],[f_303_3]) ).
cnf(f_303_7,plain,
( U_756 = c_Groups_Ozero__class_Ozero(U_755)
| ~ sP37(U_755,U_756,U_757) ),
inference(clausify,[status(thm)],[f_303_3]) ).
cnf(f_303_8,plain,
( U_757 = c_Groups_Ozero__class_Ozero(U_755)
| ~ sP37(U_755,U_756,U_757) ),
inference(clausify,[status(thm)],[f_303_3]) ).
fof(f_304_1,plain,
! [V_d,V_c,V_b,V_a,V_r,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_c)) != c_Groups_Oplus__class_Oplus(T_a,V_b,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_r),V_d))
| V_c = V_d
| V_a != V_b
| V_r = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__scale__eq__noteq]) ).
fof(f_304_2,plain,
! [U_763,U_762,U_761,U_760,U_759,U_758] :
( c_Groups_Oplus__class_Oplus(U_758,U_760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_758),U_759),U_762)) != c_Groups_Oplus__class_Oplus(U_758,U_761,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_758),U_759),U_763))
| U_762 = U_763
| U_760 != U_761
| U_759 = c_Groups_Ozero__class_Ozero(U_758)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_758) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
! [U_759,U_762,U_761,U_763,U_760,U_758] :
( c_Groups_Oplus__class_Oplus(U_758,U_760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_758),U_759),U_762)) != c_Groups_Oplus__class_Oplus(U_758,U_761,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_758),U_759),U_763))
| U_762 = U_763
| U_760 != U_761
| U_759 = c_Groups_Ozero__class_Ozero(U_758)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_758) ),
inference(definitional_conversion,[status(esa)],[f_304_2]) ).
cnf(f_304_4,plain,
( c_Groups_Oplus__class_Oplus(U_758,U_760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_758),U_759),U_762)) != c_Groups_Oplus__class_Oplus(U_758,U_761,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_758),U_759),U_763))
| U_762 = U_763
| U_760 != U_761
| U_759 = c_Groups_Ozero__class_Ozero(U_758)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_758) ),
inference(clausify,[status(thm)],[f_304_3]) ).
fof(f_305_1,plain,
! [V_d,V_c,V_b,V_a] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(V_a,V_b)),c_Complex_Ocomplex_OComplex(V_c,V_d)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_d)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_d),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b),V_c))),
inference(fof_nnf,[status(thm)],[fact_complex__mult]) ).
fof(f_305_2,plain,
! [U_767,U_766,U_765,U_764] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(U_764,U_765)),c_Complex_Ocomplex_OComplex(U_766,U_767)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_764),U_766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_765),U_767)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_764),U_767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_765),U_766))),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
! [U_764,U_765,U_766,U_767] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(U_764,U_765)),c_Complex_Ocomplex_OComplex(U_766,U_767)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_764),U_766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_765),U_767)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_764),U_767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_765),U_766))),
inference(definitional_conversion,[status(esa)],[f_305_2]) ).
cnf(f_305_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Ocomplex_OComplex(U_764,U_765)),c_Complex_Ocomplex_OComplex(U_766,U_767)) = c_Complex_Ocomplex_OComplex(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_764),U_766),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_765),U_767)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_764),U_767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_765),U_766))),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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_306_2,plain,
! [U_771,U_770,U_769,U_768] :
( c_Orderings_Oord__class_Oless__eq(U_768,hAPP(hAPP(c_Power_Opower__class_Opower(U_768),U_769),U_771),hAPP(hAPP(c_Power_Opower__class_Opower(U_768),U_770),U_771))
| ~ c_Orderings_Oord__class_Oless__eq(U_768,c_Groups_Ozero__class_Ozero(U_768),U_769)
| ~ c_Orderings_Oord__class_Oless__eq(U_768,U_769,U_770)
| ~ class_Rings_Olinordered__semidom(U_768) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
! [U_769,U_771,U_768,U_770] :
( c_Orderings_Oord__class_Oless__eq(U_768,hAPP(hAPP(c_Power_Opower__class_Opower(U_768),U_769),U_771),hAPP(hAPP(c_Power_Opower__class_Opower(U_768),U_770),U_771))
| ~ c_Orderings_Oord__class_Oless__eq(U_768,c_Groups_Ozero__class_Ozero(U_768),U_769)
| ~ c_Orderings_Oord__class_Oless__eq(U_768,U_769,U_770)
| ~ class_Rings_Olinordered__semidom(U_768) ),
inference(definitional_conversion,[status(esa)],[f_306_2]) ).
cnf(f_306_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_768,hAPP(hAPP(c_Power_Opower__class_Opower(U_768),U_769),U_771),hAPP(hAPP(c_Power_Opower__class_Opower(U_768),U_770),U_771))
| ~ c_Orderings_Oord__class_Oless__eq(U_768,c_Groups_Ozero__class_Ozero(U_768),U_769)
| ~ c_Orderings_Oord__class_Oless__eq(U_768,U_769,U_770)
| ~ class_Rings_Olinordered__semidom(U_768) ),
inference(clausify,[status(thm)],[f_306_3]) ).
fof(f_307_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_307_2,plain,
! [U_774,U_773,U_772] :
( c_Orderings_Oord__class_Oless__eq(U_772,c_Groups_Ozero__class_Ozero(U_772),hAPP(hAPP(c_Power_Opower__class_Opower(U_772),U_773),U_774))
| ~ c_Orderings_Oord__class_Oless__eq(U_772,c_Groups_Ozero__class_Ozero(U_772),U_773)
| ~ class_Rings_Olinordered__semidom(U_772) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_772,U_773,U_774] :
( c_Orderings_Oord__class_Oless__eq(U_772,c_Groups_Ozero__class_Ozero(U_772),hAPP(hAPP(c_Power_Opower__class_Opower(U_772),U_773),U_774))
| ~ c_Orderings_Oord__class_Oless__eq(U_772,c_Groups_Ozero__class_Ozero(U_772),U_773)
| ~ class_Rings_Olinordered__semidom(U_772) ),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_772,c_Groups_Ozero__class_Ozero(U_772),hAPP(hAPP(c_Power_Opower__class_Opower(U_772),U_773),U_774))
| ~ c_Orderings_Oord__class_Oless__eq(U_772,c_Groups_Ozero__class_Ozero(U_772),U_773)
| ~ class_Rings_Olinordered__semidom(U_772) ),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_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_308_2,plain,
! [U_775] :
( c_Groups_Ozero__class_Ozero(U_775) = c_Int_Onumber__class_Onumber__of(U_775,c_Int_OPls)
| ~ class_Int_Onumber__ring(U_775) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
! [U_775] :
( c_Groups_Ozero__class_Ozero(U_775) = c_Int_Onumber__class_Onumber__of(U_775,c_Int_OPls)
| ~ class_Int_Onumber__ring(U_775) ),
inference(definitional_conversion,[status(esa)],[f_308_2]) ).
cnf(f_308_4,plain,
( c_Groups_Ozero__class_Ozero(U_775) = c_Int_Onumber__class_Onumber__of(U_775,c_Int_OPls)
| ~ class_Int_Onumber__ring(U_775) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_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_309_2,plain,
! [U_776] :
( c_Int_Onumber__class_Onumber__of(U_776,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_776)
| ~ class_Int_Onumber__ring(U_776) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_776] :
( c_Int_Onumber__class_Onumber__of(U_776,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_776)
| ~ class_Int_Onumber__ring(U_776) ),
inference(definitional_conversion,[status(esa)],[f_309_2]) ).
cnf(f_309_4,plain,
( c_Int_Onumber__class_Onumber__of(U_776,c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_776)
| ~ class_Int_Onumber__ring(U_776) ),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(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_310_2,plain,
! [U_778,U_777] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_777),U_778),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_777)
| ~ class_Rings_Ocomm__semiring__1(U_777) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_777,U_778] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_777),U_778),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_777)
| ~ class_Rings_Ocomm__semiring__1(U_777) ),
inference(definitional_conversion,[status(esa)],[f_310_2]) ).
cnf(f_310_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_777),U_778),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_777)
| ~ class_Rings_Ocomm__semiring__1(U_777) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_311_2,plain,
! [U_780,U_779] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_779),U_780),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_779)
| ~ class_Power_Opower(U_779) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
! [U_779,U_780] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_779),U_780),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_779)
| ~ class_Power_Opower(U_779) ),
inference(definitional_conversion,[status(esa)],[f_311_2]) ).
cnf(f_311_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_779),U_780),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_779)
| ~ class_Power_Opower(U_779) ),
inference(clausify,[status(thm)],[f_311_3]) ).
fof(f_312_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]) ).
fof(f_312_2,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_312_1]) ).
cnf(f_312_3,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_312_2]) ).
fof(f_313_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]) ).
fof(f_313_2,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_313_1]) ).
cnf(f_313_3,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_313_2]) ).
fof(f_314_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]) ).
fof(f_314_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) = c_Int_Onumber__class_Onumber__of(tc_Int_Oint,c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_314_1]) ).
cnf(f_314_3,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_314_2]) ).
fof(f_315_1,plain,
! [V_ya_2,V_xa_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_ya_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_ya_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_xa_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_ya_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_ya_2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff]) ).
fof(f_315_2,plain,
! [U_782,U_781] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_781),U_781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_782),U_782)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_782 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_781 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_782 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_781 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_781),U_781),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_782),U_782)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
( ! [U_786,U_784] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_784),U_784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_786),U_786)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_786 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_784 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_785,U_783] :
( ( U_785 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_783 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_783),U_783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_785),U_785)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_315_2]) ).
fof(f_315_4,plain,
( ! [U_783,U_785] :
( U_785 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP39(U_783,U_785) )
& ! [U_783,U_785] :
( U_783 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP39(U_783,U_785) )
& ! [U_786,U_784] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_784),U_784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_786),U_786)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_786 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_784 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_783,U_785] :
( sP39(U_783,U_785)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_783),U_783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_785),U_785)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP39])],[f_315_3]) ).
cnf(f_315_5,plain,
( sP39(U_783,U_785)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_783),U_783),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_785),U_785)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_315_4]) ).
cnf(f_315_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_784),U_784),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_786),U_786)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_786 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_784 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_315_4]) ).
cnf(f_315_7,plain,
( U_783 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP39(U_783,U_785) ),
inference(clausify,[status(thm)],[f_315_4]) ).
cnf(f_315_8,plain,
( U_785 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP39(U_783,U_785) ),
inference(clausify,[status(thm)],[f_315_4]) ).
fof(f_316_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]) ).
fof(f_316_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(definitional_conversion,[status(esa)],[f_316_1]) ).
cnf(f_316_3,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_316_2]) ).
fof(f_317_1,plain,
! [V_y,V_x] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_x,V_y)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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_complex__norm]) ).
fof(f_317_2,plain,
! [U_788,U_787] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_787,U_788)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_787),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_788),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
! [U_787,U_788] : c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_787,U_788)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_787),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_788),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(definitional_conversion,[status(esa)],[f_317_2]) ).
cnf(f_317_4,plain,
c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_787,U_788)) = c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_787),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_788),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y),V_y)))),
inference(fof_nnf,[status(thm)],[fact_le__real__sqrt__sumsq]) ).
fof(f_318_2,plain,
! [U_790,U_789] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_789,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_789),U_789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_790),U_790)))),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
! [U_789,U_790] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_789,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_789),U_789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_790),U_790)))),
inference(definitional_conversion,[status(esa)],[f_318_2]) ).
cnf(f_318_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_789,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_789),U_789),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_790),U_790)))),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_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)
| hAPP(hAPP(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_319_2,plain,
! [U_792,U_791] :
( c_NthRoot_Osqrt(U_792) = U_791
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_791)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_791),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_792 ),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_791,U_792] :
( c_NthRoot_Osqrt(U_792) = U_791
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_791)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_791),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_792 ),
inference(definitional_conversion,[status(esa)],[f_319_2]) ).
cnf(f_319_4,plain,
( c_NthRoot_Osqrt(U_792) = U_791
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_791)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_791),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_792 ),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_1,plain,
! [V_x] :
( hAPP(hAPP(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_320_2,plain,
! [U_793] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_793)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_793
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_793) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
! [U_793] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_793)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_793
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_793) ),
inference(definitional_conversion,[status(esa)],[f_320_2]) ).
cnf(f_320_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_793)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_793
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_793) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_1,plain,
! [V_xa_2] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_xa_2)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_xa_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_xa_2)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_xa_2)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != V_xa_2 ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__pow2__iff]) ).
fof(f_321_2,plain,
! [U_794] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_794)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_794
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_794) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_794)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_794)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_794 ) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
( ! [U_796] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_796)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_796
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_796) )
& ! [U_795] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_795)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_795)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_795 ) ),
inference(miniscope,[status(thm)],[f_321_2]) ).
fof(f_321_4,plain,
( ! [U_796] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_796)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_796
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_796) )
& ! [U_795] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_795)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_795)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_795 ) ),
inference(definitional_conversion,[status(esa)],[f_321_3]) ).
cnf(f_321_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_795)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_795)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != U_795 ),
inference(clausify,[status(thm)],[f_321_4]) ).
cnf(f_321_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_796)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_796
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_796) ),
inference(clausify,[status(thm)],[f_321_4]) ).
fof(f_322_1,plain,
! [V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),c_Groups_Oone__class_Oone(T_a)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Oone__class_Oone(T_a))),c_Groups_Ominus__class_Ominus(T_a,V_x,c_Groups_Oone__class_Oone(T_a)))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_real__squared__diff__one__factored]) ).
fof(f_322_2,plain,
! [U_798,U_797] :
( c_Groups_Ominus__class_Ominus(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_798),c_Groups_Oone__class_Oone(U_797)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),c_Groups_Oplus__class_Oplus(U_797,U_798,c_Groups_Oone__class_Oone(U_797))),c_Groups_Ominus__class_Ominus(U_797,U_798,c_Groups_Oone__class_Oone(U_797)))
| ~ class_Rings_Oring__1(U_797) ),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
! [U_797,U_798] :
( c_Groups_Ominus__class_Ominus(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_798),c_Groups_Oone__class_Oone(U_797)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),c_Groups_Oplus__class_Oplus(U_797,U_798,c_Groups_Oone__class_Oone(U_797))),c_Groups_Ominus__class_Ominus(U_797,U_798,c_Groups_Oone__class_Oone(U_797)))
| ~ class_Rings_Oring__1(U_797) ),
inference(definitional_conversion,[status(esa)],[f_322_2]) ).
cnf(f_322_4,plain,
( c_Groups_Ominus__class_Ominus(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_798),c_Groups_Oone__class_Oone(U_797)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),c_Groups_Oplus__class_Oplus(U_797,U_798,c_Groups_Oone__class_Oone(U_797))),c_Groups_Ominus__class_Ominus(U_797,U_798,c_Groups_Oone__class_Oone(U_797)))
| ~ class_Rings_Oring__1(U_797) ),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_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,hAPP(hAPP(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)))),hAPP(hAPP(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_323_2,plain,
! [U_800,U_799] :
( U_799 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_799),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_800),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_800 ),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
! [U_799,U_800] :
( U_799 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_799),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_800),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_800 ),
inference(definitional_conversion,[status(esa)],[f_323_2]) ).
cnf(f_323_4,plain,
( U_799 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_799),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_800),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_800 ),
inference(clausify,[status(thm)],[f_323_3]) ).
fof(f_324_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,hAPP(hAPP(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)))),hAPP(hAPP(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_324_2,plain,
! [U_802,U_801] :
( U_802 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_801),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_802),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_801 ),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
! [U_802] :
( ! [U_801] : c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_801),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_802),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_801
| U_802 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(miniscope,[status(thm)],[f_324_2]) ).
fof(f_324_4,plain,
! [U_801,U_802] :
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_801),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_802),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_801
| U_802 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(definitional_conversion,[status(esa)],[f_324_3]) ).
cnf(f_324_5,plain,
( c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_801),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_802),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) != U_801
| U_802 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_324_4]) ).
fof(f_325_1,plain,
! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,V_l)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I4_J]) ).
fof(f_325_2,plain,
! [U_803] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_803)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,U_803)),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_803] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_803)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,U_803)),
inference(definitional_conversion,[status(esa)],[f_325_2]) ).
cnf(f_325_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OPls,c_Int_OBit1(U_803)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,U_803)),
inference(clausify,[status(thm)],[f_325_3]) ).
fof(f_326_1,plain,
! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(V_l)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,V_l)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I6_J]) ).
fof(f_326_2,plain,
! [U_804] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_804)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,U_804)),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
! [U_804] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_804)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,U_804)),
inference(definitional_conversion,[status(esa)],[f_326_2]) ).
cnf(f_326_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit1(U_804)) = c_Int_OBit0(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,U_804)),
inference(clausify,[status(thm)],[f_326_3]) ).
fof(f_327_1,plain,
! [V_l] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(V_l)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,V_l)),
inference(fof_nnf,[status(thm)],[fact_diff__bin__simps_I5_J]) ).
fof(f_327_2,plain,
! [U_805] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(U_805)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,U_805)),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
! [U_805] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(U_805)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,U_805)),
inference(definitional_conversion,[status(esa)],[f_327_2]) ).
cnf(f_327_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,c_Int_OBit0(U_805)) = c_Int_OBit1(c_Groups_Ominus__class_Ominus(tc_Int_Oint,c_Int_OMin,U_805)),
inference(clausify,[status(thm)],[f_327_3]) ).
fof(f_328_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)),c_Groups_Ozero__class_Ozero(T_a))
| V_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).
fof(f_328_2,plain,
! [U_808,U_807,U_806] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_806,c_Groups_Oplus__class_Oplus(U_806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_808),U_808)),c_Groups_Ozero__class_Ozero(U_806))
| U_808 != c_Groups_Ozero__class_Ozero(U_806)
| U_807 != c_Groups_Ozero__class_Ozero(U_806) )
& ( ( U_808 = c_Groups_Ozero__class_Ozero(U_806)
& U_807 = c_Groups_Ozero__class_Ozero(U_806) )
| ~ c_Orderings_Oord__class_Oless__eq(U_806,c_Groups_Oplus__class_Oplus(U_806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_808),U_808)),c_Groups_Ozero__class_Ozero(U_806)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_806) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
( ! [U_806,U_807,U_808] :
( U_808 = c_Groups_Ozero__class_Ozero(U_806)
| ~ sP40(U_806,U_807,U_808) )
& ! [U_806,U_807,U_808] :
( U_807 = c_Groups_Ozero__class_Ozero(U_806)
| ~ sP40(U_806,U_807,U_808) )
& ! [U_806,U_807,U_808] :
( c_Orderings_Oord__class_Oless__eq(U_806,c_Groups_Oplus__class_Oplus(U_806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_808),U_808)),c_Groups_Ozero__class_Ozero(U_806))
| U_808 != c_Groups_Ozero__class_Ozero(U_806)
| U_807 != c_Groups_Ozero__class_Ozero(U_806)
| ~ sP41(U_806,U_807,U_808) )
& ! [U_806,U_807,U_808] :
( sP40(U_806,U_807,U_808)
| ~ c_Orderings_Oord__class_Oless__eq(U_806,c_Groups_Oplus__class_Oplus(U_806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_808),U_808)),c_Groups_Ozero__class_Ozero(U_806))
| ~ sP41(U_806,U_807,U_808) )
& ! [U_806,U_807,U_808] :
( sP41(U_806,U_807,U_808)
| ~ class_Rings_Olinordered__ring__strict(U_806) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40,sP41])],[f_328_2]) ).
cnf(f_328_4,plain,
( sP41(U_806,U_807,U_808)
| ~ class_Rings_Olinordered__ring__strict(U_806) ),
inference(clausify,[status(thm)],[f_328_3]) ).
cnf(f_328_5,plain,
( sP40(U_806,U_807,U_808)
| ~ c_Orderings_Oord__class_Oless__eq(U_806,c_Groups_Oplus__class_Oplus(U_806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_808),U_808)),c_Groups_Ozero__class_Ozero(U_806))
| ~ sP41(U_806,U_807,U_808) ),
inference(clausify,[status(thm)],[f_328_3]) ).
cnf(f_328_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_806,c_Groups_Oplus__class_Oplus(U_806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_807),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_808),U_808)),c_Groups_Ozero__class_Ozero(U_806))
| U_808 != c_Groups_Ozero__class_Ozero(U_806)
| U_807 != c_Groups_Ozero__class_Ozero(U_806)
| ~ sP41(U_806,U_807,U_808) ),
inference(clausify,[status(thm)],[f_328_3]) ).
cnf(f_328_7,plain,
( U_807 = c_Groups_Ozero__class_Ozero(U_806)
| ~ sP40(U_806,U_807,U_808) ),
inference(clausify,[status(thm)],[f_328_3]) ).
cnf(f_328_8,plain,
( U_808 = c_Groups_Ozero__class_Ozero(U_806)
| ~ sP40(U_806,U_807,U_808) ),
inference(clausify,[status(thm)],[f_328_3]) ).
fof(f_329_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__ge__zero]) ).
fof(f_329_2,plain,
! [U_811,U_810,U_809] :
( c_Orderings_Oord__class_Oless__eq(U_809,c_Groups_Ozero__class_Ozero(U_809),c_Groups_Oplus__class_Oplus(U_809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_809),U_810),U_810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_809),U_811),U_811)))
| ~ class_Rings_Olinordered__ring(U_809) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
! [U_810,U_811,U_809] :
( c_Orderings_Oord__class_Oless__eq(U_809,c_Groups_Ozero__class_Ozero(U_809),c_Groups_Oplus__class_Oplus(U_809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_809),U_810),U_810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_809),U_811),U_811)))
| ~ class_Rings_Olinordered__ring(U_809) ),
inference(definitional_conversion,[status(esa)],[f_329_2]) ).
cnf(f_329_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_809,c_Groups_Ozero__class_Ozero(U_809),c_Groups_Oplus__class_Oplus(U_809,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_809),U_810),U_810),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_809),U_811),U_811)))
| ~ class_Rings_Olinordered__ring(U_809) ),
inference(clausify,[status(thm)],[f_329_3]) ).
fof(f_330_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_330_2,plain,
! [U_814,U_813,U_812] :
( c_Orderings_Oord__class_Oless__eq(U_812,U_814,U_813)
| c_Orderings_Oord__class_Oless__eq(U_812,U_813,U_814)
| ~ class_Orderings_Olinorder(U_812) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
! [U_813,U_814,U_812] :
( c_Orderings_Oord__class_Oless__eq(U_812,U_814,U_813)
| c_Orderings_Oord__class_Oless__eq(U_812,U_813,U_814)
| ~ class_Orderings_Olinorder(U_812) ),
inference(definitional_conversion,[status(esa)],[f_330_2]) ).
cnf(f_330_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_812,U_814,U_813)
| c_Orderings_Oord__class_Oless__eq(U_812,U_813,U_814)
| ~ class_Orderings_Olinorder(U_812) ),
inference(clausify,[status(thm)],[f_330_3]) ).
fof(f_331_1,plain,
! [V_xa_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funE]) ).
fof(f_331_2,plain,
! [U_819,U_818,U_817,U_816,U_815] :
( c_Orderings_Oord__class_Oless__eq(U_815,hAPP(U_817,U_819),hAPP(U_818,U_819))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_816,U_815),U_817,U_818)
| ~ class_Orderings_Oord(U_815) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_815,U_819,U_816,U_817,U_818] :
( c_Orderings_Oord__class_Oless__eq(U_815,hAPP(U_817,U_819),hAPP(U_818,U_819))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_816,U_815),U_817,U_818)
| ~ class_Orderings_Oord(U_815) ),
inference(definitional_conversion,[status(esa)],[f_331_2]) ).
cnf(f_331_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_815,hAPP(U_817,U_819),hAPP(U_818,U_819))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_816,U_815),U_817,U_818)
| ~ class_Orderings_Oord(U_815) ),
inference(clausify,[status(thm)],[f_331_3]) ).
fof(f_332_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_332_2,plain,
! [U_823,U_822,U_821,U_820] :
( c_Orderings_Oord__class_Oless__eq(U_820,U_823,U_822)
| ~ c_Orderings_Oord__class_Oless__eq(U_820,U_823,U_821)
| ~ c_Orderings_Oord__class_Oless__eq(U_820,U_821,U_822)
| ~ class_Orderings_Oorder(U_820) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
! [U_823,U_820,U_822,U_821] :
( c_Orderings_Oord__class_Oless__eq(U_820,U_823,U_822)
| ~ c_Orderings_Oord__class_Oless__eq(U_820,U_823,U_821)
| ~ c_Orderings_Oord__class_Oless__eq(U_820,U_821,U_822)
| ~ class_Orderings_Oorder(U_820) ),
inference(definitional_conversion,[status(esa)],[f_332_2]) ).
cnf(f_332_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_820,U_823,U_822)
| ~ c_Orderings_Oord__class_Oless__eq(U_820,U_823,U_821)
| ~ c_Orderings_Oord__class_Oless__eq(U_820,U_821,U_822)
| ~ class_Orderings_Oorder(U_820) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_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_333_2,plain,
! [U_826,U_825,U_824] :
( U_826 = U_825
| ~ c_Orderings_Oord__class_Oless__eq(U_824,U_826,U_825)
| ~ c_Orderings_Oord__class_Oless__eq(U_824,U_825,U_826)
| ~ class_Orderings_Oorder(U_824) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
! [U_826,U_824,U_825] :
( U_826 = U_825
| ~ c_Orderings_Oord__class_Oless__eq(U_824,U_826,U_825)
| ~ c_Orderings_Oord__class_Oless__eq(U_824,U_825,U_826)
| ~ class_Orderings_Oorder(U_824) ),
inference(definitional_conversion,[status(esa)],[f_333_2]) ).
cnf(f_333_4,plain,
( U_826 = U_825
| ~ c_Orderings_Oord__class_Oless__eq(U_824,U_826,U_825)
| ~ c_Orderings_Oord__class_Oless__eq(U_824,U_825,U_826)
| ~ class_Orderings_Oorder(U_824) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_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_334_2,plain,
! [U_830,U_829,U_828,U_827] :
( c_Orderings_Oord__class_Oless__eq(U_827,U_828,U_830)
| ~ c_Orderings_Oord__class_Oless__eq(U_827,U_829,U_830)
| ~ c_Orderings_Oord__class_Oless__eq(U_827,U_828,U_829)
| ~ class_Orderings_Opreorder(U_827) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_829,U_828,U_830,U_827] :
( c_Orderings_Oord__class_Oless__eq(U_827,U_828,U_830)
| ~ c_Orderings_Oord__class_Oless__eq(U_827,U_829,U_830)
| ~ c_Orderings_Oord__class_Oless__eq(U_827,U_828,U_829)
| ~ class_Orderings_Opreorder(U_827) ),
inference(definitional_conversion,[status(esa)],[f_334_2]) ).
cnf(f_334_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_827,U_828,U_830)
| ~ c_Orderings_Oord__class_Oless__eq(U_827,U_829,U_830)
| ~ c_Orderings_Oord__class_Oless__eq(U_827,U_828,U_829)
| ~ class_Orderings_Opreorder(U_827) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_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_335_2,plain,
! [U_833,U_832,U_831] :
( U_832 = U_833
| ~ c_Orderings_Oord__class_Oless__eq(U_831,U_833,U_832)
| ~ c_Orderings_Oord__class_Oless__eq(U_831,U_832,U_833)
| ~ class_Orderings_Oorder(U_831) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
! [U_833,U_831,U_832] :
( U_832 = U_833
| ~ c_Orderings_Oord__class_Oless__eq(U_831,U_833,U_832)
| ~ c_Orderings_Oord__class_Oless__eq(U_831,U_832,U_833)
| ~ class_Orderings_Oorder(U_831) ),
inference(definitional_conversion,[status(esa)],[f_335_2]) ).
cnf(f_335_4,plain,
( U_832 = U_833
| ~ c_Orderings_Oord__class_Oless__eq(U_831,U_833,U_832)
| ~ c_Orderings_Oord__class_Oless__eq(U_831,U_832,U_833)
| ~ class_Orderings_Oorder(U_831) ),
inference(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_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_336_2,plain,
! [U_837,U_836,U_835,U_834] :
( c_Orderings_Oord__class_Oless__eq(U_834,U_837,U_836)
| U_835 != U_837
| ~ c_Orderings_Oord__class_Oless__eq(U_834,U_835,U_836)
| ~ class_Orderings_Oorder(U_834) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
! [U_834,U_836,U_837,U_835] :
( c_Orderings_Oord__class_Oless__eq(U_834,U_837,U_836)
| U_835 != U_837
| ~ c_Orderings_Oord__class_Oless__eq(U_834,U_835,U_836)
| ~ class_Orderings_Oorder(U_834) ),
inference(definitional_conversion,[status(esa)],[f_336_2]) ).
cnf(f_336_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_834,U_837,U_836)
| U_835 != U_837
| ~ c_Orderings_Oord__class_Oless__eq(U_834,U_835,U_836)
| ~ class_Orderings_Oorder(U_834) ),
inference(clausify,[status(thm)],[f_336_3]) ).
fof(f_337_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_337_2,plain,
! [U_841,U_840,U_839,U_838] :
( c_Orderings_Oord__class_Oless__eq(U_838,U_839,U_841)
| U_840 != U_841
| ~ c_Orderings_Oord__class_Oless__eq(U_838,U_839,U_840)
| ~ class_Orderings_Oord(U_838) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
fof(f_337_3,plain,
! [U_839,U_840,U_841,U_838] :
( c_Orderings_Oord__class_Oless__eq(U_838,U_839,U_841)
| U_840 != U_841
| ~ c_Orderings_Oord__class_Oless__eq(U_838,U_839,U_840)
| ~ class_Orderings_Oord(U_838) ),
inference(definitional_conversion,[status(esa)],[f_337_2]) ).
cnf(f_337_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_838,U_839,U_841)
| U_840 != U_841
| ~ c_Orderings_Oord__class_Oless__eq(U_838,U_839,U_840)
| ~ class_Orderings_Oord(U_838) ),
inference(clausify,[status(thm)],[f_337_3]) ).
fof(f_338_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_338_2,plain,
! [U_845,U_844,U_843,U_842] :
( c_Orderings_Oord__class_Oless__eq(U_842,U_845,U_843)
| ~ c_Orderings_Oord__class_Oless__eq(U_842,U_845,U_844)
| U_843 != U_844
| ~ class_Orderings_Oorder(U_842) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_845,U_844,U_842,U_843] :
( c_Orderings_Oord__class_Oless__eq(U_842,U_845,U_843)
| ~ c_Orderings_Oord__class_Oless__eq(U_842,U_845,U_844)
| U_843 != U_844
| ~ class_Orderings_Oorder(U_842) ),
inference(definitional_conversion,[status(esa)],[f_338_2]) ).
cnf(f_338_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_842,U_845,U_843)
| ~ c_Orderings_Oord__class_Oless__eq(U_842,U_845,U_844)
| U_843 != U_844
| ~ class_Orderings_Oorder(U_842) ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_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_339_2,plain,
! [U_849,U_848,U_847,U_846] :
( c_Orderings_Oord__class_Oless__eq(U_846,U_847,U_849)
| ~ c_Orderings_Oord__class_Oless__eq(U_846,U_848,U_849)
| U_847 != U_848
| ~ class_Orderings_Oord(U_846) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
! [U_848,U_849,U_847,U_846] :
( c_Orderings_Oord__class_Oless__eq(U_846,U_847,U_849)
| ~ c_Orderings_Oord__class_Oless__eq(U_846,U_848,U_849)
| U_847 != U_848
| ~ class_Orderings_Oord(U_846) ),
inference(definitional_conversion,[status(esa)],[f_339_2]) ).
cnf(f_339_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_846,U_847,U_849)
| ~ c_Orderings_Oord__class_Oless__eq(U_846,U_848,U_849)
| U_847 != U_848
| ~ class_Orderings_Oord(U_846) ),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_1,plain,
! [V_xa_2,V_ya_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
| V_xa_2 != V_ya_2 )
& ( V_xa_2 = V_ya_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).
fof(f_340_2,plain,
! [U_852,U_851,U_850] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_850,U_852,U_851)
| U_852 != U_851 )
& ( U_852 = U_851
| ~ c_Orderings_Oord__class_Oless__eq(U_850,U_852,U_851) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_850,U_851,U_852)
| ~ class_Orderings_Oorder(U_850) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
( ! [U_851,U_852,U_850] :
( c_Orderings_Oord__class_Oless__eq(U_850,U_852,U_851)
| U_852 != U_851
| ~ sP42(U_851,U_852,U_850) )
& ! [U_851,U_852,U_850] :
( U_852 = U_851
| ~ c_Orderings_Oord__class_Oless__eq(U_850,U_852,U_851)
| ~ sP42(U_851,U_852,U_850) )
& ! [U_851,U_852,U_850] :
( sP42(U_851,U_852,U_850)
| ~ c_Orderings_Oord__class_Oless__eq(U_850,U_851,U_852)
| ~ class_Orderings_Oorder(U_850) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42])],[f_340_2]) ).
cnf(f_340_4,plain,
( sP42(U_851,U_852,U_850)
| ~ c_Orderings_Oord__class_Oless__eq(U_850,U_851,U_852)
| ~ class_Orderings_Oorder(U_850) ),
inference(clausify,[status(thm)],[f_340_3]) ).
cnf(f_340_5,plain,
( U_852 = U_851
| ~ c_Orderings_Oord__class_Oless__eq(U_850,U_852,U_851)
| ~ sP42(U_851,U_852,U_850) ),
inference(clausify,[status(thm)],[f_340_3]) ).
cnf(f_340_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_850,U_852,U_851)
| U_852 != U_851
| ~ sP42(U_851,U_852,U_850) ),
inference(clausify,[status(thm)],[f_340_3]) ).
fof(f_341_1,plain,
! [V_xa_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_xa_2),hAPP(V_g_2,V_xa_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__funD]) ).
fof(f_341_2,plain,
! [U_857,U_856,U_855,U_854,U_853] :
( c_Orderings_Oord__class_Oless__eq(U_853,hAPP(U_855,U_857),hAPP(U_856,U_857))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_854,U_853),U_855,U_856)
| ~ class_Orderings_Oord(U_853) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_856,U_854,U_857,U_855,U_853] :
( c_Orderings_Oord__class_Oless__eq(U_853,hAPP(U_855,U_857),hAPP(U_856,U_857))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_854,U_853),U_855,U_856)
| ~ class_Orderings_Oord(U_853) ),
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_853,hAPP(U_855,U_857),hAPP(U_856,U_857))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_854,U_853),U_855,U_856)
| ~ class_Orderings_Oord(U_853) ),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_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_342_2,plain,
! [U_860,U_859,U_858] :
( c_Orderings_Oord__class_Oless__eq(U_858,U_859,U_860)
| U_859 != U_860
| ~ class_Orderings_Opreorder(U_858) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
! [U_860,U_859,U_858] :
( c_Orderings_Oord__class_Oless__eq(U_858,U_859,U_860)
| U_859 != U_860
| ~ class_Orderings_Opreorder(U_858) ),
inference(definitional_conversion,[status(esa)],[f_342_2]) ).
cnf(f_342_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_858,U_859,U_860)
| U_859 != U_860
| ~ class_Orderings_Opreorder(U_858) ),
inference(clausify,[status(thm)],[f_342_3]) ).
fof(f_343_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( V_xa_2 = V_ya_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) )
| V_xa_2 != V_ya_2 ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).
fof(f_343_2,plain,
! [U_863,U_862,U_861] :
( ( ( U_862 = U_863
| ~ c_Orderings_Oord__class_Oless__eq(U_861,U_863,U_862)
| ~ c_Orderings_Oord__class_Oless__eq(U_861,U_862,U_863) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_861,U_863,U_862)
& c_Orderings_Oord__class_Oless__eq(U_861,U_862,U_863) )
| U_862 != U_863 ) )
| ~ class_Orderings_Oorder(U_861) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
( ! [U_862,U_861,U_863] :
( c_Orderings_Oord__class_Oless__eq(U_861,U_863,U_862)
| ~ sP43(U_862,U_861,U_863) )
& ! [U_862,U_861,U_863] :
( c_Orderings_Oord__class_Oless__eq(U_861,U_862,U_863)
| ~ sP43(U_862,U_861,U_863) )
& ! [U_862,U_861,U_863] :
( U_862 = U_863
| ~ c_Orderings_Oord__class_Oless__eq(U_861,U_863,U_862)
| ~ c_Orderings_Oord__class_Oless__eq(U_861,U_862,U_863)
| ~ sP44(U_862,U_861,U_863) )
& ! [U_862,U_861,U_863] :
( sP43(U_862,U_861,U_863)
| U_862 != U_863
| ~ sP44(U_862,U_861,U_863) )
& ! [U_862,U_861,U_863] :
( sP44(U_862,U_861,U_863)
| ~ class_Orderings_Oorder(U_861) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43,sP44])],[f_343_2]) ).
cnf(f_343_4,plain,
( sP44(U_862,U_861,U_863)
| ~ class_Orderings_Oorder(U_861) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_5,plain,
( sP43(U_862,U_861,U_863)
| U_862 != U_863
| ~ sP44(U_862,U_861,U_863) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_6,plain,
( U_862 = U_863
| ~ c_Orderings_Oord__class_Oless__eq(U_861,U_863,U_862)
| ~ c_Orderings_Oord__class_Oless__eq(U_861,U_862,U_863)
| ~ sP44(U_862,U_861,U_863) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_861,U_862,U_863)
| ~ sP43(U_862,U_861,U_863) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_861,U_863,U_862)
| ~ sP43(U_862,U_861,U_863) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_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_344_2,plain,
! [U_866,U_865,U_864] :
( c_Orderings_Oord__class_Oless__eq(U_864,U_866,U_865)
| c_Orderings_Oord__class_Oless__eq(U_864,U_865,U_866)
| ~ class_Orderings_Olinorder(U_864) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
! [U_864,U_865,U_866] :
( c_Orderings_Oord__class_Oless__eq(U_864,U_866,U_865)
| c_Orderings_Oord__class_Oless__eq(U_864,U_865,U_866)
| ~ class_Orderings_Olinorder(U_864) ),
inference(definitional_conversion,[status(esa)],[f_344_2]) ).
cnf(f_344_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_864,U_866,U_865)
| c_Orderings_Oord__class_Oless__eq(U_864,U_865,U_866)
| ~ class_Orderings_Olinorder(U_864) ),
inference(clausify,[status(thm)],[f_344_3]) ).
fof(f_345_1,plain,
! [V_g_2,V_f_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2)
| ? [B_x] : ~ c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x)) )
& ( ! [B_x] : c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,B_x),hAPP(V_g_2,B_x))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_le__fun__def]) ).
fof(f_345_2,plain,
! [U_872,U_871,U_870,U_869] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,U_869),U_871,U_872)
| ? [U_868] : ~ c_Orderings_Oord__class_Oless__eq(U_869,hAPP(U_871,U_868),hAPP(U_872,U_868)) )
& ( ! [U_867] : c_Orderings_Oord__class_Oless__eq(U_869,hAPP(U_871,U_867),hAPP(U_872,U_867))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,U_869),U_871,U_872) ) )
| ~ class_Orderings_Oord(U_869) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
! [U_872,U_871,U_870,U_869] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,U_869),U_871,U_872)
| ~ c_Orderings_Oord__class_Oless__eq(U_869,hAPP(U_871,sK4(U_872,U_871,U_870,U_869)),hAPP(U_872,sK4(U_872,U_871,U_870,U_869))) )
& ( ! [U_867] : c_Orderings_Oord__class_Oless__eq(U_869,hAPP(U_871,U_867),hAPP(U_872,U_867))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,U_869),U_871,U_872) ) )
| ~ class_Orderings_Oord(U_869) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_868,sK4(U_872,U_871,U_870,U_869))],[f_345_2]) ).
fof(f_345_4,plain,
( ! [U_867,U_870,U_871,U_872,U_869] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,U_869),U_871,U_872)
| ~ c_Orderings_Oord__class_Oless__eq(U_869,hAPP(U_871,sK4(U_872,U_871,U_870,U_869)),hAPP(U_872,sK4(U_872,U_871,U_870,U_869)))
| ~ sP45(U_867,U_870,U_871,U_872,U_869) )
& ! [U_867,U_870,U_871,U_872,U_869] :
( c_Orderings_Oord__class_Oless__eq(U_869,hAPP(U_871,U_867),hAPP(U_872,U_867))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,U_869),U_871,U_872)
| ~ sP45(U_867,U_870,U_871,U_872,U_869) )
& ! [U_867,U_870,U_871,U_872,U_869] :
( sP45(U_867,U_870,U_871,U_872,U_869)
| ~ class_Orderings_Oord(U_869) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_345_3]) ).
cnf(f_345_5,plain,
( sP45(U_867,U_870,U_871,U_872,U_869)
| ~ class_Orderings_Oord(U_869) ),
inference(clausify,[status(thm)],[f_345_4]) ).
cnf(f_345_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_869,hAPP(U_871,U_867),hAPP(U_872,U_867))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,U_869),U_871,U_872)
| ~ sP45(U_867,U_870,U_871,U_872,U_869) ),
inference(clausify,[status(thm)],[f_345_4]) ).
cnf(f_345_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_870,U_869),U_871,U_872)
| ~ c_Orderings_Oord__class_Oless__eq(U_869,hAPP(U_871,sK4(U_872,U_871,U_870,U_869)),hAPP(U_872,sK4(U_872,U_871,U_870,U_869)))
| ~ sP45(U_867,U_870,U_871,U_872,U_869) ),
inference(clausify,[status(thm)],[f_345_4]) ).
fof(f_346_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(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_346_2,plain,
! [U_876,U_875,U_874,U_873] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),U_874),U_875)),U_876) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),U_874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),U_875),U_876))
| ~ class_Groups_Oab__semigroup__mult(U_873) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
! [U_876,U_875,U_874,U_873] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),U_874),U_875)),U_876) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),U_874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),U_875),U_876))
| ~ class_Groups_Oab__semigroup__mult(U_873) ),
inference(definitional_conversion,[status(esa)],[f_346_2]) ).
cnf(f_346_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),U_874),U_875)),U_876) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),U_874),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_873),U_875),U_876))
| ~ class_Groups_Oab__semigroup__mult(U_873) ),
inference(clausify,[status(thm)],[f_346_3]) ).
fof(f_347_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_347_2,plain,
! [U_878,U_877] :
( c_Int_Onumber__class_Onumber__of(U_877,c_Int_OBit0(U_878)) = c_Groups_Oplus__class_Oplus(U_877,c_Groups_Oplus__class_Oplus(U_877,c_Groups_Ozero__class_Ozero(U_877),c_Int_Onumber__class_Onumber__of(U_877,U_878)),c_Int_Onumber__class_Onumber__of(U_877,U_878))
| ~ class_Int_Onumber__ring(U_877) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
! [U_878,U_877] :
( c_Int_Onumber__class_Onumber__of(U_877,c_Int_OBit0(U_878)) = c_Groups_Oplus__class_Oplus(U_877,c_Groups_Oplus__class_Oplus(U_877,c_Groups_Ozero__class_Ozero(U_877),c_Int_Onumber__class_Onumber__of(U_877,U_878)),c_Int_Onumber__class_Onumber__of(U_877,U_878))
| ~ class_Int_Onumber__ring(U_877) ),
inference(definitional_conversion,[status(esa)],[f_347_2]) ).
cnf(f_347_4,plain,
( c_Int_Onumber__class_Onumber__of(U_877,c_Int_OBit0(U_878)) = c_Groups_Oplus__class_Oplus(U_877,c_Groups_Oplus__class_Oplus(U_877,c_Groups_Ozero__class_Ozero(U_877),c_Int_Onumber__class_Onumber__of(U_877,U_878)),c_Int_Onumber__class_Onumber__of(U_877,U_878))
| ~ class_Int_Onumber__ring(U_877) ),
inference(clausify,[status(thm)],[f_347_3]) ).
fof(f_348_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_348_2,plain,
! [U_882,U_881,U_880,U_879] :
( c_Groups_Oplus__class_Oplus(U_879,c_Groups_Oplus__class_Oplus(U_879,U_880,U_881),U_882) = c_Groups_Oplus__class_Oplus(U_879,U_880,c_Groups_Oplus__class_Oplus(U_879,U_881,U_882))
| ~ class_Groups_Oab__semigroup__add(U_879) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
! [U_879,U_880,U_881,U_882] :
( c_Groups_Oplus__class_Oplus(U_879,c_Groups_Oplus__class_Oplus(U_879,U_880,U_881),U_882) = c_Groups_Oplus__class_Oplus(U_879,U_880,c_Groups_Oplus__class_Oplus(U_879,U_881,U_882))
| ~ class_Groups_Oab__semigroup__add(U_879) ),
inference(definitional_conversion,[status(esa)],[f_348_2]) ).
cnf(f_348_4,plain,
( c_Groups_Oplus__class_Oplus(U_879,c_Groups_Oplus__class_Oplus(U_879,U_880,U_881),U_882) = c_Groups_Oplus__class_Oplus(U_879,U_880,c_Groups_Oplus__class_Oplus(U_879,U_881,U_882))
| ~ class_Groups_Oab__semigroup__add(U_879) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_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_349_2,plain,
! [U_886,U_885,U_884,U_883] :
( ( ( c_Groups_Oplus__class_Oplus(U_883,U_884,U_885) = c_Groups_Oplus__class_Oplus(U_883,U_884,U_886)
| U_885 != U_886 )
& ( U_885 = U_886
| c_Groups_Oplus__class_Oplus(U_883,U_884,U_885) != c_Groups_Oplus__class_Oplus(U_883,U_884,U_886) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_883) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
( ! [U_885,U_883,U_884,U_886] :
( c_Groups_Oplus__class_Oplus(U_883,U_884,U_885) = c_Groups_Oplus__class_Oplus(U_883,U_884,U_886)
| U_885 != U_886
| ~ sP46(U_885,U_883,U_884,U_886) )
& ! [U_885,U_883,U_884,U_886] :
( U_885 = U_886
| c_Groups_Oplus__class_Oplus(U_883,U_884,U_885) != c_Groups_Oplus__class_Oplus(U_883,U_884,U_886)
| ~ sP46(U_885,U_883,U_884,U_886) )
& ! [U_885,U_883,U_884,U_886] :
( sP46(U_885,U_883,U_884,U_886)
| ~ class_Groups_Ocancel__semigroup__add(U_883) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_349_2]) ).
cnf(f_349_4,plain,
( sP46(U_885,U_883,U_884,U_886)
| ~ class_Groups_Ocancel__semigroup__add(U_883) ),
inference(clausify,[status(thm)],[f_349_3]) ).
cnf(f_349_5,plain,
( U_885 = U_886
| c_Groups_Oplus__class_Oplus(U_883,U_884,U_885) != c_Groups_Oplus__class_Oplus(U_883,U_884,U_886)
| ~ sP46(U_885,U_883,U_884,U_886) ),
inference(clausify,[status(thm)],[f_349_3]) ).
cnf(f_349_6,plain,
( c_Groups_Oplus__class_Oplus(U_883,U_884,U_885) = c_Groups_Oplus__class_Oplus(U_883,U_884,U_886)
| U_885 != U_886
| ~ sP46(U_885,U_883,U_884,U_886) ),
inference(clausify,[status(thm)],[f_349_3]) ).
fof(f_350_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_350_2,plain,
! [U_890,U_889,U_888,U_887] :
( ( ( c_Groups_Oplus__class_Oplus(U_887,U_888,U_889) = c_Groups_Oplus__class_Oplus(U_887,U_890,U_889)
| U_888 != U_890 )
& ( U_888 = U_890
| c_Groups_Oplus__class_Oplus(U_887,U_888,U_889) != c_Groups_Oplus__class_Oplus(U_887,U_890,U_889) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_887) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
( ! [U_887,U_888,U_890,U_889] :
( c_Groups_Oplus__class_Oplus(U_887,U_888,U_889) = c_Groups_Oplus__class_Oplus(U_887,U_890,U_889)
| U_888 != U_890
| ~ sP47(U_887,U_888,U_890,U_889) )
& ! [U_887,U_888,U_890,U_889] :
( U_888 = U_890
| c_Groups_Oplus__class_Oplus(U_887,U_888,U_889) != c_Groups_Oplus__class_Oplus(U_887,U_890,U_889)
| ~ sP47(U_887,U_888,U_890,U_889) )
& ! [U_887,U_888,U_890,U_889] :
( sP47(U_887,U_888,U_890,U_889)
| ~ class_Groups_Ocancel__semigroup__add(U_887) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_350_2]) ).
cnf(f_350_4,plain,
( sP47(U_887,U_888,U_890,U_889)
| ~ class_Groups_Ocancel__semigroup__add(U_887) ),
inference(clausify,[status(thm)],[f_350_3]) ).
cnf(f_350_5,plain,
( U_888 = U_890
| c_Groups_Oplus__class_Oplus(U_887,U_888,U_889) != c_Groups_Oplus__class_Oplus(U_887,U_890,U_889)
| ~ sP47(U_887,U_888,U_890,U_889) ),
inference(clausify,[status(thm)],[f_350_3]) ).
cnf(f_350_6,plain,
( c_Groups_Oplus__class_Oplus(U_887,U_888,U_889) = c_Groups_Oplus__class_Oplus(U_887,U_890,U_889)
| U_888 != U_890
| ~ sP47(U_887,U_888,U_890,U_889) ),
inference(clausify,[status(thm)],[f_350_3]) ).
fof(f_351_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_351_2,plain,
! [U_894,U_893,U_892,U_891] :
( U_893 = U_894
| c_Groups_Oplus__class_Oplus(U_891,U_892,U_893) != c_Groups_Oplus__class_Oplus(U_891,U_892,U_894)
| ~ class_Groups_Ocancel__semigroup__add(U_891) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
! [U_892,U_891,U_893,U_894] :
( U_893 = U_894
| c_Groups_Oplus__class_Oplus(U_891,U_892,U_893) != c_Groups_Oplus__class_Oplus(U_891,U_892,U_894)
| ~ class_Groups_Ocancel__semigroup__add(U_891) ),
inference(definitional_conversion,[status(esa)],[f_351_2]) ).
cnf(f_351_4,plain,
( U_893 = U_894
| c_Groups_Oplus__class_Oplus(U_891,U_892,U_893) != c_Groups_Oplus__class_Oplus(U_891,U_892,U_894)
| ~ class_Groups_Ocancel__semigroup__add(U_891) ),
inference(clausify,[status(thm)],[f_351_3]) ).
fof(f_352_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_352_2,plain,
! [U_898,U_897,U_896,U_895] :
( U_897 = U_898
| c_Groups_Oplus__class_Oplus(U_895,U_896,U_897) != c_Groups_Oplus__class_Oplus(U_895,U_896,U_898)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_895) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
! [U_897,U_895,U_896,U_898] :
( U_897 = U_898
| c_Groups_Oplus__class_Oplus(U_895,U_896,U_897) != c_Groups_Oplus__class_Oplus(U_895,U_896,U_898)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_895) ),
inference(definitional_conversion,[status(esa)],[f_352_2]) ).
cnf(f_352_4,plain,
( U_897 = U_898
| c_Groups_Oplus__class_Oplus(U_895,U_896,U_897) != c_Groups_Oplus__class_Oplus(U_895,U_896,U_898)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_895) ),
inference(clausify,[status(thm)],[f_352_3]) ).
fof(f_353_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_353_2,plain,
! [U_902,U_901,U_900,U_899] :
( U_900 = U_902
| c_Groups_Oplus__class_Oplus(U_899,U_900,U_901) != c_Groups_Oplus__class_Oplus(U_899,U_902,U_901)
| ~ class_Groups_Ocancel__semigroup__add(U_899) ),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
! [U_899,U_900,U_901,U_902] :
( U_900 = U_902
| c_Groups_Oplus__class_Oplus(U_899,U_900,U_901) != c_Groups_Oplus__class_Oplus(U_899,U_902,U_901)
| ~ class_Groups_Ocancel__semigroup__add(U_899) ),
inference(definitional_conversion,[status(esa)],[f_353_2]) ).
cnf(f_353_4,plain,
( U_900 = U_902
| c_Groups_Oplus__class_Oplus(U_899,U_900,U_901) != c_Groups_Oplus__class_Oplus(U_899,U_902,U_901)
| ~ class_Groups_Ocancel__semigroup__add(U_899) ),
inference(clausify,[status(thm)],[f_353_3]) ).
fof(f_354_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_354_2,plain,
! [U_905,U_904,U_903] :
( c_Orderings_Oord__class_Oless__eq(U_903,c_Groups_Ozero__class_Ozero(U_903),hAPP(hAPP(c_Power_Opower__class_Opower(U_903),c_Groups_Oabs__class_Oabs(U_903,U_904)),U_905))
| ~ class_Rings_Olinordered__idom(U_903) ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
! [U_903,U_904,U_905] :
( c_Orderings_Oord__class_Oless__eq(U_903,c_Groups_Ozero__class_Ozero(U_903),hAPP(hAPP(c_Power_Opower__class_Opower(U_903),c_Groups_Oabs__class_Oabs(U_903,U_904)),U_905))
| ~ class_Rings_Olinordered__idom(U_903) ),
inference(definitional_conversion,[status(esa)],[f_354_2]) ).
cnf(f_354_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_903,c_Groups_Ozero__class_Ozero(U_903),hAPP(hAPP(c_Power_Opower__class_Opower(U_903),c_Groups_Oabs__class_Oabs(U_903,U_904)),U_905))
| ~ class_Rings_Olinordered__idom(U_903) ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_1,plain,
! [V_xa_2,T_a] :
( ( ( c_Groups_Oone__class_Oone(T_a) = V_xa_2
| V_xa_2 != c_Groups_Oone__class_Oone(T_a) )
& ( V_xa_2 = c_Groups_Oone__class_Oone(T_a)
| c_Groups_Oone__class_Oone(T_a) != V_xa_2 ) )
| ~ class_Groups_Oone(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).
fof(f_355_2,plain,
! [U_907,U_906] :
( ( ( c_Groups_Oone__class_Oone(U_906) = U_907
| U_907 != c_Groups_Oone__class_Oone(U_906) )
& ( U_907 = c_Groups_Oone__class_Oone(U_906)
| c_Groups_Oone__class_Oone(U_906) != U_907 ) )
| ~ class_Groups_Oone(U_906) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
( ! [U_906,U_907] :
( c_Groups_Oone__class_Oone(U_906) = U_907
| U_907 != c_Groups_Oone__class_Oone(U_906)
| ~ sP48(U_906,U_907) )
& ! [U_906,U_907] :
( U_907 = c_Groups_Oone__class_Oone(U_906)
| c_Groups_Oone__class_Oone(U_906) != U_907
| ~ sP48(U_906,U_907) )
& ! [U_906,U_907] :
( sP48(U_906,U_907)
| ~ class_Groups_Oone(U_906) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_355_2]) ).
cnf(f_355_4,plain,
( sP48(U_906,U_907)
| ~ class_Groups_Oone(U_906) ),
inference(clausify,[status(thm)],[f_355_3]) ).
cnf(f_355_5,plain,
( U_907 = c_Groups_Oone__class_Oone(U_906)
| c_Groups_Oone__class_Oone(U_906) != U_907
| ~ sP48(U_906,U_907) ),
inference(clausify,[status(thm)],[f_355_3]) ).
cnf(f_355_6,plain,
( c_Groups_Oone__class_Oone(U_906) = U_907
| U_907 != c_Groups_Oone__class_Oone(U_906)
| ~ sP48(U_906,U_907) ),
inference(clausify,[status(thm)],[f_355_3]) ).
fof(f_356_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_356_2,plain,
! [U_908] :
( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_908) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_908,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_908,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_908) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
( ! [U_910] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_910) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_910,c_Int_OPls) )
& ! [U_909] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_909,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_909) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_356_2]) ).
fof(f_356_4,plain,
( ! [U_910] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_910) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_910,c_Int_OPls) )
& ! [U_909] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_909,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_909) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_356_3]) ).
cnf(f_356_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_909,c_Int_OPls)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_909) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_356_4]) ).
cnf(f_356_6,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_910) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_910,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_356_4]) ).
fof(f_357_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_357_2,plain,
! [U_911] :
( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_911)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_911,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_911,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_911) ) ),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
( ! [U_913] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_913)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_913,c_Int_OPls) )
& ! [U_912] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_912,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_912) ) ),
inference(miniscope,[status(thm)],[f_357_2]) ).
fof(f_357_4,plain,
( ! [U_913] :
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_913)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_913,c_Int_OPls) )
& ! [U_912] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_912,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_912) ) ),
inference(definitional_conversion,[status(esa)],[f_357_3]) ).
cnf(f_357_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_912,c_Int_OPls)
| c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_912) ),
inference(clausify,[status(thm)],[f_357_4]) ).
cnf(f_357_6,plain,
( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_913)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_913,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_357_4]) ).
fof(f_358_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,hAPP(hAPP(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)))),hAPP(hAPP(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_358_2,plain,
! [U_915,U_914] : 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_914),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_915),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
! [U_914,U_915] : 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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_914),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_915),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(definitional_conversion,[status(esa)],[f_358_2]) ).
cnf(f_358_4,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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_914),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_915),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_358_3]) ).
fof(f_359_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_359_2,plain,
! [U_917,U_916] :
( c_Groups_Oabs__class_Oabs(U_916,c_Groups_Oabs__class_Oabs(U_916,U_917)) = c_Groups_Oabs__class_Oabs(U_916,U_917)
| ~ class_Groups_Oordered__ab__group__add__abs(U_916) ),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
! [U_916,U_917] :
( c_Groups_Oabs__class_Oabs(U_916,c_Groups_Oabs__class_Oabs(U_916,U_917)) = c_Groups_Oabs__class_Oabs(U_916,U_917)
| ~ class_Groups_Oordered__ab__group__add__abs(U_916) ),
inference(definitional_conversion,[status(esa)],[f_359_2]) ).
cnf(f_359_4,plain,
( c_Groups_Oabs__class_Oabs(U_916,c_Groups_Oabs__class_Oabs(U_916,U_917)) = c_Groups_Oabs__class_Oabs(U_916,U_917)
| ~ class_Groups_Oordered__ab__group__add__abs(U_916) ),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_1,plain,
! [V_n,V_a,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),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(hAPP(hAPP(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))))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_odd__0__le__power__imp__0__le]) ).
fof(f_360_2,plain,
! [U_920,U_919,U_918] :
( c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_919)
| ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),hAPP(hAPP(c_Power_Opower__class_Opower(U_918),U_919),c_Nat_OSuc(hAPP(hAPP(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_920))))
| ~ class_Rings_Olinordered__idom(U_918) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
! [U_918,U_919,U_920] :
( c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_919)
| ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),hAPP(hAPP(c_Power_Opower__class_Opower(U_918),U_919),c_Nat_OSuc(hAPP(hAPP(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_920))))
| ~ class_Rings_Olinordered__idom(U_918) ),
inference(definitional_conversion,[status(esa)],[f_360_2]) ).
cnf(f_360_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),U_919)
| ~ c_Orderings_Oord__class_Oless__eq(U_918,c_Groups_Ozero__class_Ozero(U_918),hAPP(hAPP(c_Power_Opower__class_Opower(U_918),U_919),c_Nat_OSuc(hAPP(hAPP(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_920))))
| ~ class_Rings_Olinordered__idom(U_918) ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [V_real2_H_2,V_real1_H_2,V_real2_2,V_real1_2] :
( ( c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) = c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2)
| V_real2_2 != V_real2_H_2
| V_real1_2 != V_real1_H_2 )
& ( ( V_real2_2 = V_real2_H_2
& V_real1_2 = V_real1_H_2 )
| c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2) != c_Complex_Ocomplex_OComplex(V_real1_H_2,V_real2_H_2) ) ),
inference(fof_nnf,[status(thm)],[fact_complex_Oinject]) ).
fof(f_361_2,plain,
! [U_924,U_923,U_922,U_921] :
( ( c_Complex_Ocomplex_OComplex(U_921,U_922) = c_Complex_Ocomplex_OComplex(U_923,U_924)
| U_922 != U_924
| U_921 != U_923 )
& ( ( U_922 = U_924
& U_921 = U_923 )
| c_Complex_Ocomplex_OComplex(U_921,U_922) != c_Complex_Ocomplex_OComplex(U_923,U_924) ) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
( ! [U_932,U_930,U_928,U_926] :
( c_Complex_Ocomplex_OComplex(U_926,U_928) = c_Complex_Ocomplex_OComplex(U_930,U_932)
| U_928 != U_932
| U_926 != U_930 )
& ! [U_931,U_929,U_927,U_925] :
( ( U_927 = U_931
& U_925 = U_929 )
| c_Complex_Ocomplex_OComplex(U_925,U_927) != c_Complex_Ocomplex_OComplex(U_929,U_931) ) ),
inference(miniscope,[status(thm)],[f_361_2]) ).
fof(f_361_4,plain,
( ! [U_931,U_929,U_925,U_927] :
( U_927 = U_931
| ~ sP49(U_931,U_929,U_925,U_927) )
& ! [U_931,U_929,U_925,U_927] :
( U_925 = U_929
| ~ sP49(U_931,U_929,U_925,U_927) )
& ! [U_930,U_926,U_928,U_932] :
( c_Complex_Ocomplex_OComplex(U_926,U_928) = c_Complex_Ocomplex_OComplex(U_930,U_932)
| U_928 != U_932
| U_926 != U_930 )
& ! [U_931,U_929,U_925,U_927] :
( sP49(U_931,U_929,U_925,U_927)
| c_Complex_Ocomplex_OComplex(U_925,U_927) != c_Complex_Ocomplex_OComplex(U_929,U_931) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_361_3]) ).
cnf(f_361_5,plain,
( sP49(U_931,U_929,U_925,U_927)
| c_Complex_Ocomplex_OComplex(U_925,U_927) != c_Complex_Ocomplex_OComplex(U_929,U_931) ),
inference(clausify,[status(thm)],[f_361_4]) ).
cnf(f_361_6,plain,
( c_Complex_Ocomplex_OComplex(U_926,U_928) = c_Complex_Ocomplex_OComplex(U_930,U_932)
| U_928 != U_932
| U_926 != U_930 ),
inference(clausify,[status(thm)],[f_361_4]) ).
cnf(f_361_7,plain,
( U_925 = U_929
| ~ sP49(U_931,U_929,U_925,U_927) ),
inference(clausify,[status(thm)],[f_361_4]) ).
cnf(f_361_8,plain,
( U_927 = U_931
| ~ sP49(U_931,U_929,U_925,U_927) ),
inference(clausify,[status(thm)],[f_361_4]) ).
fof(f_362_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(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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_362_2,plain,
! [U_936,U_935,U_934,U_933] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_933),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_934),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_935),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_936),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
! [U_936,U_935,U_934,U_933] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_933),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_934),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_935),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_936),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(definitional_conversion,[status(esa)],[f_362_2]) ).
cnf(f_362_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_933),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_934),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_935),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_936),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(clausify,[status(thm)],[f_362_3]) ).
fof(f_363_1,plain,
! [V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_xa_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_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_363_2,plain,
! [U_938,U_937] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_937,c_Int_Onumber__class_Onumber__of(U_937,U_938),c_Groups_Ozero__class_Ozero(U_937))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_938,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_938,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(U_937,c_Int_Onumber__class_Onumber__of(U_937,U_938),c_Groups_Ozero__class_Ozero(U_937)) ) )
| ~ class_Rings_Olinordered__idom(U_937)
| ~ class_Int_Onumber__ring(U_937) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
fof(f_363_3,plain,
( ! [U_937,U_938] :
( c_Orderings_Oord__class_Oless__eq(U_937,c_Int_Onumber__class_Onumber__of(U_937,U_938),c_Groups_Ozero__class_Ozero(U_937))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_938,c_Int_OPls)
| ~ sP50(U_937,U_938) )
& ! [U_937,U_938] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_938,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(U_937,c_Int_Onumber__class_Onumber__of(U_937,U_938),c_Groups_Ozero__class_Ozero(U_937))
| ~ sP50(U_937,U_938) )
& ! [U_937,U_938] :
( sP50(U_937,U_938)
| ~ class_Rings_Olinordered__idom(U_937)
| ~ class_Int_Onumber__ring(U_937) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_363_2]) ).
cnf(f_363_4,plain,
( sP50(U_937,U_938)
| ~ class_Rings_Olinordered__idom(U_937)
| ~ class_Int_Onumber__ring(U_937) ),
inference(clausify,[status(thm)],[f_363_3]) ).
cnf(f_363_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_938,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless__eq(U_937,c_Int_Onumber__class_Onumber__of(U_937,U_938),c_Groups_Ozero__class_Ozero(U_937))
| ~ sP50(U_937,U_938) ),
inference(clausify,[status(thm)],[f_363_3]) ).
cnf(f_363_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_937,c_Int_Onumber__class_Onumber__of(U_937,U_938),c_Groups_Ozero__class_Ozero(U_937))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_938,c_Int_OPls)
| ~ sP50(U_937,U_938) ),
inference(clausify,[status(thm)],[f_363_3]) ).
fof(f_364_1,plain,
! [V_ya_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_ya_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_ya_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,V_ya_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_ya_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_364_2,plain,
! [U_940,U_939] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_939,c_Groups_Ozero__class_Ozero(U_939),c_Int_Onumber__class_Onumber__of(U_939,U_940))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_940) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_940)
| ~ c_Orderings_Oord__class_Oless__eq(U_939,c_Groups_Ozero__class_Ozero(U_939),c_Int_Onumber__class_Onumber__of(U_939,U_940)) ) )
| ~ class_Rings_Olinordered__idom(U_939)
| ~ class_Int_Onumber__ring(U_939) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
( ! [U_940,U_939] :
( c_Orderings_Oord__class_Oless__eq(U_939,c_Groups_Ozero__class_Ozero(U_939),c_Int_Onumber__class_Onumber__of(U_939,U_940))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_940)
| ~ sP51(U_940,U_939) )
& ! [U_940,U_939] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_940)
| ~ c_Orderings_Oord__class_Oless__eq(U_939,c_Groups_Ozero__class_Ozero(U_939),c_Int_Onumber__class_Onumber__of(U_939,U_940))
| ~ sP51(U_940,U_939) )
& ! [U_940,U_939] :
( sP51(U_940,U_939)
| ~ class_Rings_Olinordered__idom(U_939)
| ~ class_Int_Onumber__ring(U_939) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_364_2]) ).
cnf(f_364_4,plain,
( sP51(U_940,U_939)
| ~ class_Rings_Olinordered__idom(U_939)
| ~ class_Int_Onumber__ring(U_939) ),
inference(clausify,[status(thm)],[f_364_3]) ).
cnf(f_364_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_940)
| ~ c_Orderings_Oord__class_Oless__eq(U_939,c_Groups_Ozero__class_Ozero(U_939),c_Int_Onumber__class_Onumber__of(U_939,U_940))
| ~ sP51(U_940,U_939) ),
inference(clausify,[status(thm)],[f_364_3]) ).
cnf(f_364_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_939,c_Groups_Ozero__class_Ozero(U_939),c_Int_Onumber__class_Onumber__of(U_939,U_940))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Int_OPls,U_940)
| ~ sP51(U_940,U_939) ),
inference(clausify,[status(thm)],[f_364_3]) ).
fof(f_365_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(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_365_2,plain,
! [U_944,U_943,U_942,U_941] :
( c_Orderings_Oord__class_Oless__eq(U_941,hAPP(hAPP(c_Power_Opower__class_Opower(U_941),U_944),U_943),hAPP(hAPP(c_Power_Opower__class_Opower(U_941),U_944),U_942))
| ~ c_Orderings_Oord__class_Oless__eq(U_941,U_944,c_Groups_Oone__class_Oone(U_941))
| ~ c_Orderings_Oord__class_Oless__eq(U_941,c_Groups_Ozero__class_Ozero(U_941),U_944)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_942,U_943)
| ~ class_Rings_Olinordered__semidom(U_941) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
! [U_941,U_944,U_943,U_942] :
( c_Orderings_Oord__class_Oless__eq(U_941,hAPP(hAPP(c_Power_Opower__class_Opower(U_941),U_944),U_943),hAPP(hAPP(c_Power_Opower__class_Opower(U_941),U_944),U_942))
| ~ c_Orderings_Oord__class_Oless__eq(U_941,U_944,c_Groups_Oone__class_Oone(U_941))
| ~ c_Orderings_Oord__class_Oless__eq(U_941,c_Groups_Ozero__class_Ozero(U_941),U_944)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_942,U_943)
| ~ class_Rings_Olinordered__semidom(U_941) ),
inference(definitional_conversion,[status(esa)],[f_365_2]) ).
cnf(f_365_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_941,hAPP(hAPP(c_Power_Opower__class_Opower(U_941),U_944),U_943),hAPP(hAPP(c_Power_Opower__class_Opower(U_941),U_944),U_942))
| ~ c_Orderings_Oord__class_Oless__eq(U_941,U_944,c_Groups_Oone__class_Oone(U_941))
| ~ c_Orderings_Oord__class_Oless__eq(U_941,c_Groups_Ozero__class_Ozero(U_941),U_944)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_942,U_943)
| ~ class_Rings_Olinordered__semidom(U_941) ),
inference(clausify,[status(thm)],[f_365_3]) ).
fof(f_366_1,plain,
! [V_z] : hAPP(hAPP(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_z) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
inference(fof_nnf,[status(thm)],[fact_nat__mult__2]) ).
fof(f_366_2,plain,
! [U_945] : hAPP(hAPP(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_945) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_945,U_945),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
! [U_945] : hAPP(hAPP(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_945) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_945,U_945),
inference(definitional_conversion,[status(esa)],[f_366_2]) ).
cnf(f_366_4,plain,
hAPP(hAPP(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_945) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_945,U_945),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_1,plain,
! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_z),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_z,V_z),
inference(fof_nnf,[status(thm)],[fact_nat__mult__2__right]) ).
fof(f_367_2,plain,
! [U_946] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_946),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_946,U_946),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
! [U_946] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_946),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_946,U_946),
inference(definitional_conversion,[status(esa)],[f_367_2]) ).
cnf(f_367_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_946),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_946,U_946),
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_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]) ).
fof(f_368_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(definitional_conversion,[status(esa)],[f_368_1]) ).
cnf(f_368_3,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_368_2]) ).
fof(f_369_1,plain,
! [V_a_2,T_a] :
( ( ( hAPP(hAPP(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)
| hAPP(hAPP(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_369_2,plain,
! [U_948,U_947] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_947),U_948),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_947)
| U_948 != c_Groups_Ozero__class_Ozero(U_947) )
& ( U_948 = c_Groups_Ozero__class_Ozero(U_947)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_947),U_948),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_947) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_947) ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
( ! [U_948,U_947] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_947),U_948),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_947)
| U_948 != c_Groups_Ozero__class_Ozero(U_947)
| ~ sP52(U_948,U_947) )
& ! [U_948,U_947] :
( U_948 = c_Groups_Ozero__class_Ozero(U_947)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_947),U_948),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_947)
| ~ sP52(U_948,U_947) )
& ! [U_948,U_947] :
( sP52(U_948,U_947)
| ~ class_Rings_Oring__1__no__zero__divisors(U_947) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_369_2]) ).
cnf(f_369_4,plain,
( sP52(U_948,U_947)
| ~ class_Rings_Oring__1__no__zero__divisors(U_947) ),
inference(clausify,[status(thm)],[f_369_3]) ).
cnf(f_369_5,plain,
( U_948 = c_Groups_Ozero__class_Ozero(U_947)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_947),U_948),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != c_Groups_Ozero__class_Ozero(U_947)
| ~ sP52(U_948,U_947) ),
inference(clausify,[status(thm)],[f_369_3]) ).
cnf(f_369_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_947),U_948),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_947)
| U_948 != c_Groups_Ozero__class_Ozero(U_947)
| ~ sP52(U_948,U_947) ),
inference(clausify,[status(thm)],[f_369_3]) ).
fof(f_370_1,plain,
! [T_a] :
( hAPP(hAPP(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_370_2,plain,
! [U_949] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_949),c_Groups_Ozero__class_Ozero(U_949)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_949)
| ~ class_Rings_Osemiring__1(U_949) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
fof(f_370_3,plain,
! [U_949] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_949),c_Groups_Ozero__class_Ozero(U_949)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_949)
| ~ class_Rings_Osemiring__1(U_949) ),
inference(definitional_conversion,[status(esa)],[f_370_2]) ).
cnf(f_370_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_949),c_Groups_Ozero__class_Ozero(U_949)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(U_949)
| ~ class_Rings_Osemiring__1(U_949) ),
inference(clausify,[status(thm)],[f_370_3]) ).
fof(f_371_1,plain,
! [V_x] : c_NthRoot_Osqrt(hAPP(hAPP(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_371_2,plain,
! [U_950] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_950),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_950),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
! [U_950] : c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_950),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_950),
inference(definitional_conversion,[status(esa)],[f_371_2]) ).
cnf(f_371_4,plain,
c_NthRoot_Osqrt(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_950),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_950),
inference(clausify,[status(thm)],[f_371_3]) ).
fof(f_372_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)
| hAPP(hAPP(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)))) != hAPP(hAPP(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_372_2,plain,
! [U_953,U_952,U_951] :
( U_952 = U_953
| ~ c_Orderings_Oord__class_Oless__eq(U_951,c_Groups_Ozero__class_Ozero(U_951),U_953)
| ~ c_Orderings_Oord__class_Oless__eq(U_951,c_Groups_Ozero__class_Ozero(U_951),U_952)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_951),U_952),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_951),U_953),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_951) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
fof(f_372_3,plain,
! [U_951,U_952,U_953] :
( U_952 = U_953
| ~ c_Orderings_Oord__class_Oless__eq(U_951,c_Groups_Ozero__class_Ozero(U_951),U_953)
| ~ c_Orderings_Oord__class_Oless__eq(U_951,c_Groups_Ozero__class_Ozero(U_951),U_952)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_951),U_952),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_951),U_953),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_951) ),
inference(definitional_conversion,[status(esa)],[f_372_2]) ).
cnf(f_372_4,plain,
( U_952 = U_953
| ~ c_Orderings_Oord__class_Oless__eq(U_951,c_Groups_Ozero__class_Ozero(U_951),U_953)
| ~ c_Orderings_Oord__class_Oless__eq(U_951,c_Groups_Ozero__class_Ozero(U_951),U_952)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_951),U_952),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_951),U_953),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
| ~ class_Rings_Olinordered__semidom(U_951) ),
inference(clausify,[status(thm)],[f_372_3]) ).
fof(f_373_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,hAPP(hAPP(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)))),hAPP(hAPP(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_373_2,plain,
! [U_956,U_955,U_954] :
( c_Orderings_Oord__class_Oless__eq(U_954,U_955,U_956)
| ~ c_Orderings_Oord__class_Oless__eq(U_954,c_Groups_Ozero__class_Ozero(U_954),U_956)
| ~ c_Orderings_Oord__class_Oless__eq(U_954,hAPP(hAPP(c_Power_Opower__class_Opower(U_954),U_955),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_954),U_956),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_954) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
! [U_956,U_954,U_955] :
( c_Orderings_Oord__class_Oless__eq(U_954,U_955,U_956)
| ~ c_Orderings_Oord__class_Oless__eq(U_954,c_Groups_Ozero__class_Ozero(U_954),U_956)
| ~ c_Orderings_Oord__class_Oless__eq(U_954,hAPP(hAPP(c_Power_Opower__class_Opower(U_954),U_955),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_954),U_956),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_954) ),
inference(definitional_conversion,[status(esa)],[f_373_2]) ).
cnf(f_373_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_954,U_955,U_956)
| ~ c_Orderings_Oord__class_Oless__eq(U_954,c_Groups_Ozero__class_Ozero(U_954),U_956)
| ~ c_Orderings_Oord__class_Oless__eq(U_954,hAPP(hAPP(c_Power_Opower__class_Opower(U_954),U_955),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_954),U_956),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_954) ),
inference(clausify,[status(thm)],[f_373_3]) ).
fof(f_374_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_374_2,plain,
! [U_958,U_957] :
( c_Orderings_Oord__class_Oless__eq(U_957,c_Groups_Ozero__class_Ozero(U_957),hAPP(hAPP(c_Power_Opower__class_Opower(U_957),U_958),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(U_957) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
! [U_957,U_958] :
( c_Orderings_Oord__class_Oless__eq(U_957,c_Groups_Ozero__class_Ozero(U_957),hAPP(hAPP(c_Power_Opower__class_Opower(U_957),U_958),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(U_957) ),
inference(definitional_conversion,[status(esa)],[f_374_2]) ).
cnf(f_374_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_957,c_Groups_Ozero__class_Ozero(U_957),hAPP(hAPP(c_Power_Opower__class_Opower(U_957),U_958),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__idom(U_957) ),
inference(clausify,[status(thm)],[f_374_3]) ).
fof(f_375_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_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_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_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_375_2,plain,
! [U_961,U_960,U_959] :
( ( ( c_Groups_Oplus__class_Oplus(U_959,hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_960),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_961),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_959)
| U_961 != c_Groups_Ozero__class_Ozero(U_959)
| U_960 != c_Groups_Ozero__class_Ozero(U_959) )
& ( ( U_961 = c_Groups_Ozero__class_Ozero(U_959)
& U_960 = c_Groups_Ozero__class_Ozero(U_959) )
| c_Groups_Oplus__class_Oplus(U_959,hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_960),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_961),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_959) ) )
| ~ class_Rings_Olinordered__idom(U_959) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
( ! [U_959,U_960,U_961] :
( U_961 = c_Groups_Ozero__class_Ozero(U_959)
| ~ sP53(U_959,U_960,U_961) )
& ! [U_959,U_960,U_961] :
( U_960 = c_Groups_Ozero__class_Ozero(U_959)
| ~ sP53(U_959,U_960,U_961) )
& ! [U_959,U_960,U_961] :
( c_Groups_Oplus__class_Oplus(U_959,hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_960),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_961),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_959)
| U_961 != c_Groups_Ozero__class_Ozero(U_959)
| U_960 != c_Groups_Ozero__class_Ozero(U_959)
| ~ sP54(U_959,U_960,U_961) )
& ! [U_959,U_960,U_961] :
( sP53(U_959,U_960,U_961)
| c_Groups_Oplus__class_Oplus(U_959,hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_960),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_961),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_959)
| ~ sP54(U_959,U_960,U_961) )
& ! [U_959,U_960,U_961] :
( sP54(U_959,U_960,U_961)
| ~ class_Rings_Olinordered__idom(U_959) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53,sP54])],[f_375_2]) ).
cnf(f_375_4,plain,
( sP54(U_959,U_960,U_961)
| ~ class_Rings_Olinordered__idom(U_959) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_5,plain,
( sP53(U_959,U_960,U_961)
| c_Groups_Oplus__class_Oplus(U_959,hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_960),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_961),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) != c_Groups_Ozero__class_Ozero(U_959)
| ~ sP54(U_959,U_960,U_961) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_6,plain,
( c_Groups_Oplus__class_Oplus(U_959,hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_960),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_959),U_961),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(U_959)
| U_961 != c_Groups_Ozero__class_Ozero(U_959)
| U_960 != c_Groups_Ozero__class_Ozero(U_959)
| ~ sP54(U_959,U_960,U_961) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_7,plain,
( U_960 = c_Groups_Ozero__class_Ozero(U_959)
| ~ sP53(U_959,U_960,U_961) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_8,plain,
( U_961 = c_Groups_Ozero__class_Ozero(U_959)
| ~ sP53(U_959,U_960,U_961) ),
inference(clausify,[status(thm)],[f_375_3]) ).
fof(f_376_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,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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_376_2,plain,
! [U_965,U_964,U_963,U_962] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_962,U_963)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_964,U_965)),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_962),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_964),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_963),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_965),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
! [U_963,U_964,U_965,U_962] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_962,U_963)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_964,U_965)),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_962),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_964),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_963),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_965),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(definitional_conversion,[status(esa)],[f_376_2]) ).
cnf(f_376_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_962,U_963)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_964,U_965)),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_962),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_964),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_963),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_965),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),
inference(clausify,[status(thm)],[f_376_3]) ).
fof(f_377_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,hAPP(hAPP(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)))),hAPP(hAPP(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_377_2,plain,
! [U_967,U_966] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_966,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_967),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_966),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
! [U_966,U_967] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_966,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_967),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_966),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(definitional_conversion,[status(esa)],[f_377_2]) ).
cnf(f_377_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_966,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_967),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_966),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_377_3]) ).
fof(f_378_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,hAPP(hAPP(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)))),hAPP(hAPP(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_378_2,plain,
! [U_969,U_968] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_968,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_968),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_969),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
! [U_968,U_969] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_968,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_968),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_969),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(definitional_conversion,[status(esa)],[f_378_2]) ).
cnf(f_378_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_968,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_968),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_969),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_1,plain,
! [V_ya,V_xa,V_y,V_x] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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)))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(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)))),hAPP(hAPP(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,hAPP(hAPP(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)))),hAPP(hAPP(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__squared__eq]) ).
fof(f_379_2,plain,
! [U_973,U_972,U_971,U_970] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_970),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_971),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_972),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_973),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_970),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_971),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_972),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_973),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
! [U_970,U_971,U_972,U_973] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_970),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_971),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_972),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_973),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_970),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_971),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_972),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_973),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(definitional_conversion,[status(esa)],[f_379_2]) ).
cnf(f_379_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_970),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_971),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_972),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_973),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_970),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_971),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,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_972),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_973),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(clausify,[status(thm)],[f_379_3]) ).
fof(f_380_1,plain,
! [V_ya_2,V_xa_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_ya_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_ya_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_xa_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_ya_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_ya_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_380_2,plain,
! [U_975,U_974] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_974),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_975),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_975 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_974 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_975 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_974 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_974),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_975),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_380_1]) ).
fof(f_380_3,plain,
( ! [U_979,U_977] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_977),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_979),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_979 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_977 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_978,U_976] :
( ( U_978 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_976 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_976),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_978),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_380_2]) ).
fof(f_380_4,plain,
( ! [U_976,U_978] :
( U_978 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP55(U_976,U_978) )
& ! [U_976,U_978] :
( U_976 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP55(U_976,U_978) )
& ! [U_979,U_977] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_977),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_979),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_979 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_977 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_976,U_978] :
( sP55(U_976,U_978)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_976),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_978),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(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_380_3]) ).
cnf(f_380_5,plain,
( sP55(U_976,U_978)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_976),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_978),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_380_4]) ).
cnf(f_380_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_977),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_979),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_979 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_977 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_380_4]) ).
cnf(f_380_7,plain,
( U_976 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP55(U_976,U_978) ),
inference(clausify,[status(thm)],[f_380_4]) ).
cnf(f_380_8,plain,
( U_978 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP55(U_976,U_978) ),
inference(clausify,[status(thm)],[f_380_4]) ).
fof(f_381_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_381_2,plain,
! [U_983,U_982,U_981,U_980] :
( c_Orderings_Oord__class_Oless__eq(U_980,U_982,U_983)
| ~ c_Orderings_Oord__class_Oless__eq(U_980,c_Groups_Oplus__class_Oplus(U_980,U_981,U_982),c_Groups_Oplus__class_Oplus(U_980,U_981,U_983))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_980) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
! [U_980,U_983,U_981,U_982] :
( c_Orderings_Oord__class_Oless__eq(U_980,U_982,U_983)
| ~ c_Orderings_Oord__class_Oless__eq(U_980,c_Groups_Oplus__class_Oplus(U_980,U_981,U_982),c_Groups_Oplus__class_Oplus(U_980,U_981,U_983))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_980) ),
inference(definitional_conversion,[status(esa)],[f_381_2]) ).
cnf(f_381_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_980,U_982,U_983)
| ~ c_Orderings_Oord__class_Oless__eq(U_980,c_Groups_Oplus__class_Oplus(U_980,U_981,U_982),c_Groups_Oplus__class_Oplus(U_980,U_981,U_983))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_980) ),
inference(clausify,[status(thm)],[f_381_3]) ).
fof(f_382_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_382_2,plain,
! [U_987,U_986,U_985,U_984] :
( c_Orderings_Oord__class_Oless__eq(U_984,U_985,U_987)
| ~ c_Orderings_Oord__class_Oless__eq(U_984,c_Groups_Oplus__class_Oplus(U_984,U_985,U_986),c_Groups_Oplus__class_Oplus(U_984,U_987,U_986))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_984) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
! [U_985,U_986,U_984,U_987] :
( c_Orderings_Oord__class_Oless__eq(U_984,U_985,U_987)
| ~ c_Orderings_Oord__class_Oless__eq(U_984,c_Groups_Oplus__class_Oplus(U_984,U_985,U_986),c_Groups_Oplus__class_Oplus(U_984,U_987,U_986))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_984) ),
inference(definitional_conversion,[status(esa)],[f_382_2]) ).
cnf(f_382_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_984,U_985,U_987)
| ~ c_Orderings_Oord__class_Oless__eq(U_984,c_Groups_Oplus__class_Oplus(U_984,U_985,U_986),c_Groups_Oplus__class_Oplus(U_984,U_987,U_986))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_984) ),
inference(clausify,[status(thm)],[f_382_3]) ).
fof(f_383_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_383_2,plain,
! [U_992,U_991,U_990,U_989,U_988] :
( c_Orderings_Oord__class_Oless__eq(U_988,c_Groups_Oplus__class_Oplus(U_988,U_989,U_991),c_Groups_Oplus__class_Oplus(U_988,U_990,U_992))
| ~ c_Orderings_Oord__class_Oless__eq(U_988,U_991,U_992)
| ~ c_Orderings_Oord__class_Oless__eq(U_988,U_989,U_990)
| ~ class_Groups_Oordered__ab__semigroup__add(U_988) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
! [U_990,U_988,U_989,U_991,U_992] :
( c_Orderings_Oord__class_Oless__eq(U_988,c_Groups_Oplus__class_Oplus(U_988,U_989,U_991),c_Groups_Oplus__class_Oplus(U_988,U_990,U_992))
| ~ c_Orderings_Oord__class_Oless__eq(U_988,U_991,U_992)
| ~ c_Orderings_Oord__class_Oless__eq(U_988,U_989,U_990)
| ~ class_Groups_Oordered__ab__semigroup__add(U_988) ),
inference(definitional_conversion,[status(esa)],[f_383_2]) ).
cnf(f_383_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_988,c_Groups_Oplus__class_Oplus(U_988,U_989,U_991),c_Groups_Oplus__class_Oplus(U_988,U_990,U_992))
| ~ c_Orderings_Oord__class_Oless__eq(U_988,U_991,U_992)
| ~ c_Orderings_Oord__class_Oless__eq(U_988,U_989,U_990)
| ~ class_Groups_Oordered__ab__semigroup__add(U_988) ),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_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_384_2,plain,
! [U_996,U_995,U_994,U_993] :
( c_Orderings_Oord__class_Oless__eq(U_993,c_Groups_Oplus__class_Oplus(U_993,U_996,U_994),c_Groups_Oplus__class_Oplus(U_993,U_996,U_995))
| ~ c_Orderings_Oord__class_Oless__eq(U_993,U_994,U_995)
| ~ class_Groups_Oordered__ab__semigroup__add(U_993) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
! [U_995,U_993,U_996,U_994] :
( c_Orderings_Oord__class_Oless__eq(U_993,c_Groups_Oplus__class_Oplus(U_993,U_996,U_994),c_Groups_Oplus__class_Oplus(U_993,U_996,U_995))
| ~ c_Orderings_Oord__class_Oless__eq(U_993,U_994,U_995)
| ~ class_Groups_Oordered__ab__semigroup__add(U_993) ),
inference(definitional_conversion,[status(esa)],[f_384_2]) ).
cnf(f_384_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_993,c_Groups_Oplus__class_Oplus(U_993,U_996,U_994),c_Groups_Oplus__class_Oplus(U_993,U_996,U_995))
| ~ c_Orderings_Oord__class_Oless__eq(U_993,U_994,U_995)
| ~ class_Groups_Oordered__ab__semigroup__add(U_993) ),
inference(clausify,[status(thm)],[f_384_3]) ).
fof(f_385_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_385_2,plain,
! [U_1000,U_999,U_998,U_997] :
( c_Orderings_Oord__class_Oless__eq(U_997,c_Groups_Oplus__class_Oplus(U_997,U_998,U_1000),c_Groups_Oplus__class_Oplus(U_997,U_999,U_1000))
| ~ c_Orderings_Oord__class_Oless__eq(U_997,U_998,U_999)
| ~ class_Groups_Oordered__ab__semigroup__add(U_997) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
! [U_1000,U_998,U_999,U_997] :
( c_Orderings_Oord__class_Oless__eq(U_997,c_Groups_Oplus__class_Oplus(U_997,U_998,U_1000),c_Groups_Oplus__class_Oplus(U_997,U_999,U_1000))
| ~ c_Orderings_Oord__class_Oless__eq(U_997,U_998,U_999)
| ~ class_Groups_Oordered__ab__semigroup__add(U_997) ),
inference(definitional_conversion,[status(esa)],[f_385_2]) ).
cnf(f_385_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_997,c_Groups_Oplus__class_Oplus(U_997,U_998,U_1000),c_Groups_Oplus__class_Oplus(U_997,U_999,U_1000))
| ~ c_Orderings_Oord__class_Oless__eq(U_997,U_998,U_999)
| ~ class_Groups_Oordered__ab__semigroup__add(U_997) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_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_386_2,plain,
! [U_1004,U_1003,U_1002,U_1001] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1003),c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1004))
| ~ c_Orderings_Oord__class_Oless__eq(U_1001,U_1003,U_1004) )
& ( c_Orderings_Oord__class_Oless__eq(U_1001,U_1003,U_1004)
| ~ c_Orderings_Oord__class_Oless__eq(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1003),c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1004)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1001) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
( ! [U_1003,U_1001,U_1002,U_1004] :
( c_Orderings_Oord__class_Oless__eq(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1003),c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1004))
| ~ c_Orderings_Oord__class_Oless__eq(U_1001,U_1003,U_1004)
| ~ sP56(U_1003,U_1001,U_1002,U_1004) )
& ! [U_1003,U_1001,U_1002,U_1004] :
( c_Orderings_Oord__class_Oless__eq(U_1001,U_1003,U_1004)
| ~ c_Orderings_Oord__class_Oless__eq(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1003),c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1004))
| ~ sP56(U_1003,U_1001,U_1002,U_1004) )
& ! [U_1003,U_1001,U_1002,U_1004] :
( sP56(U_1003,U_1001,U_1002,U_1004)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1001) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_386_2]) ).
cnf(f_386_4,plain,
( sP56(U_1003,U_1001,U_1002,U_1004)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1001) ),
inference(clausify,[status(thm)],[f_386_3]) ).
cnf(f_386_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1001,U_1003,U_1004)
| ~ c_Orderings_Oord__class_Oless__eq(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1003),c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1004))
| ~ sP56(U_1003,U_1001,U_1002,U_1004) ),
inference(clausify,[status(thm)],[f_386_3]) ).
cnf(f_386_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1003),c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1004))
| ~ c_Orderings_Oord__class_Oless__eq(U_1001,U_1003,U_1004)
| ~ sP56(U_1003,U_1001,U_1002,U_1004) ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_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_387_2,plain,
! [U_1008,U_1007,U_1006,U_1005] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1005,c_Groups_Oplus__class_Oplus(U_1005,U_1006,U_1007),c_Groups_Oplus__class_Oplus(U_1005,U_1008,U_1007))
| ~ c_Orderings_Oord__class_Oless__eq(U_1005,U_1006,U_1008) )
& ( c_Orderings_Oord__class_Oless__eq(U_1005,U_1006,U_1008)
| ~ c_Orderings_Oord__class_Oless__eq(U_1005,c_Groups_Oplus__class_Oplus(U_1005,U_1006,U_1007),c_Groups_Oplus__class_Oplus(U_1005,U_1008,U_1007)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1005) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
( ! [U_1008,U_1005,U_1006,U_1007] :
( c_Orderings_Oord__class_Oless__eq(U_1005,c_Groups_Oplus__class_Oplus(U_1005,U_1006,U_1007),c_Groups_Oplus__class_Oplus(U_1005,U_1008,U_1007))
| ~ c_Orderings_Oord__class_Oless__eq(U_1005,U_1006,U_1008)
| ~ sP57(U_1008,U_1005,U_1006,U_1007) )
& ! [U_1008,U_1005,U_1006,U_1007] :
( c_Orderings_Oord__class_Oless__eq(U_1005,U_1006,U_1008)
| ~ c_Orderings_Oord__class_Oless__eq(U_1005,c_Groups_Oplus__class_Oplus(U_1005,U_1006,U_1007),c_Groups_Oplus__class_Oplus(U_1005,U_1008,U_1007))
| ~ sP57(U_1008,U_1005,U_1006,U_1007) )
& ! [U_1008,U_1005,U_1006,U_1007] :
( sP57(U_1008,U_1005,U_1006,U_1007)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1005) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57])],[f_387_2]) ).
cnf(f_387_4,plain,
( sP57(U_1008,U_1005,U_1006,U_1007)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1005) ),
inference(clausify,[status(thm)],[f_387_3]) ).
cnf(f_387_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1005,U_1006,U_1008)
| ~ c_Orderings_Oord__class_Oless__eq(U_1005,c_Groups_Oplus__class_Oplus(U_1005,U_1006,U_1007),c_Groups_Oplus__class_Oplus(U_1005,U_1008,U_1007))
| ~ sP57(U_1008,U_1005,U_1006,U_1007) ),
inference(clausify,[status(thm)],[f_387_3]) ).
cnf(f_387_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1005,c_Groups_Oplus__class_Oplus(U_1005,U_1006,U_1007),c_Groups_Oplus__class_Oplus(U_1005,U_1008,U_1007))
| ~ c_Orderings_Oord__class_Oless__eq(U_1005,U_1006,U_1008)
| ~ sP57(U_1008,U_1005,U_1006,U_1007) ),
inference(clausify,[status(thm)],[f_387_3]) ).
fof(f_388_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_388_2,plain,
! [U_1010,U_1009] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1010),c_Groups_Oone__class_Oone(U_1009)) = U_1010
| ~ class_Groups_Ocomm__monoid__mult(U_1009) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
! [U_1009,U_1010] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1010),c_Groups_Oone__class_Oone(U_1009)) = U_1010
| ~ class_Groups_Ocomm__monoid__mult(U_1009) ),
inference(definitional_conversion,[status(esa)],[f_388_2]) ).
cnf(f_388_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1009),U_1010),c_Groups_Oone__class_Oone(U_1009)) = U_1010
| ~ class_Groups_Ocomm__monoid__mult(U_1009) ),
inference(clausify,[status(thm)],[f_388_3]) ).
fof(f_389_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_389_2,plain,
! [U_1012,U_1011] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1011),U_1012),c_Groups_Oone__class_Oone(U_1011)) = U_1012
| ~ class_Groups_Omonoid__mult(U_1011) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
fof(f_389_3,plain,
! [U_1011,U_1012] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1011),U_1012),c_Groups_Oone__class_Oone(U_1011)) = U_1012
| ~ class_Groups_Omonoid__mult(U_1011) ),
inference(definitional_conversion,[status(esa)],[f_389_2]) ).
cnf(f_389_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1011),U_1012),c_Groups_Oone__class_Oone(U_1011)) = U_1012
| ~ class_Groups_Omonoid__mult(U_1011) ),
inference(clausify,[status(thm)],[f_389_3]) ).
fof(f_390_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_390_2,plain,
! [U_1014,U_1013] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1013),c_Groups_Oone__class_Oone(U_1013)),U_1014) = U_1014
| ~ class_Groups_Ocomm__monoid__mult(U_1013) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
! [U_1013,U_1014] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1013),c_Groups_Oone__class_Oone(U_1013)),U_1014) = U_1014
| ~ class_Groups_Ocomm__monoid__mult(U_1013) ),
inference(definitional_conversion,[status(esa)],[f_390_2]) ).
cnf(f_390_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1013),c_Groups_Oone__class_Oone(U_1013)),U_1014) = U_1014
| ~ class_Groups_Ocomm__monoid__mult(U_1013) ),
inference(clausify,[status(thm)],[f_390_3]) ).
fof(f_391_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_391_2,plain,
! [U_1016,U_1015] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1015),c_Groups_Oone__class_Oone(U_1015)),U_1016) = U_1016
| ~ class_Groups_Omonoid__mult(U_1015) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
! [U_1015,U_1016] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1015),c_Groups_Oone__class_Oone(U_1015)),U_1016) = U_1016
| ~ class_Groups_Omonoid__mult(U_1015) ),
inference(definitional_conversion,[status(esa)],[f_391_2]) ).
cnf(f_391_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1015),c_Groups_Oone__class_Oone(U_1015)),U_1016) = U_1016
| ~ class_Groups_Omonoid__mult(U_1015) ),
inference(clausify,[status(thm)],[f_391_3]) ).
fof(f_392_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_392_2,plain,
! [U_1019,U_1018,U_1017] :
( c_Orderings_Oord__class_Oless__eq(U_1017,U_1018,U_1019)
| ~ c_Orderings_Oord__class_Oless__eq(U_1017,c_Groups_Oabs__class_Oabs(U_1017,U_1018),U_1019)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1017) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
! [U_1017,U_1018,U_1019] :
( c_Orderings_Oord__class_Oless__eq(U_1017,U_1018,U_1019)
| ~ c_Orderings_Oord__class_Oless__eq(U_1017,c_Groups_Oabs__class_Oabs(U_1017,U_1018),U_1019)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1017) ),
inference(definitional_conversion,[status(esa)],[f_392_2]) ).
cnf(f_392_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1017,U_1018,U_1019)
| ~ c_Orderings_Oord__class_Oless__eq(U_1017,c_Groups_Oabs__class_Oabs(U_1017,U_1018),U_1019)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1017) ),
inference(clausify,[status(thm)],[f_392_3]) ).
fof(f_393_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_393_2,plain,
! [U_1021,U_1020] :
( c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,c_Groups_Oabs__class_Oabs(U_1020,U_1021))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1020) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
! [U_1020,U_1021] :
( c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,c_Groups_Oabs__class_Oabs(U_1020,U_1021))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1020) ),
inference(definitional_conversion,[status(esa)],[f_393_2]) ).
cnf(f_393_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1020,U_1021,c_Groups_Oabs__class_Oabs(U_1020,U_1021))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1020) ),
inference(clausify,[status(thm)],[f_393_3]) ).
fof(f_394_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_394_2,plain,
! [U_1024,U_1023,U_1022] :
( c_Groups_Oabs__class_Oabs(U_1022,c_Groups_Oplus__class_Oplus(U_1022,c_Groups_Oabs__class_Oabs(U_1022,U_1023),c_Groups_Oabs__class_Oabs(U_1022,U_1024))) = c_Groups_Oplus__class_Oplus(U_1022,c_Groups_Oabs__class_Oabs(U_1022,U_1023),c_Groups_Oabs__class_Oabs(U_1022,U_1024))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1022) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_1022,U_1023,U_1024] :
( c_Groups_Oabs__class_Oabs(U_1022,c_Groups_Oplus__class_Oplus(U_1022,c_Groups_Oabs__class_Oabs(U_1022,U_1023),c_Groups_Oabs__class_Oabs(U_1022,U_1024))) = c_Groups_Oplus__class_Oplus(U_1022,c_Groups_Oabs__class_Oabs(U_1022,U_1023),c_Groups_Oabs__class_Oabs(U_1022,U_1024))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1022) ),
inference(definitional_conversion,[status(esa)],[f_394_2]) ).
cnf(f_394_4,plain,
( c_Groups_Oabs__class_Oabs(U_1022,c_Groups_Oplus__class_Oplus(U_1022,c_Groups_Oabs__class_Oabs(U_1022,U_1023),c_Groups_Oabs__class_Oabs(U_1022,U_1024))) = c_Groups_Oplus__class_Oplus(U_1022,c_Groups_Oabs__class_Oabs(U_1022,U_1023),c_Groups_Oabs__class_Oabs(U_1022,U_1024))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1022) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_1,plain,
! [V_n,V_x,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Nat_OSuc(hAPP(hAPP(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))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(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_I37_J]) ).
fof(f_395_2,plain,
! [U_1027,U_1026,U_1025] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1025),U_1026),c_Nat_OSuc(hAPP(hAPP(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_1027))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1025),U_1026),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1025),hAPP(hAPP(c_Power_Opower__class_Opower(U_1025),U_1026),U_1027)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1025),U_1026),U_1027)))
| ~ class_Rings_Ocomm__semiring__1(U_1025) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
! [U_1027,U_1025,U_1026] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1025),U_1026),c_Nat_OSuc(hAPP(hAPP(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_1027))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1025),U_1026),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1025),hAPP(hAPP(c_Power_Opower__class_Opower(U_1025),U_1026),U_1027)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1025),U_1026),U_1027)))
| ~ class_Rings_Ocomm__semiring__1(U_1025) ),
inference(definitional_conversion,[status(esa)],[f_395_2]) ).
cnf(f_395_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1025),U_1026),c_Nat_OSuc(hAPP(hAPP(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_1027))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1025),U_1026),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1025),hAPP(hAPP(c_Power_Opower__class_Opower(U_1025),U_1026),U_1027)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1025),U_1026),U_1027)))
| ~ class_Rings_Ocomm__semiring__1(U_1025) ),
inference(clausify,[status(thm)],[f_395_3]) ).
fof(f_396_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(hAPP(hAPP(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))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__odd__eq]) ).
fof(f_396_2,plain,
! [U_1030,U_1029,U_1028] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1028),U_1029),c_Nat_OSuc(hAPP(hAPP(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_1030))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1028),U_1029),hAPP(hAPP(c_Power_Opower__class_Opower(U_1028),hAPP(hAPP(c_Power_Opower__class_Opower(U_1028),U_1029),U_1030)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_1028) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
! [U_1028,U_1029,U_1030] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1028),U_1029),c_Nat_OSuc(hAPP(hAPP(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_1030))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1028),U_1029),hAPP(hAPP(c_Power_Opower__class_Opower(U_1028),hAPP(hAPP(c_Power_Opower__class_Opower(U_1028),U_1029),U_1030)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_1028) ),
inference(definitional_conversion,[status(esa)],[f_396_2]) ).
cnf(f_396_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1028),U_1029),c_Nat_OSuc(hAPP(hAPP(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_1030))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1028),U_1029),hAPP(hAPP(c_Power_Opower__class_Opower(U_1028),hAPP(hAPP(c_Power_Opower__class_Opower(U_1028),U_1029),U_1030)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Groups_Omonoid__mult(U_1028) ),
inference(clausify,[status(thm)],[f_396_3]) ).
fof(f_397_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_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_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_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_397_2,plain,
! [U_1033,U_1032,U_1031] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1031,c_Groups_Oplus__class_Oplus(U_1031,hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1032),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1033),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1031))
| U_1033 != c_Groups_Ozero__class_Ozero(U_1031)
| U_1032 != c_Groups_Ozero__class_Ozero(U_1031) )
& ( ( U_1033 = c_Groups_Ozero__class_Ozero(U_1031)
& U_1032 = c_Groups_Ozero__class_Ozero(U_1031) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1031,c_Groups_Oplus__class_Oplus(U_1031,hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1032),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1033),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1031)) ) )
| ~ class_Rings_Olinordered__idom(U_1031) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
fof(f_397_3,plain,
( ! [U_1031,U_1032,U_1033] :
( U_1033 = c_Groups_Ozero__class_Ozero(U_1031)
| ~ sP58(U_1031,U_1032,U_1033) )
& ! [U_1031,U_1032,U_1033] :
( U_1032 = c_Groups_Ozero__class_Ozero(U_1031)
| ~ sP58(U_1031,U_1032,U_1033) )
& ! [U_1031,U_1032,U_1033] :
( c_Orderings_Oord__class_Oless__eq(U_1031,c_Groups_Oplus__class_Oplus(U_1031,hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1032),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1033),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1031))
| U_1033 != c_Groups_Ozero__class_Ozero(U_1031)
| U_1032 != c_Groups_Ozero__class_Ozero(U_1031)
| ~ sP59(U_1031,U_1032,U_1033) )
& ! [U_1031,U_1032,U_1033] :
( sP58(U_1031,U_1032,U_1033)
| ~ c_Orderings_Oord__class_Oless__eq(U_1031,c_Groups_Oplus__class_Oplus(U_1031,hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1032),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1033),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1031))
| ~ sP59(U_1031,U_1032,U_1033) )
& ! [U_1031,U_1032,U_1033] :
( sP59(U_1031,U_1032,U_1033)
| ~ class_Rings_Olinordered__idom(U_1031) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58,sP59])],[f_397_2]) ).
cnf(f_397_4,plain,
( sP59(U_1031,U_1032,U_1033)
| ~ class_Rings_Olinordered__idom(U_1031) ),
inference(clausify,[status(thm)],[f_397_3]) ).
cnf(f_397_5,plain,
( sP58(U_1031,U_1032,U_1033)
| ~ c_Orderings_Oord__class_Oless__eq(U_1031,c_Groups_Oplus__class_Oplus(U_1031,hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1032),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1033),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1031))
| ~ sP59(U_1031,U_1032,U_1033) ),
inference(clausify,[status(thm)],[f_397_3]) ).
cnf(f_397_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1031,c_Groups_Oplus__class_Oplus(U_1031,hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1032),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_1031),U_1033),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_1031))
| U_1033 != c_Groups_Ozero__class_Ozero(U_1031)
| U_1032 != c_Groups_Ozero__class_Ozero(U_1031)
| ~ sP59(U_1031,U_1032,U_1033) ),
inference(clausify,[status(thm)],[f_397_3]) ).
cnf(f_397_7,plain,
( U_1032 = c_Groups_Ozero__class_Ozero(U_1031)
| ~ sP58(U_1031,U_1032,U_1033) ),
inference(clausify,[status(thm)],[f_397_3]) ).
cnf(f_397_8,plain,
( U_1033 = c_Groups_Ozero__class_Ozero(U_1031)
| ~ sP58(U_1031,U_1032,U_1033) ),
inference(clausify,[status(thm)],[f_397_3]) ).
fof(f_398_1,plain,
! [V_k,V_a,T_a] :
( V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(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_k)),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_even__power__le__0__imp__0]) ).
fof(f_398_2,plain,
! [U_1036,U_1035,U_1034] :
( U_1035 = c_Groups_Ozero__class_Ozero(U_1034)
| ~ c_Orderings_Oord__class_Oless__eq(U_1034,hAPP(hAPP(c_Power_Opower__class_Opower(U_1034),U_1035),hAPP(hAPP(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_1036)),c_Groups_Ozero__class_Ozero(U_1034))
| ~ class_Rings_Olinordered__idom(U_1034) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
fof(f_398_3,plain,
! [U_1036,U_1034,U_1035] :
( U_1035 = c_Groups_Ozero__class_Ozero(U_1034)
| ~ c_Orderings_Oord__class_Oless__eq(U_1034,hAPP(hAPP(c_Power_Opower__class_Opower(U_1034),U_1035),hAPP(hAPP(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_1036)),c_Groups_Ozero__class_Ozero(U_1034))
| ~ class_Rings_Olinordered__idom(U_1034) ),
inference(definitional_conversion,[status(esa)],[f_398_2]) ).
cnf(f_398_4,plain,
( U_1035 = c_Groups_Ozero__class_Ozero(U_1034)
| ~ c_Orderings_Oord__class_Oless__eq(U_1034,hAPP(hAPP(c_Power_Opower__class_Opower(U_1034),U_1035),hAPP(hAPP(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_1036)),c_Groups_Ozero__class_Ozero(U_1034))
| ~ class_Rings_Olinordered__idom(U_1034) ),
inference(clausify,[status(thm)],[f_398_3]) ).
fof(f_399_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]) ).
fof(f_399_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(definitional_conversion,[status(esa)],[f_399_1]) ).
cnf(f_399_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(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_399_2]) ).
fof(f_400_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_400_2,plain,
! [U_1041,U_1040,U_1039,U_1038,U_1037] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1037,c_Groups_Ominus__class_Ominus(U_1037,c_Groups_Oplus__class_Oplus(U_1037,U_1038,U_1039),c_Groups_Oplus__class_Oplus(U_1037,U_1040,U_1041))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1037,c_Groups_Ominus__class_Ominus(U_1037,U_1038,U_1040)),c_RealVector_Onorm__class_Onorm(U_1037,c_Groups_Ominus__class_Ominus(U_1037,U_1039,U_1041))))
| ~ class_RealVector_Oreal__normed__vector(U_1037) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
fof(f_400_3,plain,
! [U_1037,U_1041,U_1038,U_1039,U_1040] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1037,c_Groups_Ominus__class_Ominus(U_1037,c_Groups_Oplus__class_Oplus(U_1037,U_1038,U_1039),c_Groups_Oplus__class_Oplus(U_1037,U_1040,U_1041))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1037,c_Groups_Ominus__class_Ominus(U_1037,U_1038,U_1040)),c_RealVector_Onorm__class_Onorm(U_1037,c_Groups_Ominus__class_Ominus(U_1037,U_1039,U_1041))))
| ~ class_RealVector_Oreal__normed__vector(U_1037) ),
inference(definitional_conversion,[status(esa)],[f_400_2]) ).
cnf(f_400_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1037,c_Groups_Ominus__class_Ominus(U_1037,c_Groups_Oplus__class_Oplus(U_1037,U_1038,U_1039),c_Groups_Oplus__class_Oplus(U_1037,U_1040,U_1041))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1037,c_Groups_Ominus__class_Ominus(U_1037,U_1038,U_1040)),c_RealVector_Onorm__class_Onorm(U_1037,c_Groups_Ominus__class_Ominus(U_1037,U_1039,U_1041))))
| ~ class_RealVector_Oreal__normed__vector(U_1037) ),
inference(clausify,[status(thm)],[f_400_3]) ).
fof(f_401_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a)
| c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_a)
| ~ class_Rings_Olinordered__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convex__bound__le]) ).
fof(f_401_2,plain,
! [U_1047,U_1046,U_1045,U_1044,U_1043,U_1042] :
( c_Orderings_Oord__class_Oless__eq(U_1042,c_Groups_Oplus__class_Oplus(U_1042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1046),U_1043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1047),U_1045)),U_1044)
| c_Groups_Oplus__class_Oplus(U_1042,U_1046,U_1047) != c_Groups_Oone__class_Oone(U_1042)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,c_Groups_Ozero__class_Ozero(U_1042),U_1047)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,c_Groups_Ozero__class_Ozero(U_1042),U_1046)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,U_1045,U_1044)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,U_1043,U_1044)
| ~ class_Rings_Olinordered__semiring__1(U_1042) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
! [U_1042,U_1043,U_1044,U_1045,U_1046,U_1047] :
( c_Orderings_Oord__class_Oless__eq(U_1042,c_Groups_Oplus__class_Oplus(U_1042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1046),U_1043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1047),U_1045)),U_1044)
| c_Groups_Oplus__class_Oplus(U_1042,U_1046,U_1047) != c_Groups_Oone__class_Oone(U_1042)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,c_Groups_Ozero__class_Ozero(U_1042),U_1047)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,c_Groups_Ozero__class_Ozero(U_1042),U_1046)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,U_1045,U_1044)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,U_1043,U_1044)
| ~ class_Rings_Olinordered__semiring__1(U_1042) ),
inference(definitional_conversion,[status(esa)],[f_401_2]) ).
cnf(f_401_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1042,c_Groups_Oplus__class_Oplus(U_1042,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1046),U_1043),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1042),U_1047),U_1045)),U_1044)
| c_Groups_Oplus__class_Oplus(U_1042,U_1046,U_1047) != c_Groups_Oone__class_Oone(U_1042)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,c_Groups_Ozero__class_Ozero(U_1042),U_1047)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,c_Groups_Ozero__class_Ozero(U_1042),U_1046)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,U_1045,U_1044)
| ~ c_Orderings_Oord__class_Oless__eq(U_1042,U_1043,U_1044)
| ~ class_Rings_Olinordered__semiring__1(U_1042) ),
inference(clausify,[status(thm)],[f_401_3]) ).
fof(f_402_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_402_2,plain,
! [U_1049,U_1048] :
( c_RealVector_Onorm__class_Onorm(U_1048,c_Int_Onumber__class_Onumber__of(U_1048,U_1049)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1049))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1048)
| ~ class_Int_Onumber__ring(U_1048) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
fof(f_402_3,plain,
! [U_1049,U_1048] :
( c_RealVector_Onorm__class_Onorm(U_1048,c_Int_Onumber__class_Onumber__of(U_1048,U_1049)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1049))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1048)
| ~ class_Int_Onumber__ring(U_1048) ),
inference(definitional_conversion,[status(esa)],[f_402_2]) ).
cnf(f_402_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1048,c_Int_Onumber__class_Onumber__of(U_1048,U_1049)) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,U_1049))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1048)
| ~ class_Int_Onumber__ring(U_1048) ),
inference(clausify,[status(thm)],[f_402_3]) ).
fof(f_403_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_403_2,plain,
! [U_1052,U_1051,U_1050] :
( 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_1050,U_1051),c_RealVector_Onorm__class_Onorm(U_1050,U_1052))),c_RealVector_Onorm__class_Onorm(U_1050,c_Groups_Ominus__class_Ominus(U_1050,U_1051,U_1052)))
| ~ class_RealVector_Oreal__normed__vector(U_1050) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
fof(f_403_3,plain,
! [U_1051,U_1052,U_1050] :
( 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_1050,U_1051),c_RealVector_Onorm__class_Onorm(U_1050,U_1052))),c_RealVector_Onorm__class_Onorm(U_1050,c_Groups_Ominus__class_Ominus(U_1050,U_1051,U_1052)))
| ~ class_RealVector_Oreal__normed__vector(U_1050) ),
inference(definitional_conversion,[status(esa)],[f_403_2]) ).
cnf(f_403_4,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_1050,U_1051),c_RealVector_Onorm__class_Onorm(U_1050,U_1052))),c_RealVector_Onorm__class_Onorm(U_1050,c_Groups_Ominus__class_Ominus(U_1050,U_1051,U_1052)))
| ~ class_RealVector_Oreal__normed__vector(U_1050) ),
inference(clausify,[status(thm)],[f_403_3]) ).
fof(f_404_1,plain,
! [V_n,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(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_404_2,plain,
! [U_1055,U_1054,U_1053] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1053,hAPP(hAPP(c_Power_Opower__class_Opower(U_1053),U_1054),U_1055)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1053,U_1054)),U_1055))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1053) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
! [U_1053,U_1054,U_1055] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1053,hAPP(hAPP(c_Power_Opower__class_Opower(U_1053),U_1054),U_1055)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1053,U_1054)),U_1055))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1053) ),
inference(definitional_conversion,[status(esa)],[f_404_2]) ).
cnf(f_404_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1053,hAPP(hAPP(c_Power_Opower__class_Opower(U_1053),U_1054),U_1055)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1053,U_1054)),U_1055))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1053) ),
inference(clausify,[status(thm)],[f_404_3]) ).
fof(f_405_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_405_2,plain,
! [U_1058,U_1057,U_1056] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1056,c_Groups_Ominus__class_Ominus(U_1056,U_1057,U_1058)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1056,U_1057),c_RealVector_Onorm__class_Onorm(U_1056,U_1058)))
| ~ class_RealVector_Oreal__normed__vector(U_1056) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
! [U_1056,U_1057,U_1058] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1056,c_Groups_Ominus__class_Ominus(U_1056,U_1057,U_1058)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1056,U_1057),c_RealVector_Onorm__class_Onorm(U_1056,U_1058)))
| ~ class_RealVector_Oreal__normed__vector(U_1056) ),
inference(definitional_conversion,[status(esa)],[f_405_2]) ).
cnf(f_405_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1056,c_Groups_Ominus__class_Ominus(U_1056,U_1057,U_1058)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1056,U_1057),c_RealVector_Onorm__class_Onorm(U_1056,U_1058)))
| ~ class_RealVector_Oreal__normed__vector(U_1056) ),
inference(clausify,[status(thm)],[f_405_3]) ).
fof(f_406_1,plain,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[fact_complex__i__not__one]) ).
fof(f_406_2,plain,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_406_1]) ).
cnf(f_406_3,plain,
c_Complex_Oii != c_Groups_Oone__class_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_406_2]) ).
fof(f_407_1,plain,
! [V_w] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,V_w),
inference(fof_nnf,[status(thm)],[fact_complex__i__not__number__of]) ).
fof(f_407_2,plain,
! [U_1059] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_1059),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
! [U_1059] : c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_1059),
inference(definitional_conversion,[status(esa)],[f_407_2]) ).
cnf(f_407_4,plain,
c_Complex_Oii != c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,U_1059),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_1,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[fact_complex__i__not__zero]) ).
fof(f_408_2,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_408_1]) ).
cnf(f_408_3,plain,
c_Complex_Oii != c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_408_2]) ).
fof(f_409_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_409_2,plain,
! [U_1060] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_1060) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1060),
inference(variable_rename,[status(thm)],[f_409_1]) ).
fof(f_409_3,plain,
! [U_1060] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_1060) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1060),
inference(definitional_conversion,[status(esa)],[f_409_2]) ).
cnf(f_409_4,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_1060) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1060),
inference(clausify,[status(thm)],[f_409_3]) ).
fof(f_410_1,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_i__squared]) ).
fof(f_410_2,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
inference(definitional_conversion,[status(esa)],[f_410_1]) ).
cnf(f_410_3,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Complex_Ocomplex),c_Complex_Oii),c_Complex_Oii) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
inference(clausify,[status(thm)],[f_410_2]) ).
fof(f_411_1,plain,
! [V_ya_2,V_xa_2] :
( ( c_Complex_Ocomplex_OComplex(V_xa_2,V_ya_2) = c_Complex_Oii
| V_ya_2 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| V_xa_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_ya_2 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& V_xa_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(V_xa_2,V_ya_2) != c_Complex_Oii ) ),
inference(fof_nnf,[status(thm)],[fact_Complex__eq__i]) ).
fof(f_411_2,plain,
! [U_1062,U_1061] :
( ( c_Complex_Ocomplex_OComplex(U_1061,U_1062) = c_Complex_Oii
| U_1062 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1061 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_1062 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& U_1061 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_1061,U_1062) != c_Complex_Oii ) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
fof(f_411_3,plain,
( ! [U_1066,U_1064] :
( c_Complex_Ocomplex_OComplex(U_1064,U_1066) = c_Complex_Oii
| U_1066 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1064 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1065,U_1063] :
( ( U_1065 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
& U_1063 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Complex_Ocomplex_OComplex(U_1063,U_1065) != c_Complex_Oii ) ),
inference(miniscope,[status(thm)],[f_411_2]) ).
fof(f_411_4,plain,
( ! [U_1065,U_1063] :
( U_1065 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ sP60(U_1065,U_1063) )
& ! [U_1065,U_1063] :
( U_1063 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP60(U_1065,U_1063) )
& ! [U_1064,U_1066] :
( c_Complex_Ocomplex_OComplex(U_1064,U_1066) = c_Complex_Oii
| U_1066 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1064 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1065,U_1063] :
( sP60(U_1065,U_1063)
| c_Complex_Ocomplex_OComplex(U_1063,U_1065) != c_Complex_Oii ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_411_3]) ).
cnf(f_411_5,plain,
( sP60(U_1065,U_1063)
| c_Complex_Ocomplex_OComplex(U_1063,U_1065) != c_Complex_Oii ),
inference(clausify,[status(thm)],[f_411_4]) ).
cnf(f_411_6,plain,
( c_Complex_Ocomplex_OComplex(U_1064,U_1066) = c_Complex_Oii
| U_1066 != c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1064 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_411_4]) ).
cnf(f_411_7,plain,
( U_1063 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP60(U_1065,U_1063) ),
inference(clausify,[status(thm)],[f_411_4]) ).
cnf(f_411_8,plain,
( U_1065 = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ sP60(U_1065,U_1063) ),
inference(clausify,[status(thm)],[f_411_4]) ).
fof(f_412_1,plain,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_i__def]) ).
fof(f_412_2,plain,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_412_1]) ).
cnf(f_412_3,plain,
c_Complex_Oii = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_412_2]) ).
fof(f_413_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]) ).
fof(f_413_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(definitional_conversion,[status(esa)],[f_413_1]) ).
cnf(f_413_3,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_413_2]) ).
fof(f_414_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_414_2,plain,
! [U_1068,U_1067] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),c_Groups_Ozero__class_Ozero(U_1067)),U_1068) = c_Groups_Ozero__class_Ozero(U_1067)
| ~ class_Rings_Omult__zero(U_1067) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
fof(f_414_3,plain,
! [U_1067,U_1068] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),c_Groups_Ozero__class_Ozero(U_1067)),U_1068) = c_Groups_Ozero__class_Ozero(U_1067)
| ~ class_Rings_Omult__zero(U_1067) ),
inference(definitional_conversion,[status(esa)],[f_414_2]) ).
cnf(f_414_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1067),c_Groups_Ozero__class_Ozero(U_1067)),U_1068) = c_Groups_Ozero__class_Ozero(U_1067)
| ~ class_Rings_Omult__zero(U_1067) ),
inference(clausify,[status(thm)],[f_414_3]) ).
fof(f_415_1,plain,
! [V_b,T_a] :
( hAPP(hAPP(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_415_2,plain,
! [U_1070,U_1069] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1069),c_Groups_Ozero__class_Ozero(U_1069)),U_1070) = c_Groups_Ozero__class_Ozero(U_1069)
| ~ class_RealVector_Oreal__normed__algebra(U_1069) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
fof(f_415_3,plain,
! [U_1069,U_1070] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1069),c_Groups_Ozero__class_Ozero(U_1069)),U_1070) = c_Groups_Ozero__class_Ozero(U_1069)
| ~ class_RealVector_Oreal__normed__algebra(U_1069) ),
inference(definitional_conversion,[status(esa)],[f_415_2]) ).
cnf(f_415_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1069),c_Groups_Ozero__class_Ozero(U_1069)),U_1070) = c_Groups_Ozero__class_Ozero(U_1069)
| ~ class_RealVector_Oreal__normed__algebra(U_1069) ),
inference(clausify,[status(thm)],[f_415_3]) ).
fof(f_416_1,plain,
! [V_y,T_a] :
( hAPP(hAPP(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_416_2,plain,
! [U_1072,U_1071] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1071),c_Groups_Ozero__class_Ozero(U_1071)),U_1072) = c_Groups_Ozero__class_Ozero(U_1071)
| ~ class_RealVector_Oreal__normed__algebra(U_1071) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
fof(f_416_3,plain,
! [U_1071,U_1072] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1071),c_Groups_Ozero__class_Ozero(U_1071)),U_1072) = c_Groups_Ozero__class_Ozero(U_1071)
| ~ class_RealVector_Oreal__normed__algebra(U_1071) ),
inference(definitional_conversion,[status(esa)],[f_416_2]) ).
cnf(f_416_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1071),c_Groups_Ozero__class_Ozero(U_1071)),U_1072) = c_Groups_Ozero__class_Ozero(U_1071)
| ~ class_RealVector_Oreal__normed__algebra(U_1071) ),
inference(clausify,[status(thm)],[f_416_3]) ).
fof(f_417_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_417_2,plain,
! [U_1074,U_1073] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1073),U_1074),c_Groups_Ozero__class_Ozero(U_1073)) = c_Groups_Ozero__class_Ozero(U_1073)
| ~ class_Rings_Omult__zero(U_1073) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
! [U_1073,U_1074] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1073),U_1074),c_Groups_Ozero__class_Ozero(U_1073)) = c_Groups_Ozero__class_Ozero(U_1073)
| ~ class_Rings_Omult__zero(U_1073) ),
inference(definitional_conversion,[status(esa)],[f_417_2]) ).
cnf(f_417_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1073),U_1074),c_Groups_Ozero__class_Ozero(U_1073)) = c_Groups_Ozero__class_Ozero(U_1073)
| ~ class_Rings_Omult__zero(U_1073) ),
inference(clausify,[status(thm)],[f_417_3]) ).
fof(f_418_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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_418_2,plain,
! [U_1076,U_1075] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1075),U_1076),c_Groups_Ozero__class_Ozero(U_1075)) = c_Groups_Ozero__class_Ozero(U_1075)
| ~ class_RealVector_Oreal__normed__algebra(U_1075) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
fof(f_418_3,plain,
! [U_1075,U_1076] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1075),U_1076),c_Groups_Ozero__class_Ozero(U_1075)) = c_Groups_Ozero__class_Ozero(U_1075)
| ~ class_RealVector_Oreal__normed__algebra(U_1075) ),
inference(definitional_conversion,[status(esa)],[f_418_2]) ).
cnf(f_418_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1075),U_1076),c_Groups_Ozero__class_Ozero(U_1075)) = c_Groups_Ozero__class_Ozero(U_1075)
| ~ class_RealVector_Oreal__normed__algebra(U_1075) ),
inference(clausify,[status(thm)],[f_418_3]) ).
fof(f_419_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(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_419_2,plain,
! [U_1078,U_1077] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),c_Groups_Ozero__class_Ozero(U_1077)) = c_Groups_Ozero__class_Ozero(U_1077)
| ~ class_RealVector_Oreal__normed__algebra(U_1077) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
fof(f_419_3,plain,
! [U_1077,U_1078] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),c_Groups_Ozero__class_Ozero(U_1077)) = c_Groups_Ozero__class_Ozero(U_1077)
| ~ class_RealVector_Oreal__normed__algebra(U_1077) ),
inference(definitional_conversion,[status(esa)],[f_419_2]) ).
cnf(f_419_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1077),U_1078),c_Groups_Ozero__class_Ozero(U_1077)) = c_Groups_Ozero__class_Ozero(U_1077)
| ~ class_RealVector_Oreal__normed__algebra(U_1077) ),
inference(clausify,[status(thm)],[f_419_3]) ).
fof(f_420_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(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)
| hAPP(hAPP(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_420_2,plain,
! [U_1081,U_1080,U_1079] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1079),U_1080),U_1081) = c_Groups_Ozero__class_Ozero(U_1079)
| ( U_1081 != c_Groups_Ozero__class_Ozero(U_1079)
& U_1080 != c_Groups_Ozero__class_Ozero(U_1079) ) )
& ( U_1081 = c_Groups_Ozero__class_Ozero(U_1079)
| U_1080 = c_Groups_Ozero__class_Ozero(U_1079)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1079),U_1080),U_1081) != c_Groups_Ozero__class_Ozero(U_1079) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_1079) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
fof(f_420_3,plain,
( ! [U_1079,U_1080,U_1081] :
( U_1081 != c_Groups_Ozero__class_Ozero(U_1079)
| ~ sP61(U_1079,U_1080,U_1081) )
& ! [U_1079,U_1080,U_1081] :
( U_1080 != c_Groups_Ozero__class_Ozero(U_1079)
| ~ sP61(U_1079,U_1080,U_1081) )
& ! [U_1079,U_1080,U_1081] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1079),U_1080),U_1081) = c_Groups_Ozero__class_Ozero(U_1079)
| sP61(U_1079,U_1080,U_1081)
| ~ sP62(U_1079,U_1080,U_1081) )
& ! [U_1079,U_1080,U_1081] :
( U_1081 = c_Groups_Ozero__class_Ozero(U_1079)
| U_1080 = c_Groups_Ozero__class_Ozero(U_1079)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1079),U_1080),U_1081) != c_Groups_Ozero__class_Ozero(U_1079)
| ~ sP62(U_1079,U_1080,U_1081) )
& ! [U_1079,U_1080,U_1081] :
( sP62(U_1079,U_1080,U_1081)
| ~ class_Rings_Oring__no__zero__divisors(U_1079) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61,sP62])],[f_420_2]) ).
cnf(f_420_4,plain,
( sP62(U_1079,U_1080,U_1081)
| ~ class_Rings_Oring__no__zero__divisors(U_1079) ),
inference(clausify,[status(thm)],[f_420_3]) ).
cnf(f_420_5,plain,
( U_1081 = c_Groups_Ozero__class_Ozero(U_1079)
| U_1080 = c_Groups_Ozero__class_Ozero(U_1079)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1079),U_1080),U_1081) != c_Groups_Ozero__class_Ozero(U_1079)
| ~ sP62(U_1079,U_1080,U_1081) ),
inference(clausify,[status(thm)],[f_420_3]) ).
cnf(f_420_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1079),U_1080),U_1081) = c_Groups_Ozero__class_Ozero(U_1079)
| sP61(U_1079,U_1080,U_1081)
| ~ sP62(U_1079,U_1080,U_1081) ),
inference(clausify,[status(thm)],[f_420_3]) ).
cnf(f_420_7,plain,
( U_1080 != c_Groups_Ozero__class_Ozero(U_1079)
| ~ sP61(U_1079,U_1080,U_1081) ),
inference(clausify,[status(thm)],[f_420_3]) ).
cnf(f_420_8,plain,
( U_1081 != c_Groups_Ozero__class_Ozero(U_1079)
| ~ sP61(U_1079,U_1080,U_1081) ),
inference(clausify,[status(thm)],[f_420_3]) ).
fof(f_421_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(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_421_2,plain,
! [U_1084,U_1083,U_1082] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1082),U_1083),U_1084) != c_Groups_Ozero__class_Ozero(U_1082)
| U_1084 = c_Groups_Ozero__class_Ozero(U_1082)
| U_1083 = c_Groups_Ozero__class_Ozero(U_1082)
| ~ class_Rings_Ono__zero__divisors(U_1082) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
fof(f_421_3,plain,
! [U_1082,U_1083,U_1084] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1082),U_1083),U_1084) != c_Groups_Ozero__class_Ozero(U_1082)
| U_1084 = c_Groups_Ozero__class_Ozero(U_1082)
| U_1083 = c_Groups_Ozero__class_Ozero(U_1082)
| ~ class_Rings_Ono__zero__divisors(U_1082) ),
inference(definitional_conversion,[status(esa)],[f_421_2]) ).
cnf(f_421_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1082),U_1083),U_1084) != c_Groups_Ozero__class_Ozero(U_1082)
| U_1084 = c_Groups_Ozero__class_Ozero(U_1082)
| U_1083 = c_Groups_Ozero__class_Ozero(U_1082)
| ~ class_Rings_Ono__zero__divisors(U_1082) ),
inference(clausify,[status(thm)],[f_421_3]) ).
fof(f_422_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)
| hAPP(hAPP(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_422_2,plain,
! [U_1087,U_1086,U_1085] :
( U_1087 = c_Groups_Ozero__class_Ozero(U_1085)
| U_1086 = c_Groups_Ozero__class_Ozero(U_1085)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1085),U_1086),U_1087) != c_Groups_Ozero__class_Ozero(U_1085)
| ~ class_Rings_Ono__zero__divisors(U_1085) ),
inference(variable_rename,[status(thm)],[f_422_1]) ).
fof(f_422_3,plain,
! [U_1087,U_1085,U_1086] :
( U_1087 = c_Groups_Ozero__class_Ozero(U_1085)
| U_1086 = c_Groups_Ozero__class_Ozero(U_1085)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1085),U_1086),U_1087) != c_Groups_Ozero__class_Ozero(U_1085)
| ~ class_Rings_Ono__zero__divisors(U_1085) ),
inference(definitional_conversion,[status(esa)],[f_422_2]) ).
cnf(f_422_4,plain,
( U_1087 = c_Groups_Ozero__class_Ozero(U_1085)
| U_1086 = c_Groups_Ozero__class_Ozero(U_1085)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1085),U_1086),U_1087) != c_Groups_Ozero__class_Ozero(U_1085)
| ~ class_Rings_Ono__zero__divisors(U_1085) ),
inference(clausify,[status(thm)],[f_422_3]) ).
fof(f_423_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_423_2,plain,
! [U_1088] :
( c_Groups_Oone__class_Oone(U_1088) != c_Groups_Ozero__class_Ozero(U_1088)
| ~ class_Rings_Ozero__neq__one(U_1088) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
! [U_1088] :
( c_Groups_Oone__class_Oone(U_1088) != c_Groups_Ozero__class_Ozero(U_1088)
| ~ class_Rings_Ozero__neq__one(U_1088) ),
inference(definitional_conversion,[status(esa)],[f_423_2]) ).
cnf(f_423_4,plain,
( c_Groups_Oone__class_Oone(U_1088) != c_Groups_Ozero__class_Ozero(U_1088)
| ~ class_Rings_Ozero__neq__one(U_1088) ),
inference(clausify,[status(thm)],[f_423_3]) ).
fof(f_424_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_424_2,plain,
! [U_1089] :
( c_Groups_Ozero__class_Ozero(U_1089) != c_Groups_Oone__class_Oone(U_1089)
| ~ class_Rings_Ozero__neq__one(U_1089) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
! [U_1089] :
( c_Groups_Ozero__class_Ozero(U_1089) != c_Groups_Oone__class_Oone(U_1089)
| ~ class_Rings_Ozero__neq__one(U_1089) ),
inference(definitional_conversion,[status(esa)],[f_424_2]) ).
cnf(f_424_4,plain,
( c_Groups_Ozero__class_Ozero(U_1089) != c_Groups_Oone__class_Oone(U_1089)
| ~ class_Rings_Ozero__neq__one(U_1089) ),
inference(clausify,[status(thm)],[f_424_3]) ).
fof(f_425_1,plain,
! [V_b_H,V_b,V_a,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(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_425_2,plain,
! [U_1093,U_1092,U_1091,U_1090] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1090),U_1091),c_Groups_Oplus__class_Oplus(U_1090,U_1092,U_1093)) = c_Groups_Oplus__class_Oplus(U_1090,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1090),U_1091),U_1092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1090),U_1091),U_1093))
| ~ class_RealVector_Oreal__normed__algebra(U_1090) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
fof(f_425_3,plain,
! [U_1090,U_1091,U_1092,U_1093] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1090),U_1091),c_Groups_Oplus__class_Oplus(U_1090,U_1092,U_1093)) = c_Groups_Oplus__class_Oplus(U_1090,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1090),U_1091),U_1092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1090),U_1091),U_1093))
| ~ class_RealVector_Oreal__normed__algebra(U_1090) ),
inference(definitional_conversion,[status(esa)],[f_425_2]) ).
cnf(f_425_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1090),U_1091),c_Groups_Oplus__class_Oplus(U_1090,U_1092,U_1093)) = c_Groups_Oplus__class_Oplus(U_1090,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1090),U_1091),U_1092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1090),U_1091),U_1093))
| ~ class_RealVector_Oreal__normed__algebra(U_1090) ),
inference(clausify,[status(thm)],[f_425_3]) ).
fof(f_426_1,plain,
! [V_y,V_x,V_xa,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(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_426_2,plain,
! [U_1097,U_1096,U_1095,U_1094] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1094),U_1095),c_Groups_Oplus__class_Oplus(U_1094,U_1096,U_1097)) = c_Groups_Oplus__class_Oplus(U_1094,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1094),U_1095),U_1096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1094),U_1095),U_1097))
| ~ class_RealVector_Oreal__normed__algebra(U_1094) ),
inference(variable_rename,[status(thm)],[f_426_1]) ).
fof(f_426_3,plain,
! [U_1094,U_1095,U_1096,U_1097] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1094),U_1095),c_Groups_Oplus__class_Oplus(U_1094,U_1096,U_1097)) = c_Groups_Oplus__class_Oplus(U_1094,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1094),U_1095),U_1096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1094),U_1095),U_1097))
| ~ class_RealVector_Oreal__normed__algebra(U_1094) ),
inference(definitional_conversion,[status(esa)],[f_426_2]) ).
cnf(f_426_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1094),U_1095),c_Groups_Oplus__class_Oplus(U_1094,U_1096,U_1097)) = c_Groups_Oplus__class_Oplus(U_1094,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1094),U_1095),U_1096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1094),U_1095),U_1097))
| ~ class_RealVector_Oreal__normed__algebra(U_1094) ),
inference(clausify,[status(thm)],[f_426_3]) ).
fof(f_427_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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_427_2,plain,
! [U_1101,U_1100,U_1099,U_1098] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1098),c_Groups_Oplus__class_Oplus(U_1098,U_1099,U_1100)),U_1101) = c_Groups_Oplus__class_Oplus(U_1098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1098),U_1099),U_1101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1098),U_1100),U_1101))
| ~ class_Rings_Ocomm__semiring(U_1098) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
! [U_1098,U_1099,U_1100,U_1101] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1098),c_Groups_Oplus__class_Oplus(U_1098,U_1099,U_1100)),U_1101) = c_Groups_Oplus__class_Oplus(U_1098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1098),U_1099),U_1101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1098),U_1100),U_1101))
| ~ class_Rings_Ocomm__semiring(U_1098) ),
inference(definitional_conversion,[status(esa)],[f_427_2]) ).
cnf(f_427_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1098),c_Groups_Oplus__class_Oplus(U_1098,U_1099,U_1100)),U_1101) = c_Groups_Oplus__class_Oplus(U_1098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1098),U_1099),U_1101),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1098),U_1100),U_1101))
| ~ class_Rings_Ocomm__semiring(U_1098) ),
inference(clausify,[status(thm)],[f_427_3]) ).
fof(f_428_1,plain,
! [V_b,V_a_H,V_a,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(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_428_2,plain,
! [U_1105,U_1104,U_1103,U_1102] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1102),c_Groups_Oplus__class_Oplus(U_1102,U_1103,U_1104)),U_1105) = c_Groups_Oplus__class_Oplus(U_1102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1102),U_1103),U_1105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1102),U_1104),U_1105))
| ~ class_RealVector_Oreal__normed__algebra(U_1102) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
! [U_1102,U_1103,U_1104,U_1105] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1102),c_Groups_Oplus__class_Oplus(U_1102,U_1103,U_1104)),U_1105) = c_Groups_Oplus__class_Oplus(U_1102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1102),U_1103),U_1105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1102),U_1104),U_1105))
| ~ class_RealVector_Oreal__normed__algebra(U_1102) ),
inference(definitional_conversion,[status(esa)],[f_428_2]) ).
cnf(f_428_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1102),c_Groups_Oplus__class_Oplus(U_1102,U_1103,U_1104)),U_1105) = c_Groups_Oplus__class_Oplus(U_1102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1102),U_1103),U_1105),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1102),U_1104),U_1105))
| ~ class_RealVector_Oreal__normed__algebra(U_1102) ),
inference(clausify,[status(thm)],[f_428_3]) ).
fof(f_429_1,plain,
! [V_ya,V_y,V_x,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(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_429_2,plain,
! [U_1109,U_1108,U_1107,U_1106] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1106),c_Groups_Oplus__class_Oplus(U_1106,U_1107,U_1108)),U_1109) = c_Groups_Oplus__class_Oplus(U_1106,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1106),U_1107),U_1109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1106),U_1108),U_1109))
| ~ class_RealVector_Oreal__normed__algebra(U_1106) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
! [U_1106,U_1107,U_1108,U_1109] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1106),c_Groups_Oplus__class_Oplus(U_1106,U_1107,U_1108)),U_1109) = c_Groups_Oplus__class_Oplus(U_1106,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1106),U_1107),U_1109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1106),U_1108),U_1109))
| ~ class_RealVector_Oreal__normed__algebra(U_1106) ),
inference(definitional_conversion,[status(esa)],[f_429_2]) ).
cnf(f_429_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1106),c_Groups_Oplus__class_Oplus(U_1106,U_1107,U_1108)),U_1109) = c_Groups_Oplus__class_Oplus(U_1106,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1106),U_1107),U_1109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1106),U_1108),U_1109))
| ~ class_RealVector_Oreal__normed__algebra(U_1106) ),
inference(clausify,[status(thm)],[f_429_3]) ).
fof(f_430_1,plain,
! [V_c,V_b,V_e,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_e),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_e),V_c)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_430_2,plain,
! [U_1114,U_1113,U_1112,U_1111,U_1110] :
( c_Groups_Oplus__class_Oplus(U_1110,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1110),U_1111),U_1112),c_Groups_Oplus__class_Oplus(U_1110,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1110),U_1113),U_1112),U_1114)) = c_Groups_Oplus__class_Oplus(U_1110,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1110),c_Groups_Oplus__class_Oplus(U_1110,U_1111,U_1113)),U_1112),U_1114)
| ~ class_Rings_Osemiring(U_1110) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
fof(f_430_3,plain,
! [U_1110,U_1111,U_1112,U_1113,U_1114] :
( c_Groups_Oplus__class_Oplus(U_1110,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1110),U_1111),U_1112),c_Groups_Oplus__class_Oplus(U_1110,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1110),U_1113),U_1112),U_1114)) = c_Groups_Oplus__class_Oplus(U_1110,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1110),c_Groups_Oplus__class_Oplus(U_1110,U_1111,U_1113)),U_1112),U_1114)
| ~ class_Rings_Osemiring(U_1110) ),
inference(definitional_conversion,[status(esa)],[f_430_2]) ).
cnf(f_430_4,plain,
( c_Groups_Oplus__class_Oplus(U_1110,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1110),U_1111),U_1112),c_Groups_Oplus__class_Oplus(U_1110,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1110),U_1113),U_1112),U_1114)) = c_Groups_Oplus__class_Oplus(U_1110,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1110),c_Groups_Oplus__class_Oplus(U_1110,U_1111,U_1113)),U_1112),U_1114)
| ~ class_Rings_Osemiring(U_1110) ),
inference(clausify,[status(thm)],[f_430_3]) ).
fof(f_431_1,plain,
! [V_b_H,V_b,V_a,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(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_431_2,plain,
! [U_1118,U_1117,U_1116,U_1115] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1115),U_1116),c_Groups_Ominus__class_Ominus(U_1115,U_1117,U_1118)) = c_Groups_Ominus__class_Ominus(U_1115,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1115),U_1116),U_1117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1115),U_1116),U_1118))
| ~ class_RealVector_Oreal__normed__algebra(U_1115) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
! [U_1116,U_1115,U_1117,U_1118] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1115),U_1116),c_Groups_Ominus__class_Ominus(U_1115,U_1117,U_1118)) = c_Groups_Ominus__class_Ominus(U_1115,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1115),U_1116),U_1117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1115),U_1116),U_1118))
| ~ class_RealVector_Oreal__normed__algebra(U_1115) ),
inference(definitional_conversion,[status(esa)],[f_431_2]) ).
cnf(f_431_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1115),U_1116),c_Groups_Ominus__class_Ominus(U_1115,U_1117,U_1118)) = c_Groups_Ominus__class_Ominus(U_1115,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1115),U_1116),U_1117),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1115),U_1116),U_1118))
| ~ class_RealVector_Oreal__normed__algebra(U_1115) ),
inference(clausify,[status(thm)],[f_431_3]) ).
fof(f_432_1,plain,
! [V_y,V_x,V_xa,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x),hAPP(hAPP(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_432_2,plain,
! [U_1122,U_1121,U_1120,U_1119] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1119),U_1120),c_Groups_Ominus__class_Ominus(U_1119,U_1121,U_1122)) = c_Groups_Ominus__class_Ominus(U_1119,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1119),U_1120),U_1121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1119),U_1120),U_1122))
| ~ class_RealVector_Oreal__normed__algebra(U_1119) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
! [U_1119,U_1120,U_1121,U_1122] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1119),U_1120),c_Groups_Ominus__class_Ominus(U_1119,U_1121,U_1122)) = c_Groups_Ominus__class_Ominus(U_1119,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1119),U_1120),U_1121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1119),U_1120),U_1122))
| ~ class_RealVector_Oreal__normed__algebra(U_1119) ),
inference(definitional_conversion,[status(esa)],[f_432_2]) ).
cnf(f_432_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1119),U_1120),c_Groups_Ominus__class_Ominus(U_1119,U_1121,U_1122)) = c_Groups_Ominus__class_Ominus(U_1119,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1119),U_1120),U_1121),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1119),U_1120),U_1122))
| ~ class_RealVector_Oreal__normed__algebra(U_1119) ),
inference(clausify,[status(thm)],[f_432_3]) ).
fof(f_433_1,plain,
! [V_b,V_a_H,V_a,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(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_433_2,plain,
! [U_1126,U_1125,U_1124,U_1123] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1123),c_Groups_Ominus__class_Ominus(U_1123,U_1124,U_1125)),U_1126) = c_Groups_Ominus__class_Ominus(U_1123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1123),U_1124),U_1126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1123),U_1125),U_1126))
| ~ class_RealVector_Oreal__normed__algebra(U_1123) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
fof(f_433_3,plain,
! [U_1123,U_1124,U_1125,U_1126] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1123),c_Groups_Ominus__class_Ominus(U_1123,U_1124,U_1125)),U_1126) = c_Groups_Ominus__class_Ominus(U_1123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1123),U_1124),U_1126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1123),U_1125),U_1126))
| ~ class_RealVector_Oreal__normed__algebra(U_1123) ),
inference(definitional_conversion,[status(esa)],[f_433_2]) ).
cnf(f_433_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1123),c_Groups_Ominus__class_Ominus(U_1123,U_1124,U_1125)),U_1126) = c_Groups_Ominus__class_Ominus(U_1123,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1123),U_1124),U_1126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1123),U_1125),U_1126))
| ~ class_RealVector_Oreal__normed__algebra(U_1123) ),
inference(clausify,[status(thm)],[f_433_3]) ).
fof(f_434_1,plain,
! [V_ya,V_y,V_x,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_ya),hAPP(hAPP(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_434_2,plain,
! [U_1130,U_1129,U_1128,U_1127] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1127),c_Groups_Ominus__class_Ominus(U_1127,U_1128,U_1129)),U_1130) = c_Groups_Ominus__class_Ominus(U_1127,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1127),U_1128),U_1130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1127),U_1129),U_1130))
| ~ class_RealVector_Oreal__normed__algebra(U_1127) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
! [U_1127,U_1128,U_1129,U_1130] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1127),c_Groups_Ominus__class_Ominus(U_1127,U_1128,U_1129)),U_1130) = c_Groups_Ominus__class_Ominus(U_1127,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1127),U_1128),U_1130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1127),U_1129),U_1130))
| ~ class_RealVector_Oreal__normed__algebra(U_1127) ),
inference(definitional_conversion,[status(esa)],[f_434_2]) ).
cnf(f_434_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1127),c_Groups_Ominus__class_Ominus(U_1127,U_1128,U_1129)),U_1130) = c_Groups_Ominus__class_Ominus(U_1127,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1127),U_1128),U_1130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1127),U_1129),U_1130))
| ~ class_RealVector_Oreal__normed__algebra(U_1127) ),
inference(clausify,[status(thm)],[f_434_3]) ).
fof(f_435_1,plain,
! [V_xa_2,T_a] :
( ( ( c_RealVector_Onorm__class_Onorm(T_a,V_xa_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_xa_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_RealVector_Onorm__class_Onorm(T_a,V_xa_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_435_2,plain,
! [U_1132,U_1131] :
( ( ( c_RealVector_Onorm__class_Onorm(U_1131,U_1132) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1132 != c_Groups_Ozero__class_Ozero(U_1131) )
& ( U_1132 = c_Groups_Ozero__class_Ozero(U_1131)
| c_RealVector_Onorm__class_Onorm(U_1131,U_1132) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1131) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
( ! [U_1132,U_1131] :
( c_RealVector_Onorm__class_Onorm(U_1131,U_1132) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1132 != c_Groups_Ozero__class_Ozero(U_1131)
| ~ sP63(U_1132,U_1131) )
& ! [U_1132,U_1131] :
( U_1132 = c_Groups_Ozero__class_Ozero(U_1131)
| c_RealVector_Onorm__class_Onorm(U_1131,U_1132) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP63(U_1132,U_1131) )
& ! [U_1132,U_1131] :
( sP63(U_1132,U_1131)
| ~ class_RealVector_Oreal__normed__vector(U_1131) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_435_2]) ).
cnf(f_435_4,plain,
( sP63(U_1132,U_1131)
| ~ class_RealVector_Oreal__normed__vector(U_1131) ),
inference(clausify,[status(thm)],[f_435_3]) ).
cnf(f_435_5,plain,
( U_1132 = c_Groups_Ozero__class_Ozero(U_1131)
| c_RealVector_Onorm__class_Onorm(U_1131,U_1132) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP63(U_1132,U_1131) ),
inference(clausify,[status(thm)],[f_435_3]) ).
cnf(f_435_6,plain,
( c_RealVector_Onorm__class_Onorm(U_1131,U_1132) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1132 != c_Groups_Ozero__class_Ozero(U_1131)
| ~ sP63(U_1132,U_1131) ),
inference(clausify,[status(thm)],[f_435_3]) ).
fof(f_436_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_436_2,plain,
! [U_1133] :
( c_RealVector_Onorm__class_Onorm(U_1133,c_Groups_Ozero__class_Ozero(U_1133)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_1133) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
! [U_1133] :
( c_RealVector_Onorm__class_Onorm(U_1133,c_Groups_Ozero__class_Ozero(U_1133)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_1133) ),
inference(definitional_conversion,[status(esa)],[f_436_2]) ).
cnf(f_436_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1133,c_Groups_Ozero__class_Ozero(U_1133)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_1133) ),
inference(clausify,[status(thm)],[f_436_3]) ).
fof(f_437_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(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_437_2,plain,
! [U_1136,U_1135,U_1134] :
( c_Groups_Oabs__class_Oabs(U_1134,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1134),U_1135),U_1136)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1134),c_Groups_Oabs__class_Oabs(U_1134,U_1135)),c_Groups_Oabs__class_Oabs(U_1134,U_1136))
| ~ class_Rings_Olinordered__idom(U_1134) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
! [U_1135,U_1134,U_1136] :
( c_Groups_Oabs__class_Oabs(U_1134,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1134),U_1135),U_1136)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1134),c_Groups_Oabs__class_Oabs(U_1134,U_1135)),c_Groups_Oabs__class_Oabs(U_1134,U_1136))
| ~ class_Rings_Olinordered__idom(U_1134) ),
inference(definitional_conversion,[status(esa)],[f_437_2]) ).
cnf(f_437_4,plain,
( c_Groups_Oabs__class_Oabs(U_1134,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1134),U_1135),U_1136)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1134),c_Groups_Oabs__class_Oabs(U_1134,U_1135)),c_Groups_Oabs__class_Oabs(U_1134,U_1136))
| ~ class_Rings_Olinordered__idom(U_1134) ),
inference(clausify,[status(thm)],[f_437_3]) ).
fof(f_438_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(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)) = hAPP(hAPP(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_438_2,plain,
! [U_1138,U_1137] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1137),c_Groups_Oabs__class_Oabs(U_1137,U_1138)),c_Groups_Oabs__class_Oabs(U_1137,U_1138)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1137),U_1138),U_1138)
| ~ class_Rings_Olinordered__idom(U_1137) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
fof(f_438_3,plain,
! [U_1137,U_1138] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1137),c_Groups_Oabs__class_Oabs(U_1137,U_1138)),c_Groups_Oabs__class_Oabs(U_1137,U_1138)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1137),U_1138),U_1138)
| ~ class_Rings_Olinordered__idom(U_1137) ),
inference(definitional_conversion,[status(esa)],[f_438_2]) ).
cnf(f_438_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1137),c_Groups_Oabs__class_Oabs(U_1137,U_1138)),c_Groups_Oabs__class_Oabs(U_1137,U_1138)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1137),U_1138),U_1138)
| ~ class_Rings_Olinordered__idom(U_1137) ),
inference(clausify,[status(thm)],[f_438_3]) ).
fof(f_439_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_439_2,plain,
! [U_1139] :
( c_Groups_Oabs__class_Oabs(U_1139,c_Groups_Oone__class_Oone(U_1139)) = c_Groups_Oone__class_Oone(U_1139)
| ~ class_Rings_Olinordered__idom(U_1139) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
fof(f_439_3,plain,
! [U_1139] :
( c_Groups_Oabs__class_Oabs(U_1139,c_Groups_Oone__class_Oone(U_1139)) = c_Groups_Oone__class_Oone(U_1139)
| ~ class_Rings_Olinordered__idom(U_1139) ),
inference(definitional_conversion,[status(esa)],[f_439_2]) ).
cnf(f_439_4,plain,
( c_Groups_Oabs__class_Oabs(U_1139,c_Groups_Oone__class_Oone(U_1139)) = c_Groups_Oone__class_Oone(U_1139)
| ~ class_Rings_Olinordered__idom(U_1139) ),
inference(clausify,[status(thm)],[f_439_3]) ).
fof(f_440_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_440_2,plain,
! [U_1142,U_1141,U_1140] :
( c_RealVector_Onorm__class_Onorm(U_1140,c_Groups_Ominus__class_Ominus(U_1140,U_1141,U_1142)) = c_RealVector_Onorm__class_Onorm(U_1140,c_Groups_Ominus__class_Ominus(U_1140,U_1142,U_1141))
| ~ class_RealVector_Oreal__normed__vector(U_1140) ),
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
! [U_1140,U_1141,U_1142] :
( c_RealVector_Onorm__class_Onorm(U_1140,c_Groups_Ominus__class_Ominus(U_1140,U_1141,U_1142)) = c_RealVector_Onorm__class_Onorm(U_1140,c_Groups_Ominus__class_Ominus(U_1140,U_1142,U_1141))
| ~ class_RealVector_Oreal__normed__vector(U_1140) ),
inference(definitional_conversion,[status(esa)],[f_440_2]) ).
cnf(f_440_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1140,c_Groups_Ominus__class_Ominus(U_1140,U_1141,U_1142)) = c_RealVector_Onorm__class_Onorm(U_1140,c_Groups_Ominus__class_Ominus(U_1140,U_1142,U_1141))
| ~ class_RealVector_Oreal__normed__vector(U_1140) ),
inference(clausify,[status(thm)],[f_440_3]) ).
fof(f_441_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_441_2,plain,
! [U_1144,U_1143] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1143,U_1144))
| ~ class_RealVector_Oreal__normed__vector(U_1143) ),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
! [U_1144,U_1143] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1143,U_1144))
| ~ class_RealVector_Oreal__normed__vector(U_1143) ),
inference(definitional_conversion,[status(esa)],[f_441_2]) ).
cnf(f_441_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1143,U_1144))
| ~ class_RealVector_Oreal__normed__vector(U_1143) ),
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_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]) ).
fof(f_442_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(definitional_conversion,[status(esa)],[f_442_1]) ).
cnf(f_442_3,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_442_2]) ).
fof(f_443_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_443_2,plain,
! [U_1146,U_1145] :
( 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_1145,U_1146))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1146)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1145) ),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
! [U_1145,U_1146] :
( 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_1145,U_1146))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1146)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1145) ),
inference(definitional_conversion,[status(esa)],[f_443_2]) ).
cnf(f_443_4,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_1145,U_1146))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1146)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1145) ),
inference(clausify,[status(thm)],[f_443_3]) ).
fof(f_444_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_I2_J]) ).
fof(f_444_2,plain,
! [U_1148,U_1147] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1147),U_1148))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1148)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1147) ),
inference(variable_rename,[status(thm)],[f_444_1]) ).
fof(f_444_3,plain,
! [U_1148,U_1147] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1147),U_1148))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1148)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1147) ),
inference(definitional_conversion,[status(esa)],[f_444_2]) ).
cnf(f_444_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1147),U_1148))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1148)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1147) ),
inference(clausify,[status(thm)],[f_444_3]) ).
fof(f_445_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_445_2,plain,
! [U_1150,U_1149] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1149,U_1150)) = c_RealVector_Onorm__class_Onorm(U_1149,U_1150)
| ~ class_RealVector_Oreal__normed__vector(U_1149) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
fof(f_445_3,plain,
! [U_1150,U_1149] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1149,U_1150)) = c_RealVector_Onorm__class_Onorm(U_1149,U_1150)
| ~ class_RealVector_Oreal__normed__vector(U_1149) ),
inference(definitional_conversion,[status(esa)],[f_445_2]) ).
cnf(f_445_4,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1149,U_1150)) = c_RealVector_Onorm__class_Onorm(U_1149,U_1150)
| ~ class_RealVector_Oreal__normed__vector(U_1149) ),
inference(clausify,[status(thm)],[f_445_3]) ).
fof(f_446_1,plain,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(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_446_2,plain,
! [U_1152,U_1151] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1151),U_1152))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1151) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
fof(f_446_3,plain,
! [U_1151,U_1152] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1151),U_1152))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1151) ),
inference(definitional_conversion,[status(esa)],[f_446_2]) ).
cnf(f_446_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1151),U_1152))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_1151) ),
inference(clausify,[status(thm)],[f_446_3]) ).
fof(f_447_1,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_power2__i]) ).
fof(f_447_2,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
inference(definitional_conversion,[status(esa)],[f_447_1]) ).
cnf(f_447_3,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Complex_Ocomplex),c_Complex_Oii),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Int_Onumber__class_Onumber__of(tc_Complex_Ocomplex,c_Int_OMin),
inference(clausify,[status(thm)],[f_447_2]) ).
fof(f_448_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_448_2,plain,
! [U_1154,U_1153] :
( c_Orderings_Oord__class_Oless__eq(U_1153,c_Groups_Ozero__class_Ozero(U_1153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1153),U_1154),U_1154))
| ~ class_Rings_Olinordered__ring(U_1153) ),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
! [U_1153,U_1154] :
( c_Orderings_Oord__class_Oless__eq(U_1153,c_Groups_Ozero__class_Ozero(U_1153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1153),U_1154),U_1154))
| ~ class_Rings_Olinordered__ring(U_1153) ),
inference(definitional_conversion,[status(esa)],[f_448_2]) ).
cnf(f_448_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1153,c_Groups_Ozero__class_Ozero(U_1153),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1153),U_1154),U_1154))
| ~ class_Rings_Olinordered__ring(U_1153) ),
inference(clausify,[status(thm)],[f_448_3]) ).
fof(f_449_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),hAPP(hAPP(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),hAPP(hAPP(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_449_2,plain,
! [U_1157,U_1156,U_1155] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1155),U_1156),U_1157))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1155,U_1157,c_Groups_Ozero__class_Ozero(U_1155))
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,U_1156,c_Groups_Ozero__class_Ozero(U_1155)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1157)
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1156) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_1155,U_1157,c_Groups_Ozero__class_Ozero(U_1155))
& c_Orderings_Oord__class_Oless__eq(U_1155,U_1156,c_Groups_Ozero__class_Ozero(U_1155)) )
| ( c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1157)
& c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1156) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1155),U_1156),U_1157)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1155) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
( ! [U_1157,U_1155,U_1156] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1155,U_1157,c_Groups_Ozero__class_Ozero(U_1155))
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,U_1156,c_Groups_Ozero__class_Ozero(U_1155))
| ~ sP66(U_1157,U_1155,U_1156) )
& ! [U_1157,U_1155,U_1156] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1157)
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1156)
| ~ sP66(U_1157,U_1155,U_1156) )
& ! [U_1157,U_1155,U_1156] :
( c_Orderings_Oord__class_Oless__eq(U_1155,U_1157,c_Groups_Ozero__class_Ozero(U_1155))
| ~ sP65(U_1157,U_1155,U_1156) )
& ! [U_1157,U_1155,U_1156] :
( c_Orderings_Oord__class_Oless__eq(U_1155,U_1156,c_Groups_Ozero__class_Ozero(U_1155))
| ~ sP65(U_1157,U_1155,U_1156) )
& ! [U_1157,U_1155,U_1156] :
( c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1157)
| ~ sP64(U_1157,U_1155,U_1156) )
& ! [U_1157,U_1155,U_1156] :
( c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1156)
| ~ sP64(U_1157,U_1155,U_1156) )
& ! [U_1157,U_1155,U_1156] :
( c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1155),U_1156),U_1157))
| sP66(U_1157,U_1155,U_1156)
| ~ sP67(U_1157,U_1155,U_1156) )
& ! [U_1157,U_1155,U_1156] :
( sP65(U_1157,U_1155,U_1156)
| sP64(U_1157,U_1155,U_1156)
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1155),U_1156),U_1157))
| ~ sP67(U_1157,U_1155,U_1156) )
& ! [U_1157,U_1155,U_1156] :
( sP67(U_1157,U_1155,U_1156)
| ~ class_Rings_Olinordered__ring__strict(U_1155) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64,sP65,sP66,sP67])],[f_449_2]) ).
cnf(f_449_4,plain,
( sP67(U_1157,U_1155,U_1156)
| ~ class_Rings_Olinordered__ring__strict(U_1155) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_5,plain,
( sP65(U_1157,U_1155,U_1156)
| sP64(U_1157,U_1155,U_1156)
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1155),U_1156),U_1157))
| ~ sP67(U_1157,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1155),U_1156),U_1157))
| sP66(U_1157,U_1155,U_1156)
| ~ sP67(U_1157,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1156)
| ~ sP64(U_1157,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1157)
| ~ sP64(U_1157,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_1155,U_1156,c_Groups_Ozero__class_Ozero(U_1155))
| ~ sP65(U_1157,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_1155,U_1157,c_Groups_Ozero__class_Ozero(U_1155))
| ~ sP65(U_1157,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_11,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1157)
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,c_Groups_Ozero__class_Ozero(U_1155),U_1156)
| ~ sP66(U_1157,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_449_3]) ).
cnf(f_449_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1155,U_1157,c_Groups_Ozero__class_Ozero(U_1155))
| ~ c_Orderings_Oord__class_Oless__eq(U_1155,U_1156,c_Groups_Ozero__class_Ozero(U_1155))
| ~ sP66(U_1157,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_449_3]) ).
fof(f_450_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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,hAPP(hAPP(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_450_2,plain,
! [U_1160,U_1159,U_1158] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1158),U_1159),U_1160),c_Groups_Ozero__class_Ozero(U_1158))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1160)
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,U_1159,c_Groups_Ozero__class_Ozero(U_1158)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_1158,U_1160,c_Groups_Ozero__class_Ozero(U_1158))
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1159) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1160)
& c_Orderings_Oord__class_Oless__eq(U_1158,U_1159,c_Groups_Ozero__class_Ozero(U_1158)) )
| ( c_Orderings_Oord__class_Oless__eq(U_1158,U_1160,c_Groups_Ozero__class_Ozero(U_1158))
& c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1159) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1158),U_1159),U_1160),c_Groups_Ozero__class_Ozero(U_1158)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1158) ),
inference(variable_rename,[status(thm)],[f_450_1]) ).
fof(f_450_3,plain,
( ! [U_1159,U_1158,U_1160] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1160)
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,U_1159,c_Groups_Ozero__class_Ozero(U_1158))
| ~ sP70(U_1159,U_1158,U_1160) )
& ! [U_1159,U_1158,U_1160] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1158,U_1160,c_Groups_Ozero__class_Ozero(U_1158))
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1159)
| ~ sP70(U_1159,U_1158,U_1160) )
& ! [U_1159,U_1158,U_1160] :
( c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1160)
| ~ sP69(U_1159,U_1158,U_1160) )
& ! [U_1159,U_1158,U_1160] :
( c_Orderings_Oord__class_Oless__eq(U_1158,U_1159,c_Groups_Ozero__class_Ozero(U_1158))
| ~ sP69(U_1159,U_1158,U_1160) )
& ! [U_1159,U_1158,U_1160] :
( c_Orderings_Oord__class_Oless__eq(U_1158,U_1160,c_Groups_Ozero__class_Ozero(U_1158))
| ~ sP68(U_1159,U_1158,U_1160) )
& ! [U_1159,U_1158,U_1160] :
( c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1159)
| ~ sP68(U_1159,U_1158,U_1160) )
& ! [U_1159,U_1158,U_1160] :
( c_Orderings_Oord__class_Oless__eq(U_1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1158),U_1159),U_1160),c_Groups_Ozero__class_Ozero(U_1158))
| sP70(U_1159,U_1158,U_1160)
| ~ sP71(U_1159,U_1158,U_1160) )
& ! [U_1159,U_1158,U_1160] :
( sP69(U_1159,U_1158,U_1160)
| sP68(U_1159,U_1158,U_1160)
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1158),U_1159),U_1160),c_Groups_Ozero__class_Ozero(U_1158))
| ~ sP71(U_1159,U_1158,U_1160) )
& ! [U_1159,U_1158,U_1160] :
( sP71(U_1159,U_1158,U_1160)
| ~ class_Rings_Olinordered__ring__strict(U_1158) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68,sP69,sP70,sP71])],[f_450_2]) ).
cnf(f_450_4,plain,
( sP71(U_1159,U_1158,U_1160)
| ~ class_Rings_Olinordered__ring__strict(U_1158) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_5,plain,
( sP69(U_1159,U_1158,U_1160)
| sP68(U_1159,U_1158,U_1160)
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1158),U_1159),U_1160),c_Groups_Ozero__class_Ozero(U_1158))
| ~ sP71(U_1159,U_1158,U_1160) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1158,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1158),U_1159),U_1160),c_Groups_Ozero__class_Ozero(U_1158))
| sP70(U_1159,U_1158,U_1160)
| ~ sP71(U_1159,U_1158,U_1160) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1159)
| ~ sP68(U_1159,U_1158,U_1160) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_1158,U_1160,c_Groups_Ozero__class_Ozero(U_1158))
| ~ sP68(U_1159,U_1158,U_1160) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_1158,U_1159,c_Groups_Ozero__class_Ozero(U_1158))
| ~ sP69(U_1159,U_1158,U_1160) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1160)
| ~ sP69(U_1159,U_1158,U_1160) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_11,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1158,U_1160,c_Groups_Ozero__class_Ozero(U_1158))
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1159)
| ~ sP70(U_1159,U_1158,U_1160) ),
inference(clausify,[status(thm)],[f_450_3]) ).
cnf(f_450_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1158,c_Groups_Ozero__class_Ozero(U_1158),U_1160)
| ~ c_Orderings_Oord__class_Oless__eq(U_1158,U_1159,c_Groups_Ozero__class_Ozero(U_1158))
| ~ sP70(U_1159,U_1158,U_1160) ),
inference(clausify,[status(thm)],[f_450_3]) ).
fof(f_451_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_451_2,plain,
! [U_1163,U_1162,U_1161] :
( c_Orderings_Oord__class_Oless__eq(U_1161,c_Groups_Ozero__class_Ozero(U_1161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1161),U_1162),U_1163))
| ~ c_Orderings_Oord__class_Oless__eq(U_1161,c_Groups_Ozero__class_Ozero(U_1161),U_1163)
| ~ c_Orderings_Oord__class_Oless__eq(U_1161,c_Groups_Ozero__class_Ozero(U_1161),U_1162)
| ~ class_Rings_Oordered__cancel__semiring(U_1161) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
fof(f_451_3,plain,
! [U_1161,U_1163,U_1162] :
( c_Orderings_Oord__class_Oless__eq(U_1161,c_Groups_Ozero__class_Ozero(U_1161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1161),U_1162),U_1163))
| ~ c_Orderings_Oord__class_Oless__eq(U_1161,c_Groups_Ozero__class_Ozero(U_1161),U_1163)
| ~ c_Orderings_Oord__class_Oless__eq(U_1161,c_Groups_Ozero__class_Ozero(U_1161),U_1162)
| ~ class_Rings_Oordered__cancel__semiring(U_1161) ),
inference(definitional_conversion,[status(esa)],[f_451_2]) ).
cnf(f_451_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1161,c_Groups_Ozero__class_Ozero(U_1161),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1161),U_1162),U_1163))
| ~ c_Orderings_Oord__class_Oless__eq(U_1161,c_Groups_Ozero__class_Ozero(U_1161),U_1163)
| ~ c_Orderings_Oord__class_Oless__eq(U_1161,c_Groups_Ozero__class_Ozero(U_1161),U_1162)
| ~ class_Rings_Oordered__cancel__semiring(U_1161) ),
inference(clausify,[status(thm)],[f_451_3]) ).
fof(f_452_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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_452_2,plain,
! [U_1166,U_1165,U_1164] :
( c_Orderings_Oord__class_Oless__eq(U_1164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1164),U_1165),U_1166),c_Groups_Ozero__class_Ozero(U_1164))
| ~ c_Orderings_Oord__class_Oless__eq(U_1164,U_1166,c_Groups_Ozero__class_Ozero(U_1164))
| ~ c_Orderings_Oord__class_Oless__eq(U_1164,c_Groups_Ozero__class_Ozero(U_1164),U_1165)
| ~ class_Rings_Oordered__cancel__semiring(U_1164) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
fof(f_452_3,plain,
! [U_1166,U_1164,U_1165] :
( c_Orderings_Oord__class_Oless__eq(U_1164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1164),U_1165),U_1166),c_Groups_Ozero__class_Ozero(U_1164))
| ~ c_Orderings_Oord__class_Oless__eq(U_1164,U_1166,c_Groups_Ozero__class_Ozero(U_1164))
| ~ c_Orderings_Oord__class_Oless__eq(U_1164,c_Groups_Ozero__class_Ozero(U_1164),U_1165)
| ~ class_Rings_Oordered__cancel__semiring(U_1164) ),
inference(definitional_conversion,[status(esa)],[f_452_2]) ).
cnf(f_452_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1164,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1164),U_1165),U_1166),c_Groups_Ozero__class_Ozero(U_1164))
| ~ c_Orderings_Oord__class_Oless__eq(U_1164,U_1166,c_Groups_Ozero__class_Ozero(U_1164))
| ~ c_Orderings_Oord__class_Oless__eq(U_1164,c_Groups_Ozero__class_Ozero(U_1164),U_1165)
| ~ class_Rings_Oordered__cancel__semiring(U_1164) ),
inference(clausify,[status(thm)],[f_452_3]) ).
fof(f_453_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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_453_2,plain,
! [U_1169,U_1168,U_1167] :
( c_Orderings_Oord__class_Oless__eq(U_1167,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1167),U_1169),U_1168),c_Groups_Ozero__class_Ozero(U_1167))
| ~ c_Orderings_Oord__class_Oless__eq(U_1167,U_1169,c_Groups_Ozero__class_Ozero(U_1167))
| ~ c_Orderings_Oord__class_Oless__eq(U_1167,c_Groups_Ozero__class_Ozero(U_1167),U_1168)
| ~ class_Rings_Oordered__cancel__semiring(U_1167) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
fof(f_453_3,plain,
! [U_1167,U_1168,U_1169] :
( c_Orderings_Oord__class_Oless__eq(U_1167,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1167),U_1169),U_1168),c_Groups_Ozero__class_Ozero(U_1167))
| ~ c_Orderings_Oord__class_Oless__eq(U_1167,U_1169,c_Groups_Ozero__class_Ozero(U_1167))
| ~ c_Orderings_Oord__class_Oless__eq(U_1167,c_Groups_Ozero__class_Ozero(U_1167),U_1168)
| ~ class_Rings_Oordered__cancel__semiring(U_1167) ),
inference(definitional_conversion,[status(esa)],[f_453_2]) ).
cnf(f_453_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1167,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1167),U_1169),U_1168),c_Groups_Ozero__class_Ozero(U_1167))
| ~ c_Orderings_Oord__class_Oless__eq(U_1167,U_1169,c_Groups_Ozero__class_Ozero(U_1167))
| ~ c_Orderings_Oord__class_Oless__eq(U_1167,c_Groups_Ozero__class_Ozero(U_1167),U_1168)
| ~ class_Rings_Oordered__cancel__semiring(U_1167) ),
inference(clausify,[status(thm)],[f_453_3]) ).
fof(f_454_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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_454_2,plain,
! [U_1172,U_1171,U_1170] :
( c_Orderings_Oord__class_Oless__eq(U_1170,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1170),U_1171),U_1172),c_Groups_Ozero__class_Ozero(U_1170))
| ~ c_Orderings_Oord__class_Oless__eq(U_1170,c_Groups_Ozero__class_Ozero(U_1170),U_1172)
| ~ c_Orderings_Oord__class_Oless__eq(U_1170,U_1171,c_Groups_Ozero__class_Ozero(U_1170))
| ~ class_Rings_Oordered__cancel__semiring(U_1170) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
! [U_1171,U_1172,U_1170] :
( c_Orderings_Oord__class_Oless__eq(U_1170,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1170),U_1171),U_1172),c_Groups_Ozero__class_Ozero(U_1170))
| ~ c_Orderings_Oord__class_Oless__eq(U_1170,c_Groups_Ozero__class_Ozero(U_1170),U_1172)
| ~ c_Orderings_Oord__class_Oless__eq(U_1170,U_1171,c_Groups_Ozero__class_Ozero(U_1170))
| ~ class_Rings_Oordered__cancel__semiring(U_1170) ),
inference(definitional_conversion,[status(esa)],[f_454_2]) ).
cnf(f_454_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1170,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1170),U_1171),U_1172),c_Groups_Ozero__class_Ozero(U_1170))
| ~ c_Orderings_Oord__class_Oless__eq(U_1170,c_Groups_Ozero__class_Ozero(U_1170),U_1172)
| ~ c_Orderings_Oord__class_Oless__eq(U_1170,U_1171,c_Groups_Ozero__class_Ozero(U_1170))
| ~ class_Rings_Oordered__cancel__semiring(U_1170) ),
inference(clausify,[status(thm)],[f_454_3]) ).
fof(f_455_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_455_2,plain,
! [U_1175,U_1174,U_1173] :
( c_Orderings_Oord__class_Oless__eq(U_1173,c_Groups_Ozero__class_Ozero(U_1173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1173),U_1174),U_1175))
| ~ c_Orderings_Oord__class_Oless__eq(U_1173,U_1175,c_Groups_Ozero__class_Ozero(U_1173))
| ~ c_Orderings_Oord__class_Oless__eq(U_1173,U_1174,c_Groups_Ozero__class_Ozero(U_1173))
| ~ class_Rings_Oordered__ring(U_1173) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
! [U_1175,U_1173,U_1174] :
( c_Orderings_Oord__class_Oless__eq(U_1173,c_Groups_Ozero__class_Ozero(U_1173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1173),U_1174),U_1175))
| ~ c_Orderings_Oord__class_Oless__eq(U_1173,U_1175,c_Groups_Ozero__class_Ozero(U_1173))
| ~ c_Orderings_Oord__class_Oless__eq(U_1173,U_1174,c_Groups_Ozero__class_Ozero(U_1173))
| ~ class_Rings_Oordered__ring(U_1173) ),
inference(definitional_conversion,[status(esa)],[f_455_2]) ).
cnf(f_455_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1173,c_Groups_Ozero__class_Ozero(U_1173),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1173),U_1174),U_1175))
| ~ c_Orderings_Oord__class_Oless__eq(U_1173,U_1175,c_Groups_Ozero__class_Ozero(U_1173))
| ~ c_Orderings_Oord__class_Oless__eq(U_1173,U_1174,c_Groups_Ozero__class_Ozero(U_1173))
| ~ class_Rings_Oordered__ring(U_1173) ),
inference(clausify,[status(thm)],[f_455_3]) ).
fof(f_456_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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_456_2,plain,
! [U_1179,U_1178,U_1177,U_1176] :
( c_Orderings_Oord__class_Oless__eq(U_1176,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1176),U_1177),U_1179),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1176),U_1178),U_1179))
| ~ c_Orderings_Oord__class_Oless__eq(U_1176,c_Groups_Ozero__class_Ozero(U_1176),U_1179)
| ~ c_Orderings_Oord__class_Oless__eq(U_1176,U_1177,U_1178)
| ~ class_Rings_Oordered__semiring(U_1176) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
! [U_1176,U_1178,U_1177,U_1179] :
( c_Orderings_Oord__class_Oless__eq(U_1176,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1176),U_1177),U_1179),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1176),U_1178),U_1179))
| ~ c_Orderings_Oord__class_Oless__eq(U_1176,c_Groups_Ozero__class_Ozero(U_1176),U_1179)
| ~ c_Orderings_Oord__class_Oless__eq(U_1176,U_1177,U_1178)
| ~ class_Rings_Oordered__semiring(U_1176) ),
inference(definitional_conversion,[status(esa)],[f_456_2]) ).
cnf(f_456_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1176,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1176),U_1177),U_1179),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1176),U_1178),U_1179))
| ~ c_Orderings_Oord__class_Oless__eq(U_1176,c_Groups_Ozero__class_Ozero(U_1176),U_1179)
| ~ c_Orderings_Oord__class_Oless__eq(U_1176,U_1177,U_1178)
| ~ class_Rings_Oordered__semiring(U_1176) ),
inference(clausify,[status(thm)],[f_456_3]) ).
fof(f_457_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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_457_2,plain,
! [U_1183,U_1182,U_1181,U_1180] :
( c_Orderings_Oord__class_Oless__eq(U_1180,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1180),U_1183),U_1181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1180),U_1183),U_1182))
| ~ c_Orderings_Oord__class_Oless__eq(U_1180,c_Groups_Ozero__class_Ozero(U_1180),U_1183)
| ~ c_Orderings_Oord__class_Oless__eq(U_1180,U_1181,U_1182)
| ~ class_Rings_Oordered__semiring(U_1180) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
fof(f_457_3,plain,
! [U_1183,U_1181,U_1180,U_1182] :
( c_Orderings_Oord__class_Oless__eq(U_1180,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1180),U_1183),U_1181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1180),U_1183),U_1182))
| ~ c_Orderings_Oord__class_Oless__eq(U_1180,c_Groups_Ozero__class_Ozero(U_1180),U_1183)
| ~ c_Orderings_Oord__class_Oless__eq(U_1180,U_1181,U_1182)
| ~ class_Rings_Oordered__semiring(U_1180) ),
inference(definitional_conversion,[status(esa)],[f_457_2]) ).
cnf(f_457_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1180,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1180),U_1183),U_1181),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1180),U_1183),U_1182))
| ~ c_Orderings_Oord__class_Oless__eq(U_1180,c_Groups_Ozero__class_Ozero(U_1180),U_1183)
| ~ c_Orderings_Oord__class_Oless__eq(U_1180,U_1181,U_1182)
| ~ class_Rings_Oordered__semiring(U_1180) ),
inference(clausify,[status(thm)],[f_457_3]) ).
fof(f_458_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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_458_2,plain,
! [U_1187,U_1186,U_1185,U_1184] :
( c_Orderings_Oord__class_Oless__eq(U_1184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1184),U_1187),U_1185),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1184),U_1187),U_1186))
| ~ c_Orderings_Oord__class_Oless__eq(U_1184,c_Groups_Ozero__class_Ozero(U_1184),U_1187)
| ~ c_Orderings_Oord__class_Oless__eq(U_1184,U_1185,U_1186)
| ~ class_Rings_Oordered__comm__semiring(U_1184) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
! [U_1187,U_1185,U_1186,U_1184] :
( c_Orderings_Oord__class_Oless__eq(U_1184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1184),U_1187),U_1185),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1184),U_1187),U_1186))
| ~ c_Orderings_Oord__class_Oless__eq(U_1184,c_Groups_Ozero__class_Ozero(U_1184),U_1187)
| ~ c_Orderings_Oord__class_Oless__eq(U_1184,U_1185,U_1186)
| ~ class_Rings_Oordered__comm__semiring(U_1184) ),
inference(definitional_conversion,[status(esa)],[f_458_2]) ).
cnf(f_458_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1184,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1184),U_1187),U_1185),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1184),U_1187),U_1186))
| ~ c_Orderings_Oord__class_Oless__eq(U_1184,c_Groups_Ozero__class_Ozero(U_1184),U_1187)
| ~ c_Orderings_Oord__class_Oless__eq(U_1184,U_1185,U_1186)
| ~ class_Rings_Oordered__comm__semiring(U_1184) ),
inference(clausify,[status(thm)],[f_458_3]) ).
fof(f_459_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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_459_2,plain,
! [U_1191,U_1190,U_1189,U_1188] :
( c_Orderings_Oord__class_Oless__eq(U_1188,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1188),U_1190),U_1191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1188),U_1189),U_1191))
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,U_1191,c_Groups_Ozero__class_Ozero(U_1188))
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,U_1189,U_1190)
| ~ class_Rings_Oordered__ring(U_1188) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
! [U_1190,U_1188,U_1189,U_1191] :
( c_Orderings_Oord__class_Oless__eq(U_1188,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1188),U_1190),U_1191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1188),U_1189),U_1191))
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,U_1191,c_Groups_Ozero__class_Ozero(U_1188))
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,U_1189,U_1190)
| ~ class_Rings_Oordered__ring(U_1188) ),
inference(definitional_conversion,[status(esa)],[f_459_2]) ).
cnf(f_459_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1188,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1188),U_1190),U_1191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1188),U_1189),U_1191))
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,U_1191,c_Groups_Ozero__class_Ozero(U_1188))
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,U_1189,U_1190)
| ~ class_Rings_Oordered__ring(U_1188) ),
inference(clausify,[status(thm)],[f_459_3]) ).
fof(f_460_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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_460_2,plain,
! [U_1195,U_1194,U_1193,U_1192] :
( c_Orderings_Oord__class_Oless__eq(U_1192,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1192),U_1195),U_1194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1192),U_1195),U_1193))
| ~ c_Orderings_Oord__class_Oless__eq(U_1192,U_1195,c_Groups_Ozero__class_Ozero(U_1192))
| ~ c_Orderings_Oord__class_Oless__eq(U_1192,U_1193,U_1194)
| ~ class_Rings_Oordered__ring(U_1192) ),
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
! [U_1195,U_1193,U_1192,U_1194] :
( c_Orderings_Oord__class_Oless__eq(U_1192,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1192),U_1195),U_1194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1192),U_1195),U_1193))
| ~ c_Orderings_Oord__class_Oless__eq(U_1192,U_1195,c_Groups_Ozero__class_Ozero(U_1192))
| ~ c_Orderings_Oord__class_Oless__eq(U_1192,U_1193,U_1194)
| ~ class_Rings_Oordered__ring(U_1192) ),
inference(definitional_conversion,[status(esa)],[f_460_2]) ).
cnf(f_460_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1192,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1192),U_1195),U_1194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1192),U_1195),U_1193))
| ~ c_Orderings_Oord__class_Oless__eq(U_1192,U_1195,c_Groups_Ozero__class_Ozero(U_1192))
| ~ c_Orderings_Oord__class_Oless__eq(U_1192,U_1193,U_1194)
| ~ class_Rings_Oordered__ring(U_1192) ),
inference(clausify,[status(thm)],[f_460_3]) ).
fof(f_461_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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_461_2,plain,
! [U_1200,U_1199,U_1198,U_1197,U_1196] :
( c_Orderings_Oord__class_Oless__eq(U_1196,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1196),U_1197),U_1199),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1196),U_1198),U_1200))
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,c_Groups_Ozero__class_Ozero(U_1196),U_1199)
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,c_Groups_Ozero__class_Ozero(U_1196),U_1197)
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,U_1199,U_1200)
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,U_1197,U_1198)
| ~ class_Rings_Oordered__semiring(U_1196) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
fof(f_461_3,plain,
! [U_1198,U_1196,U_1197,U_1199,U_1200] :
( c_Orderings_Oord__class_Oless__eq(U_1196,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1196),U_1197),U_1199),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1196),U_1198),U_1200))
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,c_Groups_Ozero__class_Ozero(U_1196),U_1199)
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,c_Groups_Ozero__class_Ozero(U_1196),U_1197)
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,U_1199,U_1200)
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,U_1197,U_1198)
| ~ class_Rings_Oordered__semiring(U_1196) ),
inference(definitional_conversion,[status(esa)],[f_461_2]) ).
cnf(f_461_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1196,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1196),U_1197),U_1199),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1196),U_1198),U_1200))
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,c_Groups_Ozero__class_Ozero(U_1196),U_1199)
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,c_Groups_Ozero__class_Ozero(U_1196),U_1197)
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,U_1199,U_1200)
| ~ c_Orderings_Oord__class_Oless__eq(U_1196,U_1197,U_1198)
| ~ class_Rings_Oordered__semiring(U_1196) ),
inference(clausify,[status(thm)],[f_461_3]) ).
fof(f_462_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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_462_2,plain,
! [U_1205,U_1204,U_1203,U_1202,U_1201] :
( c_Orderings_Oord__class_Oless__eq(U_1201,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1201),U_1202),U_1204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1201),U_1203),U_1205))
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,c_Groups_Ozero__class_Ozero(U_1201),U_1204)
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,c_Groups_Ozero__class_Ozero(U_1201),U_1203)
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,U_1204,U_1205)
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,U_1202,U_1203)
| ~ class_Rings_Oordered__semiring(U_1201) ),
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
! [U_1202,U_1203,U_1205,U_1201,U_1204] :
( c_Orderings_Oord__class_Oless__eq(U_1201,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1201),U_1202),U_1204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1201),U_1203),U_1205))
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,c_Groups_Ozero__class_Ozero(U_1201),U_1204)
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,c_Groups_Ozero__class_Ozero(U_1201),U_1203)
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,U_1204,U_1205)
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,U_1202,U_1203)
| ~ class_Rings_Oordered__semiring(U_1201) ),
inference(definitional_conversion,[status(esa)],[f_462_2]) ).
cnf(f_462_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1201,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1201),U_1202),U_1204),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1201),U_1203),U_1205))
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,c_Groups_Ozero__class_Ozero(U_1201),U_1204)
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,c_Groups_Ozero__class_Ozero(U_1201),U_1203)
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,U_1204,U_1205)
| ~ c_Orderings_Oord__class_Oless__eq(U_1201,U_1202,U_1203)
| ~ class_Rings_Oordered__semiring(U_1201) ),
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_463_2,plain,
! [U_1208,U_1207,U_1206] :
( c_Orderings_Oord__class_Oless__eq(U_1206,c_Groups_Ozero__class_Ozero(U_1206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1206),U_1207),U_1208))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1206,U_1208,c_Groups_Ozero__class_Ozero(U_1206))
| ~ c_Orderings_Oord__class_Oless__eq(U_1206,U_1207,c_Groups_Ozero__class_Ozero(U_1206)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_1206,c_Groups_Ozero__class_Ozero(U_1206),U_1208)
| ~ c_Orderings_Oord__class_Oless__eq(U_1206,c_Groups_Ozero__class_Ozero(U_1206),U_1207) ) )
| ~ class_Rings_Oordered__ring(U_1206) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
fof(f_463_3,plain,
( ! [U_1208,U_1206,U_1207] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1206,U_1208,c_Groups_Ozero__class_Ozero(U_1206))
| ~ c_Orderings_Oord__class_Oless__eq(U_1206,U_1207,c_Groups_Ozero__class_Ozero(U_1206))
| ~ sP72(U_1208,U_1206,U_1207) )
& ! [U_1208,U_1206,U_1207] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1206,c_Groups_Ozero__class_Ozero(U_1206),U_1208)
| ~ c_Orderings_Oord__class_Oless__eq(U_1206,c_Groups_Ozero__class_Ozero(U_1206),U_1207)
| ~ sP72(U_1208,U_1206,U_1207) )
& ! [U_1208,U_1206,U_1207] :
( c_Orderings_Oord__class_Oless__eq(U_1206,c_Groups_Ozero__class_Ozero(U_1206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1206),U_1207),U_1208))
| sP72(U_1208,U_1206,U_1207)
| ~ class_Rings_Oordered__ring(U_1206) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_463_2]) ).
cnf(f_463_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1206,c_Groups_Ozero__class_Ozero(U_1206),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1206),U_1207),U_1208))
| sP72(U_1208,U_1206,U_1207)
| ~ class_Rings_Oordered__ring(U_1206) ),
inference(clausify,[status(thm)],[f_463_3]) ).
cnf(f_463_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1206,c_Groups_Ozero__class_Ozero(U_1206),U_1208)
| ~ c_Orderings_Oord__class_Oless__eq(U_1206,c_Groups_Ozero__class_Ozero(U_1206),U_1207)
| ~ sP72(U_1208,U_1206,U_1207) ),
inference(clausify,[status(thm)],[f_463_3]) ).
cnf(f_463_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1206,U_1208,c_Groups_Ozero__class_Ozero(U_1206))
| ~ c_Orderings_Oord__class_Oless__eq(U_1206,U_1207,c_Groups_Ozero__class_Ozero(U_1206))
| ~ sP72(U_1208,U_1206,U_1207) ),
inference(clausify,[status(thm)],[f_463_3]) ).
fof(f_464_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(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_464_2,plain,
! [U_1211,U_1210,U_1209] :
( c_Orderings_Oord__class_Oless__eq(U_1209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1209),U_1210),U_1211),c_Groups_Ozero__class_Ozero(U_1209))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1209,c_Groups_Ozero__class_Ozero(U_1209),U_1211)
| ~ c_Orderings_Oord__class_Oless__eq(U_1209,U_1210,c_Groups_Ozero__class_Ozero(U_1209)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_1209,U_1211,c_Groups_Ozero__class_Ozero(U_1209))
| ~ c_Orderings_Oord__class_Oless__eq(U_1209,c_Groups_Ozero__class_Ozero(U_1209),U_1210) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_1209) ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
fof(f_464_3,plain,
( ! [U_1210,U_1211,U_1209] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1209,c_Groups_Ozero__class_Ozero(U_1209),U_1211)
| ~ c_Orderings_Oord__class_Oless__eq(U_1209,U_1210,c_Groups_Ozero__class_Ozero(U_1209))
| ~ sP73(U_1210,U_1211,U_1209) )
& ! [U_1210,U_1211,U_1209] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1209,U_1211,c_Groups_Ozero__class_Ozero(U_1209))
| ~ c_Orderings_Oord__class_Oless__eq(U_1209,c_Groups_Ozero__class_Ozero(U_1209),U_1210)
| ~ sP73(U_1210,U_1211,U_1209) )
& ! [U_1210,U_1211,U_1209] :
( c_Orderings_Oord__class_Oless__eq(U_1209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1209),U_1210),U_1211),c_Groups_Ozero__class_Ozero(U_1209))
| sP73(U_1210,U_1211,U_1209)
| ~ class_Rings_Oordered__cancel__semiring(U_1209) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_464_2]) ).
cnf(f_464_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1209),U_1210),U_1211),c_Groups_Ozero__class_Ozero(U_1209))
| sP73(U_1210,U_1211,U_1209)
| ~ class_Rings_Oordered__cancel__semiring(U_1209) ),
inference(clausify,[status(thm)],[f_464_3]) ).
cnf(f_464_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1209,U_1211,c_Groups_Ozero__class_Ozero(U_1209))
| ~ c_Orderings_Oord__class_Oless__eq(U_1209,c_Groups_Ozero__class_Ozero(U_1209),U_1210)
| ~ sP73(U_1210,U_1211,U_1209) ),
inference(clausify,[status(thm)],[f_464_3]) ).
cnf(f_464_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1209,c_Groups_Ozero__class_Ozero(U_1209),U_1211)
| ~ c_Orderings_Oord__class_Oless__eq(U_1209,U_1210,c_Groups_Ozero__class_Ozero(U_1209))
| ~ sP73(U_1210,U_1211,U_1209) ),
inference(clausify,[status(thm)],[f_464_3]) ).
fof(f_465_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_465_2,plain,
! [U_1212] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1212,c_Groups_Oone__class_Oone(U_1212),c_Groups_Ozero__class_Ozero(U_1212))
| ~ class_Rings_Olinordered__semidom(U_1212) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
fof(f_465_3,plain,
! [U_1212] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1212,c_Groups_Oone__class_Oone(U_1212),c_Groups_Ozero__class_Ozero(U_1212))
| ~ class_Rings_Olinordered__semidom(U_1212) ),
inference(definitional_conversion,[status(esa)],[f_465_2]) ).
cnf(f_465_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1212,c_Groups_Oone__class_Oone(U_1212),c_Groups_Ozero__class_Ozero(U_1212))
| ~ class_Rings_Olinordered__semidom(U_1212) ),
inference(clausify,[status(thm)],[f_465_3]) ).
fof(f_466_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_466_2,plain,
! [U_1213] :
( c_Orderings_Oord__class_Oless__eq(U_1213,c_Groups_Ozero__class_Ozero(U_1213),c_Groups_Oone__class_Oone(U_1213))
| ~ class_Rings_Olinordered__semidom(U_1213) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
! [U_1213] :
( c_Orderings_Oord__class_Oless__eq(U_1213,c_Groups_Ozero__class_Ozero(U_1213),c_Groups_Oone__class_Oone(U_1213))
| ~ class_Rings_Olinordered__semidom(U_1213) ),
inference(definitional_conversion,[status(esa)],[f_466_2]) ).
cnf(f_466_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1213,c_Groups_Ozero__class_Ozero(U_1213),c_Groups_Oone__class_Oone(U_1213))
| ~ class_Rings_Olinordered__semidom(U_1213) ),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_1,plain,
! [V_b,V_a,V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),hAPP(hAPP(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,hAPP(hAPP(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)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ominus__class_Ominus(T_a,V_x,V_a)),V_b)),hAPP(hAPP(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_467_2,plain,
! [U_1218,U_1217,U_1216,U_1215,U_1214] :
( c_Groups_Ominus__class_Ominus(U_1214,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),U_1215),U_1216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),U_1217),U_1218)) = c_Groups_Oplus__class_Oplus(U_1214,c_Groups_Oplus__class_Oplus(U_1214,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1217)),c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1218)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1217)),U_1218)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),U_1217),c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1218)))
| ~ class_RealVector_Oreal__normed__algebra(U_1214) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
! [U_1215,U_1214,U_1216,U_1217,U_1218] :
( c_Groups_Ominus__class_Ominus(U_1214,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),U_1215),U_1216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),U_1217),U_1218)) = c_Groups_Oplus__class_Oplus(U_1214,c_Groups_Oplus__class_Oplus(U_1214,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1217)),c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1218)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1217)),U_1218)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),U_1217),c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1218)))
| ~ class_RealVector_Oreal__normed__algebra(U_1214) ),
inference(definitional_conversion,[status(esa)],[f_467_2]) ).
cnf(f_467_4,plain,
( c_Groups_Ominus__class_Ominus(U_1214,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),U_1215),U_1216),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),U_1217),U_1218)) = c_Groups_Oplus__class_Oplus(U_1214,c_Groups_Oplus__class_Oplus(U_1214,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1217)),c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1218)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),c_Groups_Ominus__class_Ominus(U_1214,U_1215,U_1217)),U_1218)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1214),U_1217),c_Groups_Ominus__class_Ominus(U_1214,U_1216,U_1218)))
| ~ class_RealVector_Oreal__normed__algebra(U_1214) ),
inference(clausify,[status(thm)],[f_467_3]) ).
fof(f_468_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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,hAPP(hAPP(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,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_468_2,plain,
! [U_1224,U_1223,U_1222,U_1221,U_1220,U_1219] :
( ( ( c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1220),U_1221),U_1222) = c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1223),U_1221),U_1224)
| U_1222 != c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),c_Groups_Ominus__class_Ominus(U_1219,U_1223,U_1220)),U_1221),U_1224) )
& ( U_1222 = c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),c_Groups_Ominus__class_Ominus(U_1219,U_1223,U_1220)),U_1221),U_1224)
| c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1220),U_1221),U_1222) != c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1223),U_1221),U_1224) ) )
| ~ class_Rings_Oring(U_1219) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
fof(f_468_3,plain,
( ! [U_1219,U_1220,U_1221,U_1222,U_1223,U_1224] :
( c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1220),U_1221),U_1222) = c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1223),U_1221),U_1224)
| U_1222 != c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),c_Groups_Ominus__class_Ominus(U_1219,U_1223,U_1220)),U_1221),U_1224)
| ~ sP74(U_1219,U_1220,U_1221,U_1222,U_1223,U_1224) )
& ! [U_1219,U_1220,U_1221,U_1222,U_1223,U_1224] :
( U_1222 = c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),c_Groups_Ominus__class_Ominus(U_1219,U_1223,U_1220)),U_1221),U_1224)
| c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1220),U_1221),U_1222) != c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1223),U_1221),U_1224)
| ~ sP74(U_1219,U_1220,U_1221,U_1222,U_1223,U_1224) )
& ! [U_1219,U_1220,U_1221,U_1222,U_1223,U_1224] :
( sP74(U_1219,U_1220,U_1221,U_1222,U_1223,U_1224)
| ~ class_Rings_Oring(U_1219) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_468_2]) ).
cnf(f_468_4,plain,
( sP74(U_1219,U_1220,U_1221,U_1222,U_1223,U_1224)
| ~ class_Rings_Oring(U_1219) ),
inference(clausify,[status(thm)],[f_468_3]) ).
cnf(f_468_5,plain,
( U_1222 = c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),c_Groups_Ominus__class_Ominus(U_1219,U_1223,U_1220)),U_1221),U_1224)
| c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1220),U_1221),U_1222) != c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1223),U_1221),U_1224)
| ~ sP74(U_1219,U_1220,U_1221,U_1222,U_1223,U_1224) ),
inference(clausify,[status(thm)],[f_468_3]) ).
cnf(f_468_6,plain,
( c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1220),U_1221),U_1222) = c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),U_1223),U_1221),U_1224)
| U_1222 != c_Groups_Oplus__class_Oplus(U_1219,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1219),c_Groups_Ominus__class_Ominus(U_1219,U_1223,U_1220)),U_1221),U_1224)
| ~ sP74(U_1219,U_1220,U_1221,U_1222,U_1223,U_1224) ),
inference(clausify,[status(thm)],[f_468_3]) ).
fof(f_469_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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,hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_469_2,plain,
! [U_1230,U_1229,U_1228,U_1227,U_1226,U_1225] :
( ( ( c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1226),U_1227),U_1228) = c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1229),U_1227),U_1230)
| c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),c_Groups_Ominus__class_Ominus(U_1225,U_1226,U_1229)),U_1227),U_1228) != U_1230 )
& ( c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),c_Groups_Ominus__class_Ominus(U_1225,U_1226,U_1229)),U_1227),U_1228) = U_1230
| c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1226),U_1227),U_1228) != c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1229),U_1227),U_1230) ) )
| ~ class_Rings_Oring(U_1225) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
fof(f_469_3,plain,
( ! [U_1226,U_1225,U_1227,U_1228,U_1229,U_1230] :
( c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1226),U_1227),U_1228) = c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1229),U_1227),U_1230)
| c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),c_Groups_Ominus__class_Ominus(U_1225,U_1226,U_1229)),U_1227),U_1228) != U_1230
| ~ sP75(U_1226,U_1225,U_1227,U_1228,U_1229,U_1230) )
& ! [U_1226,U_1225,U_1227,U_1228,U_1229,U_1230] :
( c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),c_Groups_Ominus__class_Ominus(U_1225,U_1226,U_1229)),U_1227),U_1228) = U_1230
| c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1226),U_1227),U_1228) != c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1229),U_1227),U_1230)
| ~ sP75(U_1226,U_1225,U_1227,U_1228,U_1229,U_1230) )
& ! [U_1226,U_1225,U_1227,U_1228,U_1229,U_1230] :
( sP75(U_1226,U_1225,U_1227,U_1228,U_1229,U_1230)
| ~ class_Rings_Oring(U_1225) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75])],[f_469_2]) ).
cnf(f_469_4,plain,
( sP75(U_1226,U_1225,U_1227,U_1228,U_1229,U_1230)
| ~ class_Rings_Oring(U_1225) ),
inference(clausify,[status(thm)],[f_469_3]) ).
cnf(f_469_5,plain,
( c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),c_Groups_Ominus__class_Ominus(U_1225,U_1226,U_1229)),U_1227),U_1228) = U_1230
| c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1226),U_1227),U_1228) != c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1229),U_1227),U_1230)
| ~ sP75(U_1226,U_1225,U_1227,U_1228,U_1229,U_1230) ),
inference(clausify,[status(thm)],[f_469_3]) ).
cnf(f_469_6,plain,
( c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1226),U_1227),U_1228) = c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),U_1229),U_1227),U_1230)
| c_Groups_Oplus__class_Oplus(U_1225,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1225),c_Groups_Ominus__class_Ominus(U_1225,U_1226,U_1229)),U_1227),U_1228) != U_1230
| ~ sP75(U_1226,U_1225,U_1227,U_1228,U_1229,U_1230) ),
inference(clausify,[status(thm)],[f_469_3]) ).
fof(f_470_1,plain,
! [V_w_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_2)) = c_Groups_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_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_w_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,V_w_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_470_2,plain,
! [U_1233,U_1232,U_1231] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1231),U_1232),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233)) = c_Groups_Ozero__class_Ozero(U_1231)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1232 != c_Groups_Ozero__class_Ozero(U_1231) )
& ( ( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1232 = c_Groups_Ozero__class_Ozero(U_1231) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1231),U_1232),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233)) != c_Groups_Ozero__class_Ozero(U_1231) ) )
| ~ class_Rings_Ozero__neq__one(U_1231)
| ~ class_Rings_Ono__zero__divisors(U_1231)
| ~ class_Rings_Omult__zero(U_1231)
| ~ class_Power_Opower(U_1231) ),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
( ! [U_1233,U_1231,U_1232] :
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP76(U_1233,U_1231,U_1232) )
& ! [U_1233,U_1231,U_1232] :
( U_1232 = c_Groups_Ozero__class_Ozero(U_1231)
| ~ sP76(U_1233,U_1231,U_1232) )
& ! [U_1233,U_1231,U_1232] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1231),U_1232),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233)) = c_Groups_Ozero__class_Ozero(U_1231)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1232 != c_Groups_Ozero__class_Ozero(U_1231)
| ~ sP77(U_1233,U_1231,U_1232) )
& ! [U_1233,U_1231,U_1232] :
( sP76(U_1233,U_1231,U_1232)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1231),U_1232),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233)) != c_Groups_Ozero__class_Ozero(U_1231)
| ~ sP77(U_1233,U_1231,U_1232) )
& ! [U_1233,U_1231,U_1232] :
( sP77(U_1233,U_1231,U_1232)
| ~ class_Rings_Ozero__neq__one(U_1231)
| ~ class_Rings_Ono__zero__divisors(U_1231)
| ~ class_Rings_Omult__zero(U_1231)
| ~ class_Power_Opower(U_1231) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP76,sP77])],[f_470_2]) ).
cnf(f_470_4,plain,
( sP77(U_1233,U_1231,U_1232)
| ~ class_Rings_Ozero__neq__one(U_1231)
| ~ class_Rings_Ono__zero__divisors(U_1231)
| ~ class_Rings_Omult__zero(U_1231)
| ~ class_Power_Opower(U_1231) ),
inference(clausify,[status(thm)],[f_470_3]) ).
cnf(f_470_5,plain,
( sP76(U_1233,U_1231,U_1232)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1231),U_1232),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233)) != c_Groups_Ozero__class_Ozero(U_1231)
| ~ sP77(U_1233,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_470_3]) ).
cnf(f_470_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1231),U_1232),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233)) = c_Groups_Ozero__class_Ozero(U_1231)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1232 != c_Groups_Ozero__class_Ozero(U_1231)
| ~ sP77(U_1233,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_470_3]) ).
cnf(f_470_7,plain,
( U_1232 = c_Groups_Ozero__class_Ozero(U_1231)
| ~ sP76(U_1233,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_470_3]) ).
cnf(f_470_8,plain,
( c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1233) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP76(U_1233,U_1231,U_1232) ),
inference(clausify,[status(thm)],[f_470_3]) ).
fof(f_471_1,plain,
! [V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| V_xa_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_xa_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_xa_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_471_2,plain,
! [U_1235,U_1234] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1234,U_1235),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_1235 != c_Groups_Ozero__class_Ozero(U_1234) )
& ( U_1235 = c_Groups_Ozero__class_Ozero(U_1234)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1234,U_1235),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1234) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
fof(f_471_3,plain,
( ! [U_1235,U_1234] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1234,U_1235),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_1235 != c_Groups_Ozero__class_Ozero(U_1234)
| ~ sP78(U_1235,U_1234) )
& ! [U_1235,U_1234] :
( U_1235 = c_Groups_Ozero__class_Ozero(U_1234)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1234,U_1235),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP78(U_1235,U_1234) )
& ! [U_1235,U_1234] :
( sP78(U_1235,U_1234)
| ~ class_RealVector_Oreal__normed__vector(U_1234) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_471_2]) ).
cnf(f_471_4,plain,
( sP78(U_1235,U_1234)
| ~ class_RealVector_Oreal__normed__vector(U_1234) ),
inference(clausify,[status(thm)],[f_471_3]) ).
cnf(f_471_5,plain,
( U_1235 = c_Groups_Ozero__class_Ozero(U_1234)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1234,U_1235),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP78(U_1235,U_1234) ),
inference(clausify,[status(thm)],[f_471_3]) ).
cnf(f_471_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1234,U_1235),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_1235 != c_Groups_Ozero__class_Ozero(U_1234)
| ~ sP78(U_1235,U_1234) ),
inference(clausify,[status(thm)],[f_471_3]) ).
fof(f_472_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_472_2,plain,
! [U_1238,U_1237,U_1236] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1236,U_1237),c_RealVector_Onorm__class_Onorm(U_1236,U_1238)),c_RealVector_Onorm__class_Onorm(U_1236,c_Groups_Oplus__class_Oplus(U_1236,U_1237,U_1238)))
| ~ class_RealVector_Oreal__normed__vector(U_1236) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
! [U_1238,U_1237,U_1236] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1236,U_1237),c_RealVector_Onorm__class_Onorm(U_1236,U_1238)),c_RealVector_Onorm__class_Onorm(U_1236,c_Groups_Oplus__class_Oplus(U_1236,U_1237,U_1238)))
| ~ class_RealVector_Oreal__normed__vector(U_1236) ),
inference(definitional_conversion,[status(esa)],[f_472_2]) ).
cnf(f_472_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1236,U_1237),c_RealVector_Onorm__class_Onorm(U_1236,U_1238)),c_RealVector_Onorm__class_Onorm(U_1236,c_Groups_Oplus__class_Oplus(U_1236,U_1237,U_1238)))
| ~ class_RealVector_Oreal__normed__vector(U_1236) ),
inference(clausify,[status(thm)],[f_472_3]) ).
fof(f_473_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_473_2,plain,
! [U_1241,U_1240,U_1239] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1239,U_1240),c_RealVector_Onorm__class_Onorm(U_1239,U_1241)),c_RealVector_Onorm__class_Onorm(U_1239,c_Groups_Ominus__class_Ominus(U_1239,U_1240,U_1241)))
| ~ class_RealVector_Oreal__normed__vector(U_1239) ),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
! [U_1239,U_1240,U_1241] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1239,U_1240),c_RealVector_Onorm__class_Onorm(U_1239,U_1241)),c_RealVector_Onorm__class_Onorm(U_1239,c_Groups_Ominus__class_Ominus(U_1239,U_1240,U_1241)))
| ~ class_RealVector_Oreal__normed__vector(U_1239) ),
inference(definitional_conversion,[status(esa)],[f_473_2]) ).
cnf(f_473_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1239,U_1240),c_RealVector_Onorm__class_Onorm(U_1239,U_1241)),c_RealVector_Onorm__class_Onorm(U_1239,c_Groups_Ominus__class_Ominus(U_1239,U_1240,U_1241)))
| ~ class_RealVector_Oreal__normed__vector(U_1239) ),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_1,plain,
! [V_y,V_x,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(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_474_2,plain,
! [U_1244,U_1243,U_1242] :
( c_RealVector_Onorm__class_Onorm(U_1242,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1242),U_1243),U_1244)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1242,U_1243)),c_RealVector_Onorm__class_Onorm(U_1242,U_1244))
| ~ class_RealVector_Oreal__normed__div__algebra(U_1242) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
fof(f_474_3,plain,
! [U_1242,U_1243,U_1244] :
( c_RealVector_Onorm__class_Onorm(U_1242,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1242),U_1243),U_1244)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1242,U_1243)),c_RealVector_Onorm__class_Onorm(U_1242,U_1244))
| ~ class_RealVector_Oreal__normed__div__algebra(U_1242) ),
inference(definitional_conversion,[status(esa)],[f_474_2]) ).
cnf(f_474_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1242,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1242),U_1243),U_1244)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1242,U_1243)),c_RealVector_Onorm__class_Onorm(U_1242,U_1244))
| ~ class_RealVector_Oreal__normed__div__algebra(U_1242) ),
inference(clausify,[status(thm)],[f_474_3]) ).
fof(f_475_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_475_2,plain,
! [U_1245] :
( c_RealVector_Onorm__class_Onorm(U_1245,c_Groups_Oone__class_Oone(U_1245)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1245) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
fof(f_475_3,plain,
! [U_1245] :
( c_RealVector_Onorm__class_Onorm(U_1245,c_Groups_Oone__class_Oone(U_1245)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1245) ),
inference(definitional_conversion,[status(esa)],[f_475_2]) ).
cnf(f_475_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1245,c_Groups_Oone__class_Oone(U_1245)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1245) ),
inference(clausify,[status(thm)],[f_475_3]) ).
fof(f_476_1,plain,
! [V_n,V_x,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) = hAPP(hAPP(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_476_2,plain,
! [U_1248,U_1247,U_1246] :
( c_RealVector_Onorm__class_Onorm(U_1246,hAPP(hAPP(c_Power_Opower__class_Opower(U_1246),U_1247),U_1248)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1246,U_1247)),U_1248)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1246) ),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
! [U_1246,U_1247,U_1248] :
( c_RealVector_Onorm__class_Onorm(U_1246,hAPP(hAPP(c_Power_Opower__class_Opower(U_1246),U_1247),U_1248)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1246,U_1247)),U_1248)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1246) ),
inference(definitional_conversion,[status(esa)],[f_476_2]) ).
cnf(f_476_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1246,hAPP(hAPP(c_Power_Opower__class_Opower(U_1246),U_1247),U_1248)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1246,U_1247)),U_1248)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1246) ),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ 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)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__le__one__le]) ).
fof(f_477_2,plain,
! [U_1251,U_1250,U_1249] :
( c_Orderings_Oord__class_Oless__eq(U_1249,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1249),U_1250),U_1251),U_1250)
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1251,c_Groups_Oone__class_Oone(U_1249))
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),U_1251)
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),U_1250)
| ~ class_Rings_Olinordered__idom(U_1249) ),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
! [U_1249,U_1250,U_1251] :
( c_Orderings_Oord__class_Oless__eq(U_1249,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1249),U_1250),U_1251),U_1250)
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1251,c_Groups_Oone__class_Oone(U_1249))
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),U_1251)
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),U_1250)
| ~ class_Rings_Olinordered__idom(U_1249) ),
inference(definitional_conversion,[status(esa)],[f_477_2]) ).
cnf(f_477_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1249,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1249),U_1250),U_1251),U_1250)
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1251,c_Groups_Oone__class_Oone(U_1249))
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),U_1251)
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),U_1250)
| ~ class_Rings_Olinordered__idom(U_1249) ),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x),V_x)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y,c_Groups_Oone__class_Oone(T_a))
| ~ 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)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__le__one__le]) ).
fof(f_478_2,plain,
! [U_1254,U_1253,U_1252] :
( c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1252),U_1254),U_1253),U_1253)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,U_1254,c_Groups_Oone__class_Oone(U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1254)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1253)
| ~ class_Rings_Olinordered__idom(U_1252) ),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
! [U_1252,U_1254,U_1253] :
( c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1252),U_1254),U_1253),U_1253)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,U_1254,c_Groups_Oone__class_Oone(U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1254)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1253)
| ~ class_Rings_Olinordered__idom(U_1252) ),
inference(definitional_conversion,[status(esa)],[f_478_2]) ).
cnf(f_478_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1252,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1252),U_1254),U_1253),U_1253)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,U_1254,c_Groups_Oone__class_Oone(U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1254)
| ~ c_Orderings_Oord__class_Oless__eq(U_1252,c_Groups_Ozero__class_Ozero(U_1252),U_1253)
| ~ class_Rings_Olinordered__idom(U_1252) ),
inference(clausify,[status(thm)],[f_478_3]) ).
fof(f_479_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_Orderings_Oord__class_Oless__eq(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff2]) ).
fof(f_479_2,plain,
! [U_1260,U_1259,U_1258,U_1257,U_1256,U_1255] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1256),U_1257),U_1258),c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1259),U_1257),U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,U_1258,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),c_Groups_Ominus__class_Ominus(U_1255,U_1259,U_1256)),U_1257),U_1260)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1255,U_1258,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),c_Groups_Ominus__class_Ominus(U_1255,U_1259,U_1256)),U_1257),U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1256),U_1257),U_1258),c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1259),U_1257),U_1260)) ) )
| ~ class_Rings_Oordered__ring(U_1255) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
( ! [U_1255,U_1256,U_1257,U_1258,U_1259,U_1260] :
( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1256),U_1257),U_1258),c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1259),U_1257),U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,U_1258,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),c_Groups_Ominus__class_Ominus(U_1255,U_1259,U_1256)),U_1257),U_1260))
| ~ sP79(U_1255,U_1256,U_1257,U_1258,U_1259,U_1260) )
& ! [U_1255,U_1256,U_1257,U_1258,U_1259,U_1260] :
( c_Orderings_Oord__class_Oless__eq(U_1255,U_1258,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),c_Groups_Ominus__class_Ominus(U_1255,U_1259,U_1256)),U_1257),U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1256),U_1257),U_1258),c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1259),U_1257),U_1260))
| ~ sP79(U_1255,U_1256,U_1257,U_1258,U_1259,U_1260) )
& ! [U_1255,U_1256,U_1257,U_1258,U_1259,U_1260] :
( sP79(U_1255,U_1256,U_1257,U_1258,U_1259,U_1260)
| ~ class_Rings_Oordered__ring(U_1255) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_479_2]) ).
cnf(f_479_4,plain,
( sP79(U_1255,U_1256,U_1257,U_1258,U_1259,U_1260)
| ~ class_Rings_Oordered__ring(U_1255) ),
inference(clausify,[status(thm)],[f_479_3]) ).
cnf(f_479_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1255,U_1258,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),c_Groups_Ominus__class_Ominus(U_1255,U_1259,U_1256)),U_1257),U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1256),U_1257),U_1258),c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1259),U_1257),U_1260))
| ~ sP79(U_1255,U_1256,U_1257,U_1258,U_1259,U_1260) ),
inference(clausify,[status(thm)],[f_479_3]) ).
cnf(f_479_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1256),U_1257),U_1258),c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),U_1259),U_1257),U_1260))
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,U_1258,c_Groups_Oplus__class_Oplus(U_1255,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1255),c_Groups_Ominus__class_Ominus(U_1255,U_1259,U_1256)),U_1257),U_1260))
| ~ sP79(U_1255,U_1256,U_1257,U_1258,U_1259,U_1260) ),
inference(clausify,[status(thm)],[f_479_3]) ).
fof(f_480_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__add__iff1]) ).
fof(f_480_2,plain,
! [U_1266,U_1265,U_1264,U_1263,U_1262,U_1261] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1262),U_1263),U_1264),c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1265),U_1263),U_1266))
| ~ c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),c_Groups_Ominus__class_Ominus(U_1261,U_1262,U_1265)),U_1263),U_1264),U_1266) )
& ( c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),c_Groups_Ominus__class_Ominus(U_1261,U_1262,U_1265)),U_1263),U_1264),U_1266)
| ~ c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1262),U_1263),U_1264),c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1265),U_1263),U_1266)) ) )
| ~ class_Rings_Oordered__ring(U_1261) ),
inference(variable_rename,[status(thm)],[f_480_1]) ).
fof(f_480_3,plain,
( ! [U_1261,U_1262,U_1263,U_1264,U_1265,U_1266] :
( c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1262),U_1263),U_1264),c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1265),U_1263),U_1266))
| ~ c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),c_Groups_Ominus__class_Ominus(U_1261,U_1262,U_1265)),U_1263),U_1264),U_1266)
| ~ sP80(U_1261,U_1262,U_1263,U_1264,U_1265,U_1266) )
& ! [U_1261,U_1262,U_1263,U_1264,U_1265,U_1266] :
( c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),c_Groups_Ominus__class_Ominus(U_1261,U_1262,U_1265)),U_1263),U_1264),U_1266)
| ~ c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1262),U_1263),U_1264),c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1265),U_1263),U_1266))
| ~ sP80(U_1261,U_1262,U_1263,U_1264,U_1265,U_1266) )
& ! [U_1261,U_1262,U_1263,U_1264,U_1265,U_1266] :
( sP80(U_1261,U_1262,U_1263,U_1264,U_1265,U_1266)
| ~ class_Rings_Oordered__ring(U_1261) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80])],[f_480_2]) ).
cnf(f_480_4,plain,
( sP80(U_1261,U_1262,U_1263,U_1264,U_1265,U_1266)
| ~ class_Rings_Oordered__ring(U_1261) ),
inference(clausify,[status(thm)],[f_480_3]) ).
cnf(f_480_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),c_Groups_Ominus__class_Ominus(U_1261,U_1262,U_1265)),U_1263),U_1264),U_1266)
| ~ c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1262),U_1263),U_1264),c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1265),U_1263),U_1266))
| ~ sP80(U_1261,U_1262,U_1263,U_1264,U_1265,U_1266) ),
inference(clausify,[status(thm)],[f_480_3]) ).
cnf(f_480_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1262),U_1263),U_1264),c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),U_1265),U_1263),U_1266))
| ~ c_Orderings_Oord__class_Oless__eq(U_1261,c_Groups_Oplus__class_Oplus(U_1261,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1261),c_Groups_Ominus__class_Ominus(U_1261,U_1262,U_1265)),U_1263),U_1264),U_1266)
| ~ sP80(U_1261,U_1262,U_1263,U_1264,U_1265,U_1266) ),
inference(clausify,[status(thm)],[f_480_3]) ).
fof(f_481_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oabs__class_Oabs(T_a,V_y)),V_x) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_x))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__mult__pos]) ).
fof(f_481_2,plain,
! [U_1269,U_1268,U_1267] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1267),c_Groups_Oabs__class_Oabs(U_1267,U_1269)),U_1268) = c_Groups_Oabs__class_Oabs(U_1267,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1267),U_1269),U_1268))
| ~ c_Orderings_Oord__class_Oless__eq(U_1267,c_Groups_Ozero__class_Ozero(U_1267),U_1268)
| ~ class_Rings_Olinordered__idom(U_1267) ),
inference(variable_rename,[status(thm)],[f_481_1]) ).
fof(f_481_3,plain,
! [U_1269,U_1267,U_1268] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1267),c_Groups_Oabs__class_Oabs(U_1267,U_1269)),U_1268) = c_Groups_Oabs__class_Oabs(U_1267,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1267),U_1269),U_1268))
| ~ c_Orderings_Oord__class_Oless__eq(U_1267,c_Groups_Ozero__class_Ozero(U_1267),U_1268)
| ~ class_Rings_Olinordered__idom(U_1267) ),
inference(definitional_conversion,[status(esa)],[f_481_2]) ).
cnf(f_481_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1267),c_Groups_Oabs__class_Oabs(U_1267,U_1269)),U_1268) = c_Groups_Oabs__class_Oabs(U_1267,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1267),U_1269),U_1268))
| ~ c_Orderings_Oord__class_Oless__eq(U_1267,c_Groups_Ozero__class_Ozero(U_1267),U_1268)
| ~ class_Rings_Olinordered__idom(U_1267) ),
inference(clausify,[status(thm)],[f_481_3]) ).
fof(f_482_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(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_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_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,c_Groups_Ozero__class_Ozero(T_a),V_a) )
| ~ class_Rings_Oordered__ring__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__eq__mult]) ).
fof(f_482_2,plain,
! [U_1272,U_1271,U_1270] :
( c_Groups_Oabs__class_Oabs(U_1270,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1270),U_1271),U_1272)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1270),c_Groups_Oabs__class_Oabs(U_1270,U_1271)),c_Groups_Oabs__class_Oabs(U_1270,U_1272))
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1270,U_1272,c_Groups_Ozero__class_Ozero(U_1270))
& ~ c_Orderings_Oord__class_Oless__eq(U_1270,c_Groups_Ozero__class_Ozero(U_1270),U_1272) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1270,U_1271,c_Groups_Ozero__class_Ozero(U_1270))
& ~ c_Orderings_Oord__class_Oless__eq(U_1270,c_Groups_Ozero__class_Ozero(U_1270),U_1271) )
| ~ class_Rings_Oordered__ring__abs(U_1270) ),
inference(variable_rename,[status(thm)],[f_482_1]) ).
fof(f_482_3,plain,
( ! [U_1270,U_1272] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1270,U_1272,c_Groups_Ozero__class_Ozero(U_1270))
| ~ sP82(U_1270,U_1272) )
& ! [U_1270,U_1272] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1270,c_Groups_Ozero__class_Ozero(U_1270),U_1272)
| ~ sP82(U_1270,U_1272) )
& ! [U_1270,U_1271] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1270,U_1271,c_Groups_Ozero__class_Ozero(U_1270))
| ~ sP81(U_1270,U_1271) )
& ! [U_1270,U_1271] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1270,c_Groups_Ozero__class_Ozero(U_1270),U_1271)
| ~ sP81(U_1270,U_1271) )
& ! [U_1270,U_1271,U_1272] :
( c_Groups_Oabs__class_Oabs(U_1270,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1270),U_1271),U_1272)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1270),c_Groups_Oabs__class_Oabs(U_1270,U_1271)),c_Groups_Oabs__class_Oabs(U_1270,U_1272))
| sP82(U_1270,U_1272)
| sP81(U_1270,U_1271)
| ~ class_Rings_Oordered__ring__abs(U_1270) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP81,sP82])],[f_482_2]) ).
cnf(f_482_4,plain,
( c_Groups_Oabs__class_Oabs(U_1270,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1270),U_1271),U_1272)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1270),c_Groups_Oabs__class_Oabs(U_1270,U_1271)),c_Groups_Oabs__class_Oabs(U_1270,U_1272))
| sP82(U_1270,U_1272)
| sP81(U_1270,U_1271)
| ~ class_Rings_Oordered__ring__abs(U_1270) ),
inference(clausify,[status(thm)],[f_482_3]) ).
cnf(f_482_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1270,c_Groups_Ozero__class_Ozero(U_1270),U_1271)
| ~ sP81(U_1270,U_1271) ),
inference(clausify,[status(thm)],[f_482_3]) ).
cnf(f_482_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1270,U_1271,c_Groups_Ozero__class_Ozero(U_1270))
| ~ sP81(U_1270,U_1271) ),
inference(clausify,[status(thm)],[f_482_3]) ).
cnf(f_482_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1270,c_Groups_Ozero__class_Ozero(U_1270),U_1272)
| ~ sP82(U_1270,U_1272) ),
inference(clausify,[status(thm)],[f_482_3]) ).
cnf(f_482_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1270,U_1272,c_Groups_Ozero__class_Ozero(U_1270))
| ~ sP82(U_1270,U_1272) ),
inference(clausify,[status(thm)],[f_482_3]) ).
fof(f_483_1,plain,
! [V_w,T_a] :
( ( ( hAPP(hAPP(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) )
& ( hAPP(hAPP(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_483_2,plain,
! [U_1274,U_1273] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274)) = c_Groups_Ozero__class_Ozero(U_1273)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274)) = c_Groups_Oone__class_Oone(U_1273)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_1273)
| ~ class_Power_Opower(U_1273) ),
inference(variable_rename,[status(thm)],[f_483_1]) ).
fof(f_483_3,plain,
( ! [U_1273,U_1274] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274)) = c_Groups_Ozero__class_Ozero(U_1273)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP83(U_1273,U_1274) )
& ! [U_1273,U_1274] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274)) = c_Groups_Oone__class_Oone(U_1273)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP83(U_1273,U_1274) )
& ! [U_1273,U_1274] :
( sP83(U_1273,U_1274)
| ~ class_Rings_Osemiring__0(U_1273)
| ~ class_Power_Opower(U_1273) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_483_2]) ).
cnf(f_483_4,plain,
( sP83(U_1273,U_1274)
| ~ class_Rings_Osemiring__0(U_1273)
| ~ class_Power_Opower(U_1273) ),
inference(clausify,[status(thm)],[f_483_3]) ).
cnf(f_483_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274)) = c_Groups_Oone__class_Oone(U_1273)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP83(U_1273,U_1274) ),
inference(clausify,[status(thm)],[f_483_3]) ).
cnf(f_483_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274)) = c_Groups_Ozero__class_Ozero(U_1273)
| c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_1274) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP83(U_1273,U_1274) ),
inference(clausify,[status(thm)],[f_483_3]) ).
fof(f_484_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(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_484_2,plain,
! [U_1277,U_1276,U_1275] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1275,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1275),U_1276),U_1277)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1275,U_1276)),c_RealVector_Onorm__class_Onorm(U_1275,U_1277)))
| ~ class_RealVector_Oreal__normed__algebra(U_1275) ),
inference(variable_rename,[status(thm)],[f_484_1]) ).
fof(f_484_3,plain,
! [U_1276,U_1277,U_1275] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1275,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1275),U_1276),U_1277)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1275,U_1276)),c_RealVector_Onorm__class_Onorm(U_1275,U_1277)))
| ~ class_RealVector_Oreal__normed__algebra(U_1275) ),
inference(definitional_conversion,[status(esa)],[f_484_2]) ).
cnf(f_484_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1275,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1275),U_1276),U_1277)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1275,U_1276)),c_RealVector_Onorm__class_Onorm(U_1275,U_1277)))
| ~ class_RealVector_Oreal__normed__algebra(U_1275) ),
inference(clausify,[status(thm)],[f_484_3]) ).
fof(f_485_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]) ).
fof(f_485_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(definitional_conversion,[status(esa)],[f_485_1]) ).
cnf(f_485_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_OBit1(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_485_2]) ).
fof(f_486_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_486_2,plain,
! [U_1280,U_1279,U_1278] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1278,c_Groups_Oplus__class_Oplus(U_1278,U_1279,U_1280)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1278,U_1279),c_RealVector_Onorm__class_Onorm(U_1278,U_1280)))
| ~ class_RealVector_Oreal__normed__vector(U_1278) ),
inference(variable_rename,[status(thm)],[f_486_1]) ).
fof(f_486_3,plain,
! [U_1278,U_1279,U_1280] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1278,c_Groups_Oplus__class_Oplus(U_1278,U_1279,U_1280)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1278,U_1279),c_RealVector_Onorm__class_Onorm(U_1278,U_1280)))
| ~ class_RealVector_Oreal__normed__vector(U_1278) ),
inference(definitional_conversion,[status(esa)],[f_486_2]) ).
cnf(f_486_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1278,c_Groups_Oplus__class_Oplus(U_1278,U_1279,U_1280)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1278,U_1279),c_RealVector_Onorm__class_Onorm(U_1278,U_1280)))
| ~ class_RealVector_Oreal__normed__vector(U_1278) ),
inference(clausify,[status(thm)],[f_486_3]) ).
fof(f_487_1,plain,
! [V_m,V_n,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_m),V_n) = c_Groups_Oone__class_Oone(T_a)
| V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Power_Opower(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__num__eq__if]) ).
fof(f_487_2,plain,
! [U_1283,U_1282,U_1281] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1281),U_1283),U_1282) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1281),U_1283),hAPP(hAPP(c_Power_Opower__class_Opower(U_1281),U_1283),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1282,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_1282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1281),U_1283),U_1282) = c_Groups_Oone__class_Oone(U_1281)
| U_1282 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Power_Opower(U_1281) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
fof(f_487_3,plain,
( ! [U_1281,U_1282,U_1283] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1281),U_1283),U_1282) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1281),U_1283),hAPP(hAPP(c_Power_Opower__class_Opower(U_1281),U_1283),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1282,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_1282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP84(U_1281,U_1282,U_1283) )
& ! [U_1281,U_1282,U_1283] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1281),U_1283),U_1282) = c_Groups_Oone__class_Oone(U_1281)
| U_1282 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP84(U_1281,U_1282,U_1283) )
& ! [U_1281,U_1282,U_1283] :
( sP84(U_1281,U_1282,U_1283)
| ~ class_Power_Opower(U_1281) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_487_2]) ).
cnf(f_487_4,plain,
( sP84(U_1281,U_1282,U_1283)
| ~ class_Power_Opower(U_1281) ),
inference(clausify,[status(thm)],[f_487_3]) ).
cnf(f_487_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1281),U_1283),U_1282) = c_Groups_Oone__class_Oone(U_1281)
| U_1282 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP84(U_1281,U_1282,U_1283) ),
inference(clausify,[status(thm)],[f_487_3]) ).
cnf(f_487_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1281),U_1283),U_1282) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1281),U_1283),hAPP(hAPP(c_Power_Opower__class_Opower(U_1281),U_1283),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1282,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| U_1282 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP84(U_1281,U_1282,U_1283) ),
inference(clausify,[status(thm)],[f_487_3]) ).
fof(f_488_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_488_2,plain,
! [U_1284] :
( ( 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_1284)))
& 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_1284))) )
| ~ 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_1284)) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
fof(f_488_3,plain,
( ! [U_1284] :
( 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_1284)))
| ~ sP85(U_1284) )
& ! [U_1284] :
( 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_1284)))
| ~ sP85(U_1284) )
& ! [U_1284] :
( sP85(U_1284)
| ~ 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_1284)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_488_2]) ).
cnf(f_488_4,plain,
( sP85(U_1284)
| ~ 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_1284)) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_5,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_1284)))
| ~ sP85(U_1284) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_6,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_1284)))
| ~ sP85(U_1284) ),
inference(clausify,[status(thm)],[f_488_3]) ).
fof(f_489_1,plain,
! [V_y,V_n,V_p,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(V_n),V_p)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_p))),V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_p,V_n)
| ~ class_Groups_Omonoid__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_lemma__realpow__diff]) ).
fof(f_489_2,plain,
! [U_1288,U_1287,U_1286,U_1285] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1285),U_1288),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1287),U_1286)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1285),hAPP(hAPP(c_Power_Opower__class_Opower(U_1285),U_1288),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1287,U_1286))),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1286,U_1287)
| ~ class_Groups_Omonoid__mult(U_1285) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
fof(f_489_3,plain,
! [U_1287,U_1285,U_1286,U_1288] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1285),U_1288),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1287),U_1286)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1285),hAPP(hAPP(c_Power_Opower__class_Opower(U_1285),U_1288),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1287,U_1286))),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1286,U_1287)
| ~ class_Groups_Omonoid__mult(U_1285) ),
inference(definitional_conversion,[status(esa)],[f_489_2]) ).
cnf(f_489_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1285),U_1288),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1287),U_1286)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1285),hAPP(hAPP(c_Power_Opower__class_Opower(U_1285),U_1288),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1287,U_1286))),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1286,U_1287)
| ~ class_Groups_Omonoid__mult(U_1285) ),
inference(clausify,[status(thm)],[f_489_3]) ).
fof(f_490_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_490_2,plain,
! [U_1289] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1289),
inference(variable_rename,[status(thm)],[f_490_1]) ).
fof(f_490_3,plain,
! [U_1289] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1289),
inference(definitional_conversion,[status(esa)],[f_490_2]) ).
cnf(f_490_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1289),
inference(clausify,[status(thm)],[f_490_3]) ).
fof(f_491_1,plain,
! [V_y,V_x,V_c,T_a] :
( V_x = 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_RealVector_Onorm__class_Onorm(T_a,V_y)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__ratiotest__lemma]) ).
fof(f_491_2,plain,
! [U_1293,U_1292,U_1291,U_1290] :
( U_1292 = c_Groups_Ozero__class_Ozero(U_1290)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1290,U_1292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1291),c_RealVector_Onorm__class_Onorm(U_1290,U_1293)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1291,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_1290) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
fof(f_491_3,plain,
! [U_1290,U_1291,U_1292,U_1293] :
( U_1292 = c_Groups_Ozero__class_Ozero(U_1290)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1290,U_1292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1291),c_RealVector_Onorm__class_Onorm(U_1290,U_1293)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1291,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_1290) ),
inference(definitional_conversion,[status(esa)],[f_491_2]) ).
cnf(f_491_4,plain,
( U_1292 = c_Groups_Ozero__class_Ozero(U_1290)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1290,U_1292),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1291),c_RealVector_Onorm__class_Onorm(U_1290,U_1293)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1291,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_1290) ),
inference(clausify,[status(thm)],[f_491_3]) ).
fof(f_492_1,plain,
! [V_n] : V_n != c_Nat_OSuc(V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_492_2,plain,
! [U_1294] : U_1294 != c_Nat_OSuc(U_1294),
inference(variable_rename,[status(thm)],[f_492_1]) ).
fof(f_492_3,plain,
! [U_1294] : U_1294 != c_Nat_OSuc(U_1294),
inference(definitional_conversion,[status(esa)],[f_492_2]) ).
cnf(f_492_4,plain,
U_1294 != c_Nat_OSuc(U_1294),
inference(clausify,[status(thm)],[f_492_3]) ).
fof(f_493_1,plain,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_493_2,plain,
! [U_1295] : c_Nat_OSuc(U_1295) != U_1295,
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
! [U_1295] : c_Nat_OSuc(U_1295) != U_1295,
inference(definitional_conversion,[status(esa)],[f_493_2]) ).
cnf(f_493_4,plain,
c_Nat_OSuc(U_1295) != U_1295,
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_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_494_2,plain,
! [U_1297,U_1296] :
( ( c_Nat_OSuc(U_1296) = c_Nat_OSuc(U_1297)
| U_1296 != U_1297 )
& ( U_1296 = U_1297
| c_Nat_OSuc(U_1296) != c_Nat_OSuc(U_1297) ) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
( ! [U_1301,U_1299] :
( c_Nat_OSuc(U_1299) = c_Nat_OSuc(U_1301)
| U_1299 != U_1301 )
& ! [U_1300,U_1298] :
( U_1298 = U_1300
| c_Nat_OSuc(U_1298) != c_Nat_OSuc(U_1300) ) ),
inference(miniscope,[status(thm)],[f_494_2]) ).
fof(f_494_4,plain,
( ! [U_1299,U_1301] :
( c_Nat_OSuc(U_1299) = c_Nat_OSuc(U_1301)
| U_1299 != U_1301 )
& ! [U_1300,U_1298] :
( U_1298 = U_1300
| c_Nat_OSuc(U_1298) != c_Nat_OSuc(U_1300) ) ),
inference(definitional_conversion,[status(esa)],[f_494_3]) ).
cnf(f_494_5,plain,
( U_1298 = U_1300
| c_Nat_OSuc(U_1298) != c_Nat_OSuc(U_1300) ),
inference(clausify,[status(thm)],[f_494_4]) ).
cnf(f_494_6,plain,
( c_Nat_OSuc(U_1299) = c_Nat_OSuc(U_1301)
| U_1299 != U_1301 ),
inference(clausify,[status(thm)],[f_494_4]) ).
fof(f_495_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_495_2,plain,
! [U_1303,U_1302] :
( U_1302 = U_1303
| c_Nat_OSuc(U_1302) != c_Nat_OSuc(U_1303) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
fof(f_495_3,plain,
! [U_1302,U_1303] :
( U_1302 = U_1303
| c_Nat_OSuc(U_1302) != c_Nat_OSuc(U_1303) ),
inference(definitional_conversion,[status(esa)],[f_495_2]) ).
cnf(f_495_4,plain,
( U_1302 = U_1303
| c_Nat_OSuc(U_1302) != c_Nat_OSuc(U_1303) ),
inference(clausify,[status(thm)],[f_495_3]) ).
fof(f_496_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_496_2,plain,
! [U_1305,U_1304] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1304,U_1305) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,U_1304),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
! [U_1305,U_1304] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1304,U_1305) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,U_1304),
inference(definitional_conversion,[status(esa)],[f_496_2]) ).
cnf(f_496_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1304,U_1305) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1305,U_1304),
inference(clausify,[status(thm)],[f_496_3]) ).
fof(f_497_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_497_2,plain,
! [U_1308,U_1307,U_1306] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1306,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1307,U_1308)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1307,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1306,U_1308)),
inference(variable_rename,[status(thm)],[f_497_1]) ).
fof(f_497_3,plain,
! [U_1306,U_1307,U_1308] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1306,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1307,U_1308)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1307,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1306,U_1308)),
inference(definitional_conversion,[status(esa)],[f_497_2]) ).
cnf(f_497_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1306,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1307,U_1308)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1307,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1306,U_1308)),
inference(clausify,[status(thm)],[f_497_3]) ).
fof(f_498_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_498_2,plain,
! [U_1311,U_1310,U_1309] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,U_1310),U_1311) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1310,U_1311)),
inference(variable_rename,[status(thm)],[f_498_1]) ).
fof(f_498_3,plain,
! [U_1310,U_1309,U_1311] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,U_1310),U_1311) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1310,U_1311)),
inference(definitional_conversion,[status(esa)],[f_498_2]) ).
cnf(f_498_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,U_1310),U_1311) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1309,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1310,U_1311)),
inference(clausify,[status(thm)],[f_498_3]) ).
fof(f_499_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_499_2,plain,
! [U_1314,U_1313,U_1312] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1312,U_1313) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1312,U_1314)
| U_1313 != U_1314 )
& ( U_1313 = U_1314
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1312,U_1313) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1312,U_1314) ) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
( ! [U_1320,U_1318] :
( ! [U_1316] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1316,U_1318) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1316,U_1320)
| U_1318 != U_1320 )
& ! [U_1319,U_1317] :
( ! [U_1315] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1315,U_1317) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1315,U_1319)
| U_1317 = U_1319 ) ),
inference(miniscope,[status(thm)],[f_499_2]) ).
fof(f_499_4,plain,
( ! [U_1318,U_1316,U_1320] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1316,U_1318) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1316,U_1320)
| U_1318 != U_1320 )
& ! [U_1315,U_1317,U_1319] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1315,U_1317) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1315,U_1319)
| U_1317 = U_1319 ) ),
inference(definitional_conversion,[status(esa)],[f_499_3]) ).
cnf(f_499_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1315,U_1317) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1315,U_1319)
| U_1317 = U_1319 ),
inference(clausify,[status(thm)],[f_499_4]) ).
cnf(f_499_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1316,U_1318) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1316,U_1320)
| U_1318 != U_1320 ),
inference(clausify,[status(thm)],[f_499_4]) ).
fof(f_500_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_500_2,plain,
! [U_1323,U_1322,U_1321] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1321,U_1322) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1323,U_1322)
| U_1321 != U_1323 )
& ( U_1321 = U_1323
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1321,U_1322) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1323,U_1322) ) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
fof(f_500_3,plain,
( ! [U_1329,U_1327,U_1325] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1325,U_1327) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1329,U_1327)
| U_1325 != U_1329 )
& ! [U_1328,U_1326,U_1324] :
( U_1324 = U_1328
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1324,U_1326) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1328,U_1326) ) ),
inference(miniscope,[status(thm)],[f_500_2]) ).
fof(f_500_4,plain,
( ! [U_1327,U_1329,U_1325] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1325,U_1327) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1329,U_1327)
| U_1325 != U_1329 )
& ! [U_1324,U_1326,U_1328] :
( U_1324 = U_1328
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1324,U_1326) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1328,U_1326) ) ),
inference(definitional_conversion,[status(esa)],[f_500_3]) ).
cnf(f_500_5,plain,
( U_1324 = U_1328
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1324,U_1326) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1328,U_1326) ),
inference(clausify,[status(thm)],[f_500_4]) ).
cnf(f_500_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1325,U_1327) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1329,U_1327)
| U_1325 != U_1329 ),
inference(clausify,[status(thm)],[f_500_4]) ).
fof(f_501_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_501_2,plain,
! [U_1330] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1330,U_1330),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
! [U_1330] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1330,U_1330),
inference(definitional_conversion,[status(esa)],[f_501_2]) ).
cnf(f_501_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1330,U_1330),
inference(clausify,[status(thm)],[f_501_3]) ).
fof(f_502_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_502_2,plain,
! [U_1332,U_1331] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1332,U_1331)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1331,U_1332) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
! [U_1331,U_1332] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1332,U_1331)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1331,U_1332) ),
inference(definitional_conversion,[status(esa)],[f_502_2]) ).
cnf(f_502_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1332,U_1331)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1331,U_1332) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_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_503_2,plain,
! [U_1334,U_1333] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333,U_1334)
| U_1333 != U_1334 ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
! [U_1334,U_1333] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333,U_1334)
| U_1333 != U_1334 ),
inference(definitional_conversion,[status(esa)],[f_503_2]) ).
cnf(f_503_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1333,U_1334)
| U_1333 != U_1334 ),
inference(clausify,[status(thm)],[f_503_3]) ).
fof(f_504_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_504_2,plain,
! [U_1337,U_1336,U_1335] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1335,U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1336,U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1335,U_1336) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
fof(f_504_3,plain,
! [U_1336,U_1335,U_1337] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1335,U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1336,U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1335,U_1336) ),
inference(definitional_conversion,[status(esa)],[f_504_2]) ).
cnf(f_504_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1335,U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1336,U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1335,U_1336) ),
inference(clausify,[status(thm)],[f_504_3]) ).
fof(f_505_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_505_2,plain,
! [U_1339,U_1338] :
( U_1338 = U_1339
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1339,U_1338)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1338,U_1339) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
fof(f_505_3,plain,
! [U_1339,U_1338] :
( U_1338 = U_1339
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1339,U_1338)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1338,U_1339) ),
inference(definitional_conversion,[status(esa)],[f_505_2]) ).
cnf(f_505_4,plain,
( U_1338 = U_1339
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1339,U_1338)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1338,U_1339) ),
inference(clausify,[status(thm)],[f_505_3]) ).
fof(f_506_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m),
inference(fof_nnf,[status(thm)],[fact_nat__mult__commute]) ).
fof(f_506_2,plain,
! [U_1341,U_1340] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1340),U_1341) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1341),U_1340),
inference(variable_rename,[status(thm)],[f_506_1]) ).
fof(f_506_3,plain,
! [U_1340,U_1341] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1340),U_1341) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1341),U_1340),
inference(definitional_conversion,[status(esa)],[f_506_2]) ).
cnf(f_506_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1340),U_1341) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1341),U_1340),
inference(clausify,[status(thm)],[f_506_3]) ).
fof(f_507_1,plain,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
inference(fof_nnf,[status(thm)],[fact_nat__mult__assoc]) ).
fof(f_507_2,plain,
! [U_1344,U_1343,U_1342] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1342),U_1343)),U_1344) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1343),U_1344)),
inference(variable_rename,[status(thm)],[f_507_1]) ).
fof(f_507_3,plain,
! [U_1342,U_1343,U_1344] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1342),U_1343)),U_1344) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1343),U_1344)),
inference(definitional_conversion,[status(esa)],[f_507_2]) ).
cnf(f_507_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1342),U_1343)),U_1344) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1342),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1343),U_1344)),
inference(clausify,[status(thm)],[f_507_3]) ).
fof(f_508_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_508_2,plain,
! [U_1347,U_1346,U_1345] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1345,U_1346),U_1347) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1345,U_1347),U_1346),
inference(variable_rename,[status(thm)],[f_508_1]) ).
fof(f_508_3,plain,
! [U_1346,U_1345,U_1347] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1345,U_1346),U_1347) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1345,U_1347),U_1346),
inference(definitional_conversion,[status(esa)],[f_508_2]) ).
cnf(f_508_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1345,U_1346),U_1347) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1345,U_1347),U_1346),
inference(clausify,[status(thm)],[f_508_3]) ).
fof(f_509_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_509_2,plain,
! [U_1348] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1348),
inference(variable_rename,[status(thm)],[f_509_1]) ).
fof(f_509_3,plain,
! [U_1348] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1348),
inference(definitional_conversion,[status(esa)],[f_509_2]) ).
cnf(f_509_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1348),
inference(clausify,[status(thm)],[f_509_3]) ).
fof(f_510_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_510_2,plain,
! [U_1349] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1349),
inference(variable_rename,[status(thm)],[f_510_1]) ).
fof(f_510_3,plain,
! [U_1349] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1349),
inference(definitional_conversion,[status(esa)],[f_510_2]) ).
cnf(f_510_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1349),
inference(clausify,[status(thm)],[f_510_3]) ).
fof(f_511_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_511_2,plain,
! [U_1350] : c_Nat_OSuc(U_1350) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
! [U_1350] : c_Nat_OSuc(U_1350) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_511_2]) ).
cnf(f_511_4,plain,
c_Nat_OSuc(U_1350) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_511_3]) ).
fof(f_512_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_512_2,plain,
! [U_1351] : c_Nat_OSuc(U_1351) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
! [U_1351] : c_Nat_OSuc(U_1351) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_512_2]) ).
cnf(f_512_4,plain,
c_Nat_OSuc(U_1351) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_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_513_2,plain,
! [U_1352] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1352),
inference(variable_rename,[status(thm)],[f_513_1]) ).
fof(f_513_3,plain,
! [U_1352] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1352),
inference(definitional_conversion,[status(esa)],[f_513_2]) ).
cnf(f_513_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_1352),
inference(clausify,[status(thm)],[f_513_3]) ).
fof(f_514_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_514_2,plain,
! [U_1353] : c_Nat_OSuc(U_1353) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_514_1]) ).
fof(f_514_3,plain,
! [U_1353] : c_Nat_OSuc(U_1353) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_514_2]) ).
cnf(f_514_4,plain,
c_Nat_OSuc(U_1353) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_514_3]) ).
fof(f_515_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_515_2,plain,
! [U_1354] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1354) = U_1354,
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_1354] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1354) = U_1354,
inference(definitional_conversion,[status(esa)],[f_515_2]) ).
cnf(f_515_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1354) = U_1354,
inference(clausify,[status(thm)],[f_515_3]) ).
fof(f_516_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_516_2,plain,
! [U_1355] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1355,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1355,
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
! [U_1355] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1355,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1355,
inference(definitional_conversion,[status(esa)],[f_516_2]) ).
cnf(f_516_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1355,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1355,
inference(clausify,[status(thm)],[f_516_3]) ).
fof(f_517_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_517_2,plain,
! [U_1357,U_1356] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1356,U_1357) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1357 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1356 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_1357 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1356 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1356,U_1357) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
fof(f_517_3,plain,
( ! [U_1361,U_1359] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1359,U_1361) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1361 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1359 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1360,U_1358] :
( ( U_1360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1358,U_1360) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_517_2]) ).
fof(f_517_4,plain,
( ! [U_1358,U_1360] :
( U_1360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP86(U_1358,U_1360) )
& ! [U_1358,U_1360] :
( U_1358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP86(U_1358,U_1360) )
& ! [U_1359,U_1361] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1359,U_1361) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1361 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1359 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1358,U_1360] :
( sP86(U_1358,U_1360)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1358,U_1360) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_517_3]) ).
cnf(f_517_5,plain,
( sP86(U_1358,U_1360)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1358,U_1360) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_517_4]) ).
cnf(f_517_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1359,U_1361) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1361 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1359 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_517_4]) ).
cnf(f_517_7,plain,
( U_1358 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP86(U_1358,U_1360) ),
inference(clausify,[status(thm)],[f_517_4]) ).
cnf(f_517_8,plain,
( U_1360 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP86(U_1358,U_1360) ),
inference(clausify,[status(thm)],[f_517_4]) ).
fof(f_518_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_518_2,plain,
! [U_1363,U_1362] :
( U_1363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1362,U_1363) != U_1362 ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
fof(f_518_3,plain,
! [U_1363] :
( ! [U_1362] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1362,U_1363) != U_1362
| U_1363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_518_2]) ).
fof(f_518_4,plain,
! [U_1363,U_1362] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1362,U_1363) != U_1362
| U_1363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_518_3]) ).
cnf(f_518_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1362,U_1363) != U_1362
| U_1363 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_518_4]) ).
fof(f_519_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_519_2,plain,
! [U_1364] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1364),
inference(variable_rename,[status(thm)],[f_519_1]) ).
fof(f_519_3,plain,
! [U_1364] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1364),
inference(definitional_conversion,[status(esa)],[f_519_2]) ).
cnf(f_519_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1364),
inference(clausify,[status(thm)],[f_519_3]) ).
fof(f_520_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_520_2,plain,
! [U_1365] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1365,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1365 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1365 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1365,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
( ! [U_1367] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1367,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1367 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1366] :
( U_1366 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1366,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_520_2]) ).
fof(f_520_4,plain,
( ! [U_1367] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1367,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1367 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1366] :
( U_1366 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1366,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa)],[f_520_3]) ).
cnf(f_520_5,plain,
( U_1366 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1366,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_520_4]) ).
cnf(f_520_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1367,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1367 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_520_4]) ).
fof(f_521_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_521_2,plain,
! [U_1369,U_1368] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1368),U_1369) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1368,c_Nat_OSuc(U_1369)),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
! [U_1369,U_1368] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1368),U_1369) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1368,c_Nat_OSuc(U_1369)),
inference(definitional_conversion,[status(esa)],[f_521_2]) ).
cnf(f_521_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1368),U_1369) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1368,c_Nat_OSuc(U_1369)),
inference(clausify,[status(thm)],[f_521_3]) ).
fof(f_522_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_522_2,plain,
! [U_1371,U_1370] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1370),U_1371) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1370,U_1371)),
inference(variable_rename,[status(thm)],[f_522_1]) ).
fof(f_522_3,plain,
! [U_1370,U_1371] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1370),U_1371) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1370,U_1371)),
inference(definitional_conversion,[status(esa)],[f_522_2]) ).
cnf(f_522_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_1370),U_1371) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1370,U_1371)),
inference(clausify,[status(thm)],[f_522_3]) ).
fof(f_523_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_523_2,plain,
! [U_1373,U_1372] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1372,c_Nat_OSuc(U_1373)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1372,U_1373)),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
! [U_1372,U_1373] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1372,c_Nat_OSuc(U_1373)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1372,U_1373)),
inference(definitional_conversion,[status(esa)],[f_523_2]) ).
cnf(f_523_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1372,c_Nat_OSuc(U_1373)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1372,U_1373)),
inference(clausify,[status(thm)],[f_523_3]) ).
fof(f_524_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_524_2,plain,
! [U_1374] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1374),U_1374),
inference(variable_rename,[status(thm)],[f_524_1]) ).
fof(f_524_3,plain,
! [U_1374] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1374),U_1374),
inference(definitional_conversion,[status(esa)],[f_524_2]) ).
cnf(f_524_4,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1374),U_1374),
inference(clausify,[status(thm)],[f_524_3]) ).
fof(f_525_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_525_2,plain,
! [U_1376,U_1375] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1375,U_1376)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1376),U_1375) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1376),U_1375)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1375,U_1376) ) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
fof(f_525_3,plain,
( ! [U_1380,U_1378] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1378,U_1380)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1380),U_1378) )
& ! [U_1379,U_1377] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1379),U_1377)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1377,U_1379) ) ),
inference(miniscope,[status(thm)],[f_525_2]) ).
fof(f_525_4,plain,
( ! [U_1378,U_1380] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1378,U_1380)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1380),U_1378) )
& ! [U_1377,U_1379] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1379),U_1377)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1377,U_1379) ) ),
inference(definitional_conversion,[status(esa)],[f_525_3]) ).
cnf(f_525_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1379),U_1377)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1377,U_1379) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1378,U_1380)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1380),U_1378) ),
inference(clausify,[status(thm)],[f_525_4]) ).
fof(f_526_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_526_2,plain,
! [U_1382,U_1381] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1381,c_Nat_OSuc(U_1382))
| ( U_1381 != c_Nat_OSuc(U_1382)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1381,U_1382) ) )
& ( U_1381 = c_Nat_OSuc(U_1382)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1381,U_1382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1381,c_Nat_OSuc(U_1382)) ) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
fof(f_526_3,plain,
( ! [U_1386,U_1384] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,c_Nat_OSuc(U_1386))
| ( U_1384 != c_Nat_OSuc(U_1386)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,U_1386) ) )
& ! [U_1385,U_1383] :
( U_1383 = c_Nat_OSuc(U_1385)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1383,U_1385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1383,c_Nat_OSuc(U_1385)) ) ),
inference(miniscope,[status(thm)],[f_526_2]) ).
fof(f_526_4,plain,
( ! [U_1384,U_1386] :
( U_1384 != c_Nat_OSuc(U_1386)
| ~ sP87(U_1384,U_1386) )
& ! [U_1384,U_1386] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,U_1386)
| ~ sP87(U_1384,U_1386) )
& ! [U_1384,U_1386] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,c_Nat_OSuc(U_1386))
| sP87(U_1384,U_1386) )
& ! [U_1385,U_1383] :
( U_1383 = c_Nat_OSuc(U_1385)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1383,U_1385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1383,c_Nat_OSuc(U_1385)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_526_3]) ).
cnf(f_526_5,plain,
( U_1383 = c_Nat_OSuc(U_1385)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1383,U_1385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1383,c_Nat_OSuc(U_1385)) ),
inference(clausify,[status(thm)],[f_526_4]) ).
cnf(f_526_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,c_Nat_OSuc(U_1386))
| sP87(U_1384,U_1386) ),
inference(clausify,[status(thm)],[f_526_4]) ).
cnf(f_526_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1384,U_1386)
| ~ sP87(U_1384,U_1386) ),
inference(clausify,[status(thm)],[f_526_4]) ).
cnf(f_526_8,plain,
( U_1384 != c_Nat_OSuc(U_1386)
| ~ sP87(U_1384,U_1386) ),
inference(clausify,[status(thm)],[f_526_4]) ).
fof(f_527_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_527_2,plain,
! [U_1388,U_1387] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1387),c_Nat_OSuc(U_1388))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1387,U_1388) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1387,U_1388)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1387),c_Nat_OSuc(U_1388)) ) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
fof(f_527_3,plain,
( ! [U_1392,U_1390] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1390),c_Nat_OSuc(U_1392))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1390,U_1392) )
& ! [U_1391,U_1389] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1389,U_1391)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1389),c_Nat_OSuc(U_1391)) ) ),
inference(miniscope,[status(thm)],[f_527_2]) ).
fof(f_527_4,plain,
( ! [U_1390,U_1392] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1390),c_Nat_OSuc(U_1392))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1390,U_1392) )
& ! [U_1391,U_1389] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1389,U_1391)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1389),c_Nat_OSuc(U_1391)) ) ),
inference(definitional_conversion,[status(esa)],[f_527_3]) ).
cnf(f_527_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1389,U_1391)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1389),c_Nat_OSuc(U_1391)) ),
inference(clausify,[status(thm)],[f_527_4]) ).
cnf(f_527_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1390),c_Nat_OSuc(U_1392))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1390,U_1392) ),
inference(clausify,[status(thm)],[f_527_4]) ).
fof(f_528_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_528_2,plain,
! [U_1394,U_1393] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1393,c_Nat_OSuc(U_1394))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1393,U_1394) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
fof(f_528_3,plain,
! [U_1393,U_1394] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1393,c_Nat_OSuc(U_1394))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1393,U_1394) ),
inference(definitional_conversion,[status(esa)],[f_528_2]) ).
cnf(f_528_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1393,c_Nat_OSuc(U_1394))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1393,U_1394) ),
inference(clausify,[status(thm)],[f_528_3]) ).
fof(f_529_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_529_2,plain,
! [U_1396,U_1395] :
( U_1395 = c_Nat_OSuc(U_1396)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1395,U_1396)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1395,c_Nat_OSuc(U_1396)) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
! [U_1395,U_1396] :
( U_1395 = c_Nat_OSuc(U_1396)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1395,U_1396)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1395,c_Nat_OSuc(U_1396)) ),
inference(definitional_conversion,[status(esa)],[f_529_2]) ).
cnf(f_529_4,plain,
( U_1395 = c_Nat_OSuc(U_1396)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1395,U_1396)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1395,c_Nat_OSuc(U_1396)) ),
inference(clausify,[status(thm)],[f_529_3]) ).
fof(f_530_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_530_2,plain,
! [U_1398,U_1397] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1397,U_1398)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1397),U_1398) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
! [U_1398,U_1397] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1397,U_1398)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1397),U_1398) ),
inference(definitional_conversion,[status(esa)],[f_530_2]) ).
cnf(f_530_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1397,U_1398)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_1397),U_1398) ),
inference(clausify,[status(thm)],[f_530_3]) ).
fof(f_531_1,plain,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_mult__0]) ).
fof(f_531_2,plain,
! [U_1399] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_531_1]) ).
fof(f_531_3,plain,
! [U_1399] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_531_2]) ).
cnf(f_531_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1399) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_531_3]) ).
fof(f_532_1,plain,
! [V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_mult__0__right]) ).
fof(f_532_2,plain,
! [U_1400] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1400),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_532_1]) ).
fof(f_532_3,plain,
! [U_1400] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1400),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_532_2]) ).
cnf(f_532_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1400),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_532_3]) ).
fof(f_533_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).
fof(f_533_2,plain,
! [U_1402,U_1401] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1401),U_1402) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_1402 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1401 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1402 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1401 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1401),U_1402) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
fof(f_533_3,plain,
( ! [U_1406,U_1404] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1404),U_1406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_1406 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1404 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1405,U_1403] :
( U_1405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1403),U_1405) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_533_2]) ).
fof(f_533_4,plain,
( ! [U_1406,U_1404] :
( U_1406 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP88(U_1406,U_1404) )
& ! [U_1406,U_1404] :
( U_1404 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP88(U_1406,U_1404) )
& ! [U_1406,U_1404] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1404),U_1406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP88(U_1406,U_1404) )
& ! [U_1405,U_1403] :
( U_1405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1403),U_1405) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_533_3]) ).
cnf(f_533_5,plain,
( U_1405 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1403 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1403),U_1405) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_533_4]) ).
cnf(f_533_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1404),U_1406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP88(U_1406,U_1404) ),
inference(clausify,[status(thm)],[f_533_4]) ).
cnf(f_533_7,plain,
( U_1404 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP88(U_1406,U_1404) ),
inference(clausify,[status(thm)],[f_533_4]) ).
cnf(f_533_8,plain,
( U_1406 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP88(U_1406,U_1404) ),
inference(clausify,[status(thm)],[f_533_4]) ).
fof(f_534_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel1]) ).
fof(f_534_2,plain,
! [U_1409,U_1408,U_1407] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1407),U_1408) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1407),U_1409)
| ( U_1407 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1408 != U_1409 ) )
& ( U_1407 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1408 = U_1409
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1407),U_1408) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1407),U_1409) ) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
fof(f_534_3,plain,
( ! [U_1415,U_1413,U_1411] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1411),U_1413) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1411),U_1415)
| ( U_1411 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1413 != U_1415 ) )
& ! [U_1414,U_1412,U_1410] :
( U_1410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1412 = U_1414
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1410),U_1412) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1410),U_1414) ) ),
inference(miniscope,[status(thm)],[f_534_2]) ).
fof(f_534_4,plain,
( ! [U_1415,U_1413,U_1411] :
( U_1411 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP89(U_1415,U_1413,U_1411) )
& ! [U_1415,U_1413,U_1411] :
( U_1413 != U_1415
| ~ sP89(U_1415,U_1413,U_1411) )
& ! [U_1415,U_1413,U_1411] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1411),U_1413) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1411),U_1415)
| sP89(U_1415,U_1413,U_1411) )
& ! [U_1412,U_1410,U_1414] :
( U_1410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1412 = U_1414
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1410),U_1412) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1410),U_1414) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_534_3]) ).
cnf(f_534_5,plain,
( U_1410 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1412 = U_1414
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1410),U_1412) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1410),U_1414) ),
inference(clausify,[status(thm)],[f_534_4]) ).
cnf(f_534_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1411),U_1413) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1411),U_1415)
| sP89(U_1415,U_1413,U_1411) ),
inference(clausify,[status(thm)],[f_534_4]) ).
cnf(f_534_7,plain,
( U_1413 != U_1415
| ~ sP89(U_1415,U_1413,U_1411) ),
inference(clausify,[status(thm)],[f_534_4]) ).
cnf(f_534_8,plain,
( U_1411 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP89(U_1415,U_1413,U_1411) ),
inference(clausify,[status(thm)],[f_534_4]) ).
fof(f_535_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)
| ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_m_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_m_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__cancel2]) ).
fof(f_535_2,plain,
! [U_1418,U_1417,U_1416] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1416),U_1417) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1418),U_1417)
| ( U_1417 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1416 != U_1418 ) )
& ( U_1417 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1416 = U_1418
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1416),U_1417) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1418),U_1417) ) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
fof(f_535_3,plain,
( ! [U_1424,U_1422,U_1420] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1420),U_1422) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1424),U_1422)
| ( U_1422 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1420 != U_1424 ) )
& ! [U_1423,U_1421,U_1419] :
( U_1421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1419 = U_1423
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1419),U_1421) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1423),U_1421) ) ),
inference(miniscope,[status(thm)],[f_535_2]) ).
fof(f_535_4,plain,
( ! [U_1422,U_1420,U_1424] :
( U_1422 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP90(U_1422,U_1420,U_1424) )
& ! [U_1422,U_1420,U_1424] :
( U_1420 != U_1424
| ~ sP90(U_1422,U_1420,U_1424) )
& ! [U_1422,U_1420,U_1424] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1420),U_1422) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1424),U_1422)
| sP90(U_1422,U_1420,U_1424) )
& ! [U_1421,U_1419,U_1423] :
( U_1421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1419 = U_1423
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1419),U_1421) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1423),U_1421) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_535_3]) ).
cnf(f_535_5,plain,
( U_1421 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1419 = U_1423
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1419),U_1421) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1423),U_1421) ),
inference(clausify,[status(thm)],[f_535_4]) ).
cnf(f_535_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1420),U_1422) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1424),U_1422)
| sP90(U_1422,U_1420,U_1424) ),
inference(clausify,[status(thm)],[f_535_4]) ).
cnf(f_535_7,plain,
( U_1420 != U_1424
| ~ sP90(U_1422,U_1420,U_1424) ),
inference(clausify,[status(thm)],[f_535_4]) ).
cnf(f_535_8,plain,
( U_1422 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP90(U_1422,U_1420,U_1424) ),
inference(clausify,[status(thm)],[f_535_4]) ).
fof(f_536_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_536_2,plain,
! [U_1426,U_1425] :
( U_1425 = U_1426
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1426,U_1425) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1425,U_1426) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
fof(f_536_3,plain,
! [U_1426,U_1425] :
( U_1425 = U_1426
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1426,U_1425) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1425,U_1426) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_536_2]) ).
cnf(f_536_4,plain,
( U_1425 = U_1426
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1426,U_1425) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1425,U_1426) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_536_3]) ).
fof(f_537_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_537_2,plain,
! [U_1427] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1427,U_1427) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_537_1]) ).
fof(f_537_3,plain,
! [U_1427] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1427,U_1427) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_537_2]) ).
cnf(f_537_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1427,U_1427) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_537_3]) ).
fof(f_538_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_538_2,plain,
! [U_1428] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1428,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1428,
inference(variable_rename,[status(thm)],[f_538_1]) ).
fof(f_538_3,plain,
! [U_1428] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1428,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1428,
inference(definitional_conversion,[status(esa)],[f_538_2]) ).
cnf(f_538_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1428,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1428,
inference(clausify,[status(thm)],[f_538_3]) ).
fof(f_539_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_539_2,plain,
! [U_1429] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1429) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_539_1]) ).
fof(f_539_3,plain,
! [U_1429] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1429) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_539_2]) ).
cnf(f_539_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1429) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_539_3]) ).
fof(f_540_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
| V_m_2 != V_n_2 )
& ( V_m_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__cancel1]) ).
fof(f_540_2,plain,
! [U_1432,U_1431,U_1430] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1430)),U_1431) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1430)),U_1432)
| U_1431 != U_1432 )
& ( U_1431 = U_1432
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1430)),U_1431) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1430)),U_1432) ) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
fof(f_540_3,plain,
( ! [U_1438,U_1436] :
( ! [U_1434] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1434)),U_1436) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1434)),U_1438)
| U_1436 != U_1438 )
& ! [U_1437,U_1435] :
( ! [U_1433] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1433)),U_1435) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1433)),U_1437)
| U_1435 = U_1437 ) ),
inference(miniscope,[status(thm)],[f_540_2]) ).
fof(f_540_4,plain,
( ! [U_1438,U_1434,U_1436] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1434)),U_1436) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1434)),U_1438)
| U_1436 != U_1438 )
& ! [U_1437,U_1435,U_1433] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1433)),U_1435) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1433)),U_1437)
| U_1435 = U_1437 ) ),
inference(definitional_conversion,[status(esa)],[f_540_3]) ).
cnf(f_540_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1433)),U_1435) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1433)),U_1437)
| U_1435 = U_1437 ),
inference(clausify,[status(thm)],[f_540_4]) ).
cnf(f_540_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1434)),U_1436) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1434)),U_1438)
| U_1436 != U_1438 ),
inference(clausify,[status(thm)],[f_540_4]) ).
fof(f_541_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_541_2,plain,
! [U_1440,U_1439] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1439,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1440,U_1439)),
inference(variable_rename,[status(thm)],[f_541_1]) ).
fof(f_541_3,plain,
! [U_1439,U_1440] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1439,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1440,U_1439)),
inference(definitional_conversion,[status(esa)],[f_541_2]) ).
cnf(f_541_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1439,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1440,U_1439)),
inference(clausify,[status(thm)],[f_541_3]) ).
fof(f_542_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_542_2,plain,
! [U_1442,U_1441] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1441,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1441,U_1442)),
inference(variable_rename,[status(thm)],[f_542_1]) ).
fof(f_542_3,plain,
! [U_1442,U_1441] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1441,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1441,U_1442)),
inference(definitional_conversion,[status(esa)],[f_542_2]) ).
cnf(f_542_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1441,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1441,U_1442)),
inference(clausify,[status(thm)],[f_542_3]) ).
fof(f_543_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_543_2,plain,
! [U_1446,U_1445] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1445,U_1446)
| ! [U_1444] : U_1446 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1445,U_1444) )
& ( ? [U_1443] : U_1446 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1445,U_1443)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1445,U_1446) ) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
fof(f_543_3,plain,
( ! [U_1450,U_1448] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1448,U_1450)
| ! [U_1444] : U_1450 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1448,U_1444) )
& ! [U_1449,U_1447] :
( ? [U_1443] : U_1449 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1447,U_1443)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1447,U_1449) ) ),
inference(miniscope,[status(thm)],[f_543_2]) ).
fof(f_543_4,plain,
( ! [U_1450,U_1448] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1448,U_1450)
| ! [U_1444] : U_1450 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1448,U_1444) )
& ! [U_1449,U_1447] :
( U_1449 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1447,sK5(U_1449,U_1447))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1447,U_1449) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_1443,sK5(U_1449,U_1447))],[f_543_3]) ).
fof(f_543_5,plain,
( ! [U_1450,U_1444,U_1448] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1448,U_1450)
| U_1450 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1448,U_1444) )
& ! [U_1447,U_1449] :
( U_1449 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1447,sK5(U_1449,U_1447))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1447,U_1449) ) ),
inference(definitional_conversion,[status(esa)],[f_543_4]) ).
cnf(f_543_6,plain,
( U_1449 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1447,sK5(U_1449,U_1447))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1447,U_1449) ),
inference(clausify,[status(thm)],[f_543_5]) ).
cnf(f_543_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1448,U_1450)
| U_1450 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1448,U_1444) ),
inference(clausify,[status(thm)],[f_543_5]) ).
fof(f_544_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_544_2,plain,
! [U_1454,U_1453] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1453,U_1454)
| ! [U_1452] : U_1454 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1453,U_1452) )
& ( ? [U_1451] : U_1454 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1453,U_1451)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1453,U_1454) ) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
fof(f_544_3,plain,
( ! [U_1458,U_1456] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1456,U_1458)
| ! [U_1452] : U_1458 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1456,U_1452) )
& ! [U_1457,U_1455] :
( ? [U_1451] : U_1457 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1455,U_1451)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1455,U_1457) ) ),
inference(miniscope,[status(thm)],[f_544_2]) ).
fof(f_544_4,plain,
( ! [U_1458,U_1456] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1456,U_1458)
| ! [U_1452] : U_1458 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1456,U_1452) )
& ! [U_1457,U_1455] :
( U_1457 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1455,sK6(U_1457,U_1455))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1455,U_1457) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_1451,sK6(U_1457,U_1455))],[f_544_3]) ).
fof(f_544_5,plain,
( ! [U_1452,U_1458,U_1456] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1456,U_1458)
| U_1458 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1456,U_1452) )
& ! [U_1455,U_1457] :
( U_1457 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1455,sK6(U_1457,U_1455))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1455,U_1457) ) ),
inference(definitional_conversion,[status(esa)],[f_544_4]) ).
cnf(f_544_6,plain,
( U_1457 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1455,sK6(U_1457,U_1455))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1455,U_1457) ),
inference(clausify,[status(thm)],[f_544_5]) ).
cnf(f_544_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1456,U_1458)
| U_1458 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1456,U_1452) ),
inference(clausify,[status(thm)],[f_544_5]) ).
fof(f_545_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_545_2,plain,
! [U_1461,U_1460,U_1459] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1459,U_1460),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1459,U_1461))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1460,U_1461) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1460,U_1461)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1459,U_1460),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1459,U_1461)) ) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
fof(f_545_3,plain,
( ! [U_1467,U_1465] :
( ! [U_1463] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1463,U_1465),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1463,U_1467))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1465,U_1467) )
& ! [U_1466,U_1464] :
( ! [U_1462] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1462,U_1464),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1462,U_1466))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1464,U_1466) ) ),
inference(miniscope,[status(thm)],[f_545_2]) ).
fof(f_545_4,plain,
( ! [U_1465,U_1463,U_1467] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1463,U_1465),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1463,U_1467))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1465,U_1467) )
& ! [U_1462,U_1464,U_1466] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1462,U_1464),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1462,U_1466))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1464,U_1466) ) ),
inference(definitional_conversion,[status(esa)],[f_545_3]) ).
cnf(f_545_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1462,U_1464),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1462,U_1466))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1464,U_1466) ),
inference(clausify,[status(thm)],[f_545_4]) ).
cnf(f_545_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1463,U_1465),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1463,U_1467))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1465,U_1467) ),
inference(clausify,[status(thm)],[f_545_4]) ).
fof(f_546_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_546_2,plain,
! [U_1470,U_1469,U_1468] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1468,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1469,U_1470))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1468,U_1469) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
fof(f_546_3,plain,
! [U_1470,U_1469,U_1468] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1468,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1469,U_1470))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1468,U_1469) ),
inference(definitional_conversion,[status(esa)],[f_546_2]) ).
cnf(f_546_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1468,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1469,U_1470))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1468,U_1469) ),
inference(clausify,[status(thm)],[f_546_3]) ).
fof(f_547_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_547_2,plain,
! [U_1473,U_1472,U_1471] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1471,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1473,U_1472))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1471,U_1472) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
fof(f_547_3,plain,
! [U_1472,U_1471,U_1473] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1471,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1473,U_1472))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1471,U_1472) ),
inference(definitional_conversion,[status(esa)],[f_547_2]) ).
cnf(f_547_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1471,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1473,U_1472))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1471,U_1472) ),
inference(clausify,[status(thm)],[f_547_3]) ).
fof(f_548_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_548_2,plain,
! [U_1476,U_1475,U_1474] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1474,U_1476),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1475,U_1476))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1474,U_1475) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
fof(f_548_3,plain,
! [U_1475,U_1474,U_1476] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1474,U_1476),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1475,U_1476))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1474,U_1475) ),
inference(definitional_conversion,[status(esa)],[f_548_2]) ).
cnf(f_548_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1474,U_1476),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1475,U_1476))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1474,U_1475) ),
inference(clausify,[status(thm)],[f_548_3]) ).
fof(f_549_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_549_2,plain,
! [U_1480,U_1479,U_1478,U_1477] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1477,U_1479),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1478,U_1480))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1479,U_1480)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1477,U_1478) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
fof(f_549_3,plain,
! [U_1477,U_1478,U_1479,U_1480] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1477,U_1479),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1478,U_1480))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1479,U_1480)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1477,U_1478) ),
inference(definitional_conversion,[status(esa)],[f_549_2]) ).
cnf(f_549_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1477,U_1479),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1478,U_1480))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1479,U_1480)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1477,U_1478) ),
inference(clausify,[status(thm)],[f_549_3]) ).
fof(f_550_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_550_2,plain,
! [U_1483,U_1482,U_1481] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1482,U_1483)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1481,U_1482),U_1483) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
fof(f_550_3,plain,
! [U_1483,U_1482] :
( ! [U_1481] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1481,U_1482),U_1483)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1482,U_1483) ),
inference(miniscope,[status(thm)],[f_550_2]) ).
fof(f_550_4,plain,
! [U_1483,U_1482,U_1481] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1481,U_1482),U_1483)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1482,U_1483) ),
inference(definitional_conversion,[status(esa)],[f_550_3]) ).
cnf(f_550_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1481,U_1482),U_1483)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1482,U_1483) ),
inference(clausify,[status(thm)],[f_550_4]) ).
fof(f_551_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_551_2,plain,
! [U_1486,U_1485,U_1484] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1484,U_1486)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1484,U_1485),U_1486) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
fof(f_551_3,plain,
! [U_1485,U_1484,U_1486] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1484,U_1486)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1484,U_1485),U_1486) ),
inference(definitional_conversion,[status(esa)],[f_551_2]) ).
cnf(f_551_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1484,U_1486)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1484,U_1485),U_1486) ),
inference(clausify,[status(thm)],[f_551_3]) ).
fof(f_552_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_552_2,plain,
! [U_1489,U_1488,U_1487] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1488,U_1489)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1487,U_1489) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1487,U_1488),U_1489) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
fof(f_552_3,plain,
( ! [U_1488,U_1487,U_1489] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1488,U_1489)
| ~ sP91(U_1488,U_1487,U_1489) )
& ! [U_1488,U_1487,U_1489] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1487,U_1489)
| ~ sP91(U_1488,U_1487,U_1489) )
& ! [U_1488,U_1487,U_1489] :
( sP91(U_1488,U_1487,U_1489)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1487,U_1488),U_1489) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_552_2]) ).
cnf(f_552_4,plain,
( sP91(U_1488,U_1487,U_1489)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1487,U_1488),U_1489) ),
inference(clausify,[status(thm)],[f_552_3]) ).
cnf(f_552_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1487,U_1489)
| ~ sP91(U_1488,U_1487,U_1489) ),
inference(clausify,[status(thm)],[f_552_3]) ).
cnf(f_552_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1488,U_1489)
| ~ sP91(U_1488,U_1487,U_1489) ),
inference(clausify,[status(thm)],[f_552_3]) ).
fof(f_553_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_553_2,plain,
! [U_1491,U_1490] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1490),c_Nat_OSuc(U_1491)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1490,U_1491),
inference(variable_rename,[status(thm)],[f_553_1]) ).
fof(f_553_3,plain,
! [U_1491,U_1490] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1490),c_Nat_OSuc(U_1491)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1490,U_1491),
inference(definitional_conversion,[status(esa)],[f_553_2]) ).
cnf(f_553_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1490),c_Nat_OSuc(U_1491)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1490,U_1491),
inference(clausify,[status(thm)],[f_553_3]) ).
fof(f_554_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_554_2,plain,
! [U_1494,U_1493,U_1492] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1492),U_1493),c_Nat_OSuc(U_1494)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1492,U_1493),U_1494),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
! [U_1492,U_1493,U_1494] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1492),U_1493),c_Nat_OSuc(U_1494)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1492,U_1493),U_1494),
inference(definitional_conversion,[status(esa)],[f_554_2]) ).
cnf(f_554_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1492),U_1493),c_Nat_OSuc(U_1494)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1492,U_1493),U_1494),
inference(clausify,[status(thm)],[f_554_3]) ).
fof(f_555_1,plain,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib2]) ).
fof(f_555_2,plain,
! [U_1497,U_1496,U_1495] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1495),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1496,U_1497)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1495),U_1496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1495),U_1497)),
inference(variable_rename,[status(thm)],[f_555_1]) ).
fof(f_555_3,plain,
! [U_1495,U_1496,U_1497] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1495),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1496,U_1497)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1495),U_1496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1495),U_1497)),
inference(definitional_conversion,[status(esa)],[f_555_2]) ).
cnf(f_555_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1495),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1496,U_1497)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1495),U_1496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1495),U_1497)),
inference(clausify,[status(thm)],[f_555_3]) ).
fof(f_556_1,plain,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
inference(fof_nnf,[status(thm)],[fact_add__mult__distrib]) ).
fof(f_556_2,plain,
! [U_1500,U_1499,U_1498] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1498,U_1499)),U_1500) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1498),U_1500),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1499),U_1500)),
inference(variable_rename,[status(thm)],[f_556_1]) ).
fof(f_556_3,plain,
! [U_1498,U_1499,U_1500] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1498,U_1499)),U_1500) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1498),U_1500),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1499),U_1500)),
inference(definitional_conversion,[status(esa)],[f_556_2]) ).
cnf(f_556_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1498,U_1499)),U_1500) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1498),U_1500),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1499),U_1500)),
inference(clausify,[status(thm)],[f_556_3]) ).
fof(f_557_1,plain,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m)),
inference(fof_nnf,[status(thm)],[fact_le__square]) ).
fof(f_557_2,plain,
! [U_1501] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1501),U_1501)),
inference(variable_rename,[status(thm)],[f_557_1]) ).
fof(f_557_3,plain,
! [U_1501] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1501),U_1501)),
inference(definitional_conversion,[status(esa)],[f_557_2]) ).
cnf(f_557_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1501,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1501),U_1501)),
inference(clausify,[status(thm)],[f_557_3]) ).
fof(f_558_1,plain,
! [V_m] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_m))),
inference(fof_nnf,[status(thm)],[fact_le__cube]) ).
fof(f_558_2,plain,
! [U_1502] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1502,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1502),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1502),U_1502))),
inference(variable_rename,[status(thm)],[f_558_1]) ).
fof(f_558_3,plain,
! [U_1502] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1502,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1502),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1502),U_1502))),
inference(definitional_conversion,[status(esa)],[f_558_2]) ).
cnf(f_558_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1502,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1502),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1502),U_1502))),
inference(clausify,[status(thm)],[f_558_3]) ).
fof(f_559_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_mult__le__mono1]) ).
fof(f_559_2,plain,
! [U_1505,U_1504,U_1503] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1503),U_1505),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1504),U_1505))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1503,U_1504) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
fof(f_559_3,plain,
! [U_1503,U_1504,U_1505] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1503),U_1505),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1504),U_1505))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1503,U_1504) ),
inference(definitional_conversion,[status(esa)],[f_559_2]) ).
cnf(f_559_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1503),U_1505),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1504),U_1505))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1503,U_1504) ),
inference(clausify,[status(thm)],[f_559_3]) ).
fof(f_560_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__mono2]) ).
fof(f_560_2,plain,
! [U_1508,U_1507,U_1506] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1506),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1507))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1506,U_1507) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
fof(f_560_3,plain,
! [U_1506,U_1507,U_1508] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1506),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1507))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1506,U_1507) ),
inference(definitional_conversion,[status(esa)],[f_560_2]) ).
cnf(f_560_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1506),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1508),U_1507))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1506,U_1507) ),
inference(clausify,[status(thm)],[f_560_3]) ).
fof(f_561_1,plain,
! [V_l,V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_mult__le__mono]) ).
fof(f_561_2,plain,
! [U_1512,U_1511,U_1510,U_1509] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1509),U_1511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1510),U_1512))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1511,U_1512)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1509,U_1510) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
fof(f_561_3,plain,
! [U_1509,U_1510,U_1511,U_1512] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1509),U_1511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1510),U_1512))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1511,U_1512)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1509,U_1510) ),
inference(definitional_conversion,[status(esa)],[f_561_2]) ).
cnf(f_561_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1509),U_1511),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1510),U_1512))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1511,U_1512)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1509,U_1510) ),
inference(clausify,[status(thm)],[f_561_3]) ).
fof(f_562_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_562_2,plain,
! [U_1514,U_1513] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1513,U_1514),U_1514) = U_1513,
inference(variable_rename,[status(thm)],[f_562_1]) ).
fof(f_562_3,plain,
! [U_1513,U_1514] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1513,U_1514),U_1514) = U_1513,
inference(definitional_conversion,[status(esa)],[f_562_2]) ).
cnf(f_562_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1513,U_1514),U_1514) = U_1513,
inference(clausify,[status(thm)],[f_562_3]) ).
fof(f_563_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_563_2,plain,
! [U_1516,U_1515] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1515,U_1516),U_1515) = U_1516,
inference(variable_rename,[status(thm)],[f_563_1]) ).
fof(f_563_3,plain,
! [U_1516,U_1515] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1515,U_1516),U_1515) = U_1516,
inference(definitional_conversion,[status(esa)],[f_563_2]) ).
cnf(f_563_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1515,U_1516),U_1515) = U_1516,
inference(clausify,[status(thm)],[f_563_3]) ).
fof(f_564_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_564_2,plain,
! [U_1519,U_1518,U_1517] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1517,U_1518),U_1519) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1517,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1518,U_1519)),
inference(variable_rename,[status(thm)],[f_564_1]) ).
fof(f_564_3,plain,
! [U_1518,U_1517,U_1519] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1517,U_1518),U_1519) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1517,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1518,U_1519)),
inference(definitional_conversion,[status(esa)],[f_564_2]) ).
cnf(f_564_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1517,U_1518),U_1519) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1517,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1518,U_1519)),
inference(clausify,[status(thm)],[f_564_3]) ).
fof(f_565_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_565_2,plain,
! [U_1522,U_1521,U_1520] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1521),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1522)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1521,U_1522),
inference(variable_rename,[status(thm)],[f_565_1]) ).
fof(f_565_3,plain,
! [U_1521,U_1520,U_1522] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1521),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1522)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1521,U_1522),
inference(definitional_conversion,[status(esa)],[f_565_2]) ).
cnf(f_565_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1521),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1522)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1521,U_1522),
inference(clausify,[status(thm)],[f_565_3]) ).
fof(f_566_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_566_2,plain,
! [U_1525,U_1524,U_1523] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1523,U_1524),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1525,U_1524)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1523,U_1525),
inference(variable_rename,[status(thm)],[f_566_1]) ).
fof(f_566_3,plain,
! [U_1524,U_1523,U_1525] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1523,U_1524),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1525,U_1524)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1523,U_1525),
inference(definitional_conversion,[status(esa)],[f_566_2]) ).
cnf(f_566_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1523,U_1524),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1525,U_1524)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1523,U_1525),
inference(clausify,[status(thm)],[f_566_3]) ).
fof(f_567_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_567_2,plain,
! [U_1527,U_1526] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1526,U_1527),U_1526),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
! [U_1527,U_1526] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1526,U_1527),U_1526),
inference(definitional_conversion,[status(esa)],[f_567_2]) ).
cnf(f_567_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1526,U_1527),U_1526),
inference(clausify,[status(thm)],[f_567_3]) ).
fof(f_568_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_568_2,plain,
! [U_1530,U_1529,U_1528] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1530,U_1529),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1530,U_1528))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1528,U_1529) ),
inference(variable_rename,[status(thm)],[f_568_1]) ).
fof(f_568_3,plain,
! [U_1529,U_1528,U_1530] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1530,U_1529),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1530,U_1528))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1528,U_1529) ),
inference(definitional_conversion,[status(esa)],[f_568_2]) ).
cnf(f_568_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1530,U_1529),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1530,U_1528))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1528,U_1529) ),
inference(clausify,[status(thm)],[f_568_3]) ).
fof(f_569_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_569_2,plain,
! [U_1533,U_1532,U_1531] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1531,U_1533),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1532,U_1533))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1531,U_1532) ),
inference(variable_rename,[status(thm)],[f_569_1]) ).
fof(f_569_3,plain,
! [U_1531,U_1532,U_1533] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1531,U_1533),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1532,U_1533))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1531,U_1532) ),
inference(definitional_conversion,[status(esa)],[f_569_2]) ).
cnf(f_569_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1531,U_1533),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1532,U_1533))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1531,U_1532) ),
inference(clausify,[status(thm)],[f_569_3]) ).
fof(f_570_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_570_2,plain,
! [U_1535,U_1534] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1535,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1535,U_1534)) = U_1534
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1534,U_1535) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
fof(f_570_3,plain,
! [U_1534,U_1535] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1535,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1535,U_1534)) = U_1534
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1534,U_1535) ),
inference(definitional_conversion,[status(esa)],[f_570_2]) ).
cnf(f_570_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1535,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1535,U_1534)) = U_1534
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1534,U_1535) ),
inference(clausify,[status(thm)],[f_570_3]) ).
fof(f_571_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_571_2,plain,
! [U_1538,U_1537,U_1536] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1537,U_1536) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1538,U_1536)
| U_1537 != U_1538 )
& ( U_1537 = U_1538
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1537,U_1536) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1538,U_1536) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1536,U_1538)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1536,U_1537) ),
inference(variable_rename,[status(thm)],[f_571_1]) ).
fof(f_571_3,plain,
( ! [U_1536,U_1537,U_1538] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1537,U_1536) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1538,U_1536)
| U_1537 != U_1538
| ~ sP92(U_1536,U_1537,U_1538) )
& ! [U_1536,U_1537,U_1538] :
( U_1537 = U_1538
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1537,U_1536) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1538,U_1536)
| ~ sP92(U_1536,U_1537,U_1538) )
& ! [U_1536,U_1537,U_1538] :
( sP92(U_1536,U_1537,U_1538)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1536,U_1538)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1536,U_1537) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92])],[f_571_2]) ).
cnf(f_571_4,plain,
( sP92(U_1536,U_1537,U_1538)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1536,U_1538)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1536,U_1537) ),
inference(clausify,[status(thm)],[f_571_3]) ).
cnf(f_571_5,plain,
( U_1537 = U_1538
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1537,U_1536) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1538,U_1536)
| ~ sP92(U_1536,U_1537,U_1538) ),
inference(clausify,[status(thm)],[f_571_3]) ).
cnf(f_571_6,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1537,U_1536) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1538,U_1536)
| U_1537 != U_1538
| ~ sP92(U_1536,U_1537,U_1538) ),
inference(clausify,[status(thm)],[f_571_3]) ).
fof(f_572_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_572_2,plain,
! [U_1541,U_1540,U_1539] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1540,U_1539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1541,U_1539)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1540,U_1541)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1539,U_1541)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1539,U_1540) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
fof(f_572_3,plain,
! [U_1541,U_1540,U_1539] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1540,U_1539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1541,U_1539)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1540,U_1541)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1539,U_1541)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1539,U_1540) ),
inference(definitional_conversion,[status(esa)],[f_572_2]) ).
cnf(f_572_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1540,U_1539),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1541,U_1539)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1540,U_1541)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1539,U_1541)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1539,U_1540) ),
inference(clausify,[status(thm)],[f_572_3]) ).
fof(f_573_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_573_2,plain,
! [U_1544,U_1543,U_1542] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1543,U_1542),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1544,U_1542))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1543,U_1544) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1543,U_1544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1543,U_1542),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1544,U_1542)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1542,U_1544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1542,U_1543) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
fof(f_573_3,plain,
( ! [U_1543,U_1542,U_1544] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1543,U_1542),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1544,U_1542))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1543,U_1544)
| ~ sP93(U_1543,U_1542,U_1544) )
& ! [U_1543,U_1542,U_1544] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1543,U_1544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1543,U_1542),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1544,U_1542))
| ~ sP93(U_1543,U_1542,U_1544) )
& ! [U_1543,U_1542,U_1544] :
( sP93(U_1543,U_1542,U_1544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1542,U_1544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1542,U_1543) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_573_2]) ).
cnf(f_573_4,plain,
( sP93(U_1543,U_1542,U_1544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1542,U_1544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1542,U_1543) ),
inference(clausify,[status(thm)],[f_573_3]) ).
cnf(f_573_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1543,U_1544)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1543,U_1542),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1544,U_1542))
| ~ sP93(U_1543,U_1542,U_1544) ),
inference(clausify,[status(thm)],[f_573_3]) ).
cnf(f_573_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1543,U_1542),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1544,U_1542))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1543,U_1544)
| ~ sP93(U_1543,U_1542,U_1544) ),
inference(clausify,[status(thm)],[f_573_3]) ).
fof(f_574_1,plain,
! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib2]) ).
fof(f_574_2,plain,
! [U_1547,U_1546,U_1545] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1545),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1546,U_1547)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1545),U_1546),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1545),U_1547)),
inference(variable_rename,[status(thm)],[f_574_1]) ).
fof(f_574_3,plain,
! [U_1546,U_1547,U_1545] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1545),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1546,U_1547)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1545),U_1546),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1545),U_1547)),
inference(definitional_conversion,[status(esa)],[f_574_2]) ).
cnf(f_574_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1545),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1546,U_1547)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1545),U_1546),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1545),U_1547)),
inference(clausify,[status(thm)],[f_574_3]) ).
fof(f_575_1,plain,
! [V_k,V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)),V_k) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_k)),
inference(fof_nnf,[status(thm)],[fact_diff__mult__distrib]) ).
fof(f_575_2,plain,
! [U_1550,U_1549,U_1548] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1548,U_1549)),U_1550) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1548),U_1550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1549),U_1550)),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
! [U_1548,U_1549,U_1550] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1548,U_1549)),U_1550) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1548),U_1550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1549),U_1550)),
inference(definitional_conversion,[status(esa)],[f_575_2]) ).
cnf(f_575_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1548,U_1549)),U_1550) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1548),U_1550),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1549),U_1550)),
inference(clausify,[status(thm)],[f_575_3]) ).
fof(f_576_1,plain,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n,
inference(fof_nnf,[status(thm)],[fact_nat__mult__1]) ).
fof(f_576_2,plain,
! [U_1551] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1551) = U_1551,
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
! [U_1551] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1551) = U_1551,
inference(definitional_conversion,[status(esa)],[f_576_2]) ).
cnf(f_576_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1551) = U_1551,
inference(clausify,[status(thm)],[f_576_3]) ).
fof(f_577_1,plain,
! [V_n_2,V_m_2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).
fof(f_577_2,plain,
! [U_1553,U_1552] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1552),U_1553)
| U_1553 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1552 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1553 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1552 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1552),U_1553) ) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
fof(f_577_3,plain,
( ! [U_1557,U_1555] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1555),U_1557)
| U_1557 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1555 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1556,U_1554] :
( ( U_1556 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1554 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1554),U_1556) ) ),
inference(miniscope,[status(thm)],[f_577_2]) ).
fof(f_577_4,plain,
( ! [U_1556,U_1554] :
( U_1556 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP94(U_1556,U_1554) )
& ! [U_1556,U_1554] :
( U_1554 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP94(U_1556,U_1554) )
& ! [U_1557,U_1555] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1555),U_1557)
| U_1557 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1555 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1556,U_1554] :
( sP94(U_1556,U_1554)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1554),U_1556) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94])],[f_577_3]) ).
cnf(f_577_5,plain,
( sP94(U_1556,U_1554)
| c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1554),U_1556) ),
inference(clausify,[status(thm)],[f_577_4]) ).
cnf(f_577_6,plain,
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1555),U_1557)
| U_1557 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1555 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_577_4]) ).
cnf(f_577_7,plain,
( U_1554 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP94(U_1556,U_1554) ),
inference(clausify,[status(thm)],[f_577_4]) ).
cnf(f_577_8,plain,
( U_1556 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP94(U_1556,U_1554) ),
inference(clausify,[status(thm)],[f_577_4]) ).
fof(f_578_1,plain,
! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n,
inference(fof_nnf,[status(thm)],[fact_nat__mult__1__right]) ).
fof(f_578_2,plain,
! [U_1558] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1558),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1558,
inference(variable_rename,[status(thm)],[f_578_1]) ).
fof(f_578_3,plain,
! [U_1558] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1558),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1558,
inference(definitional_conversion,[status(esa)],[f_578_2]) ).
cnf(f_578_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1558),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1558,
inference(clausify,[status(thm)],[f_578_3]) ).
fof(f_579_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__1__iff]) ).
fof(f_579_2,plain,
! [U_1560,U_1559] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1559),U_1560) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1560 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1559 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1560 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1559 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1559),U_1560) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
fof(f_579_3,plain,
( ! [U_1564,U_1562] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1562),U_1564) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1564 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1562 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1563,U_1561] :
( ( U_1563 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1561 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1561),U_1563) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_579_2]) ).
fof(f_579_4,plain,
( ! [U_1563,U_1561] :
( U_1563 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP95(U_1563,U_1561) )
& ! [U_1563,U_1561] :
( U_1561 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP95(U_1563,U_1561) )
& ! [U_1564,U_1562] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1562),U_1564) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1564 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1562 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1563,U_1561] :
( sP95(U_1563,U_1561)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1561),U_1563) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP95])],[f_579_3]) ).
cnf(f_579_5,plain,
( sP95(U_1563,U_1561)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1561),U_1563) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_579_4]) ).
cnf(f_579_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1562),U_1564) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1564 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1562 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_579_4]) ).
cnf(f_579_7,plain,
( U_1561 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP95(U_1563,U_1561) ),
inference(clausify,[status(thm)],[f_579_4]) ).
cnf(f_579_8,plain,
( U_1563 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP95(U_1563,U_1561) ),
inference(clausify,[status(thm)],[f_579_4]) ).
fof(f_580_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_580_2,plain,
! [U_1566,U_1565] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1565,U_1566) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_1566 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1565 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1566 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1565 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_1566 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1565 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_1566 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1565 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1565,U_1566) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
fof(f_580_3,plain,
( ! [U_1570,U_1568] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1568,U_1570) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_1570 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1568 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1570 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1568 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_1569,U_1567] :
( ( U_1569 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_1569 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1567 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1567,U_1569) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_580_2]) ).
fof(f_580_4,plain,
( ! [U_1568,U_1570] :
( U_1570 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1568 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP98(U_1568,U_1570) )
& ! [U_1568,U_1570] :
( U_1570 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1568 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP98(U_1568,U_1570) )
& ! [U_1567,U_1569] :
( U_1569 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP97(U_1567,U_1569) )
& ! [U_1567,U_1569] :
( U_1567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP97(U_1567,U_1569) )
& ! [U_1567,U_1569] :
( U_1569 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP96(U_1567,U_1569) )
& ! [U_1567,U_1569] :
( U_1567 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP96(U_1567,U_1569) )
& ! [U_1568,U_1570] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1568,U_1570) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP98(U_1568,U_1570) )
& ! [U_1567,U_1569] :
( sP97(U_1567,U_1569)
| sP96(U_1567,U_1569)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1567,U_1569) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96,sP97,sP98])],[f_580_3]) ).
cnf(f_580_5,plain,
( sP97(U_1567,U_1569)
| sP96(U_1567,U_1569)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1567,U_1569) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1568,U_1570) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP98(U_1568,U_1570) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_7,plain,
( U_1567 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP96(U_1567,U_1569) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_8,plain,
( U_1569 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP96(U_1567,U_1569) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_9,plain,
( U_1567 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP97(U_1567,U_1569) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_10,plain,
( U_1569 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP97(U_1567,U_1569) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_11,plain,
( U_1570 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1568 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP98(U_1568,U_1570) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_12,plain,
( U_1570 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1568 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP98(U_1568,U_1570) ),
inference(clausify,[status(thm)],[f_580_4]) ).
fof(f_581_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_581_2,plain,
! [U_1572,U_1571] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1571,U_1572)
| ( ( U_1572 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1571 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1572 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1571 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_1572 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1571 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_1572 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1571 = 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_1571,U_1572) ) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
( ! [U_1576,U_1574] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1574,U_1576)
| ( ( U_1576 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1574 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1576 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1574 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_1575,U_1573] :
( ( U_1575 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_1575 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1573 = 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_1573,U_1575) ) ),
inference(miniscope,[status(thm)],[f_581_2]) ).
fof(f_581_4,plain,
( ! [U_1574,U_1576] :
( U_1576 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1574 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP101(U_1574,U_1576) )
& ! [U_1574,U_1576] :
( U_1576 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1574 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP101(U_1574,U_1576) )
& ! [U_1573,U_1575] :
( U_1575 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP100(U_1573,U_1575) )
& ! [U_1573,U_1575] :
( U_1573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP100(U_1573,U_1575) )
& ! [U_1573,U_1575] :
( U_1575 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP99(U_1573,U_1575) )
& ! [U_1573,U_1575] :
( U_1573 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP99(U_1573,U_1575) )
& ! [U_1574,U_1576] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1574,U_1576)
| sP101(U_1574,U_1576) )
& ! [U_1573,U_1575] :
( sP100(U_1573,U_1575)
| sP99(U_1573,U_1575)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1573,U_1575) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99,sP100,sP101])],[f_581_3]) ).
cnf(f_581_5,plain,
( sP100(U_1573,U_1575)
| sP99(U_1573,U_1575)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1573,U_1575) ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_6,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1574,U_1576)
| sP101(U_1574,U_1576) ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_7,plain,
( U_1573 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP99(U_1573,U_1575) ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_8,plain,
( U_1575 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP99(U_1573,U_1575) ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_9,plain,
( U_1573 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP100(U_1573,U_1575) ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_10,plain,
( U_1575 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP100(U_1573,U_1575) ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_11,plain,
( U_1576 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1574 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP101(U_1574,U_1576) ),
inference(clausify,[status(thm)],[f_581_4]) ).
cnf(f_581_12,plain,
( U_1576 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1574 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP101(U_1574,U_1576) ),
inference(clausify,[status(thm)],[f_581_4]) ).
fof(f_582_1,plain,
! [V_n_2,V_m_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_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_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(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_mult__eq__1__iff]) ).
fof(f_582_2,plain,
! [U_1578,U_1577] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1577),U_1578) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1578 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1577 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( U_1578 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1577 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1577),U_1578) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
fof(f_582_3,plain,
( ! [U_1582,U_1580] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1580),U_1582) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1582 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1580 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_1581,U_1579] :
( ( U_1581 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_1579 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1579),U_1581) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_582_2]) ).
fof(f_582_4,plain,
( ! [U_1581,U_1579] :
( U_1581 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP102(U_1581,U_1579) )
& ! [U_1581,U_1579] :
( U_1579 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP102(U_1581,U_1579) )
& ! [U_1582,U_1580] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1580),U_1582) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1582 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1580 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_1581,U_1579] :
( sP102(U_1581,U_1579)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1579),U_1581) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_582_3]) ).
cnf(f_582_5,plain,
( sP102(U_1581,U_1579)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1579),U_1581) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_582_4]) ).
cnf(f_582_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1580),U_1582) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1582 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1580 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_582_4]) ).
cnf(f_582_7,plain,
( U_1579 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP102(U_1581,U_1579) ),
inference(clausify,[status(thm)],[f_582_4]) ).
cnf(f_582_8,plain,
( U_1581 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP102(U_1581,U_1579) ),
inference(clausify,[status(thm)],[f_582_4]) ).
fof(f_583_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]) ).
fof(f_583_2,plain,
c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_583_1]) ).
cnf(f_583_3,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_583_2]) ).
fof(f_584_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_584_2,plain,
! [U_1584,U_1583] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1583,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1583,U_1584)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_584_1]) ).
fof(f_584_3,plain,
! [U_1584,U_1583] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1583,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1583,U_1584)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_584_2]) ).
cnf(f_584_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1583,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1583,U_1584)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_584_3]) ).
fof(f_585_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_585_2,plain,
! [U_1586,U_1585] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1585,U_1586) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1585,U_1586) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
fof(f_585_3,plain,
! [U_1585,U_1586] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1585,U_1586) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1585,U_1586) ),
inference(definitional_conversion,[status(esa)],[f_585_2]) ).
cnf(f_585_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1585,U_1586) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1585,U_1586) ),
inference(clausify,[status(thm)],[f_585_3]) ).
fof(f_586_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_586_2,plain,
! [U_1588,U_1587] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1587,U_1588) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1587,U_1588) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1587,U_1588)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1587,U_1588) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_586_1]) ).
fof(f_586_3,plain,
( ! [U_1592,U_1590] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1590,U_1592) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1590,U_1592) )
& ! [U_1591,U_1589] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1589,U_1591)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1589,U_1591) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_586_2]) ).
fof(f_586_4,plain,
( ! [U_1592,U_1590] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1590,U_1592) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1590,U_1592) )
& ! [U_1589,U_1591] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1589,U_1591)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1589,U_1591) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_586_3]) ).
cnf(f_586_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1589,U_1591)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1589,U_1591) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_586_4]) ).
cnf(f_586_6,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1590,U_1592) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1590,U_1592) ),
inference(clausify,[status(thm)],[f_586_4]) ).
fof(f_587_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_mult__Suc__right]) ).
fof(f_587_2,plain,
! [U_1594,U_1593] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1593),c_Nat_OSuc(U_1594)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1593,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1593),U_1594)),
inference(variable_rename,[status(thm)],[f_587_1]) ).
fof(f_587_3,plain,
! [U_1594,U_1593] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1593),c_Nat_OSuc(U_1594)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1593,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1593),U_1594)),
inference(definitional_conversion,[status(esa)],[f_587_2]) ).
cnf(f_587_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1593),c_Nat_OSuc(U_1594)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1593,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1593),U_1594)),
inference(clausify,[status(thm)],[f_587_3]) ).
fof(f_588_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_m)),V_n) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_mult__Suc]) ).
fof(f_588_2,plain,
! [U_1596,U_1595] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1595)),U_1596) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1595),U_1596)),
inference(variable_rename,[status(thm)],[f_588_1]) ).
fof(f_588_3,plain,
! [U_1595,U_1596] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1595)),U_1596) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1595),U_1596)),
inference(definitional_conversion,[status(esa)],[f_588_2]) ).
cnf(f_588_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1595)),U_1596) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1595),U_1596)),
inference(clausify,[status(thm)],[f_588_3]) ).
fof(f_589_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__mult__le__cancel1]) ).
fof(f_589_2,plain,
! [U_1599,U_1598,U_1597] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1597)),U_1598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1597)),U_1599))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1598,U_1599) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1598,U_1599)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1597)),U_1598),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1597)),U_1599)) ) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
fof(f_589_3,plain,
( ! [U_1605,U_1603] :
( ! [U_1601] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1601)),U_1603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1601)),U_1605))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1603,U_1605) )
& ! [U_1604,U_1602] :
( ! [U_1600] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1600)),U_1602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1600)),U_1604))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1602,U_1604) ) ),
inference(miniscope,[status(thm)],[f_589_2]) ).
fof(f_589_4,plain,
( ! [U_1605,U_1601,U_1603] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1601)),U_1603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1601)),U_1605))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1603,U_1605) )
& ! [U_1600,U_1602,U_1604] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1600)),U_1602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1600)),U_1604))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1602,U_1604) ) ),
inference(definitional_conversion,[status(esa)],[f_589_3]) ).
cnf(f_589_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1600)),U_1602),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1600)),U_1604))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1602,U_1604) ),
inference(clausify,[status(thm)],[f_589_4]) ).
cnf(f_589_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1601)),U_1603),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_1601)),U_1605))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1603,U_1605) ),
inference(clausify,[status(thm)],[f_589_4]) ).
fof(f_590_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_590_2,plain,
! [U_1607,U_1606] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1607),U_1606) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1607,U_1606))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1606,U_1607) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
fof(f_590_3,plain,
! [U_1607,U_1606] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1607),U_1606) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1607,U_1606))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1606,U_1607) ),
inference(definitional_conversion,[status(esa)],[f_590_2]) ).
cnf(f_590_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1607),U_1606) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1607,U_1606))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1606,U_1607) ),
inference(clausify,[status(thm)],[f_590_3]) ).
fof(f_591_1,plain,
! [V_n,V_m] :
( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_m != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) ),
inference(fof_nnf,[status(thm)],[fact_mult__eq__self__implies__10]) ).
fof(f_591_2,plain,
! [U_1609,U_1608] :
( U_1608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1609 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1608 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1608),U_1609) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
fof(f_591_3,plain,
! [U_1608,U_1609] :
( U_1608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1609 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1608 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1608),U_1609) ),
inference(definitional_conversion,[status(esa)],[f_591_2]) ).
cnf(f_591_4,plain,
( U_1608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1609 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1608 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1608),U_1609) ),
inference(clausify,[status(thm)],[f_591_3]) ).
fof(f_592_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_592_2,plain,
! [U_1612,U_1611,U_1610] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1611,U_1612),U_1610) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1611,U_1610),U_1612)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1610,U_1611) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
fof(f_592_3,plain,
! [U_1612,U_1610,U_1611] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1611,U_1612),U_1610) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1611,U_1610),U_1612)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1610,U_1611) ),
inference(definitional_conversion,[status(esa)],[f_592_2]) ).
cnf(f_592_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1611,U_1612),U_1610) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1611,U_1610),U_1612)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1610,U_1611) ),
inference(clausify,[status(thm)],[f_592_3]) ).
fof(f_593_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_593_2,plain,
! [U_1615,U_1614,U_1613] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1614,U_1613),U_1615) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1614,U_1615),U_1613)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1613,U_1614) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
fof(f_593_3,plain,
! [U_1614,U_1613,U_1615] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1614,U_1613),U_1615) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1614,U_1615),U_1613)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1613,U_1614) ),
inference(definitional_conversion,[status(esa)],[f_593_2]) ).
cnf(f_593_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1614,U_1613),U_1615) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1614,U_1615),U_1613)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1613,U_1614) ),
inference(clausify,[status(thm)],[f_593_3]) ).
fof(f_594_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_594_2,plain,
! [U_1618,U_1617,U_1616] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1618,U_1617),U_1616) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1618,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1617,U_1616))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1616,U_1617) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
fof(f_594_3,plain,
! [U_1617,U_1616,U_1618] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1618,U_1617),U_1616) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1618,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1617,U_1616))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1616,U_1617) ),
inference(definitional_conversion,[status(esa)],[f_594_2]) ).
cnf(f_594_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1618,U_1617),U_1616) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1618,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1617,U_1616))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1616,U_1617) ),
inference(clausify,[status(thm)],[f_594_3]) ).
fof(f_595_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_595_2,plain,
! [U_1621,U_1620,U_1619] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1620,U_1619) = U_1621
| U_1620 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1621,U_1619) )
& ( U_1620 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1621,U_1619)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1620,U_1619) != U_1621 ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1619,U_1620) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
fof(f_595_3,plain,
( ! [U_1619,U_1620,U_1621] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1620,U_1619) = U_1621
| U_1620 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1621,U_1619)
| ~ sP103(U_1619,U_1620,U_1621) )
& ! [U_1619,U_1620,U_1621] :
( U_1620 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1621,U_1619)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1620,U_1619) != U_1621
| ~ sP103(U_1619,U_1620,U_1621) )
& ! [U_1619,U_1620,U_1621] :
( sP103(U_1619,U_1620,U_1621)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1619,U_1620) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_595_2]) ).
cnf(f_595_4,plain,
( sP103(U_1619,U_1620,U_1621)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1619,U_1620) ),
inference(clausify,[status(thm)],[f_595_3]) ).
cnf(f_595_5,plain,
( U_1620 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1621,U_1619)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1620,U_1619) != U_1621
| ~ sP103(U_1619,U_1620,U_1621) ),
inference(clausify,[status(thm)],[f_595_3]) ).
cnf(f_595_6,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1620,U_1619) = U_1621
| U_1620 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1621,U_1619)
| ~ sP103(U_1619,U_1620,U_1621) ),
inference(clausify,[status(thm)],[f_595_3]) ).
fof(f_596_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_596_2,plain,
! [U_1623,U_1622] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1623,U_1622),U_1622) = U_1623
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1622,U_1623) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
fof(f_596_3,plain,
! [U_1622,U_1623] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1623,U_1622),U_1622) = U_1623
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1622,U_1623) ),
inference(definitional_conversion,[status(esa)],[f_596_2]) ).
cnf(f_596_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1623,U_1622),U_1622) = U_1623
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1622,U_1623) ),
inference(clausify,[status(thm)],[f_596_3]) ).
fof(f_597_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_597_2,plain,
! [U_1626,U_1625,U_1624] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1626,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1625,U_1624))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1626,U_1624),U_1625) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1626,U_1624),U_1625)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1626,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1625,U_1624)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1624,U_1625) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
fof(f_597_3,plain,
( ! [U_1624,U_1625,U_1626] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1626,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1625,U_1624))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1626,U_1624),U_1625)
| ~ sP104(U_1624,U_1625,U_1626) )
& ! [U_1624,U_1625,U_1626] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1626,U_1624),U_1625)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1626,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1625,U_1624))
| ~ sP104(U_1624,U_1625,U_1626) )
& ! [U_1624,U_1625,U_1626] :
( sP104(U_1624,U_1625,U_1626)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1624,U_1625) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_597_2]) ).
cnf(f_597_4,plain,
( sP104(U_1624,U_1625,U_1626)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1624,U_1625) ),
inference(clausify,[status(thm)],[f_597_3]) ).
cnf(f_597_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1626,U_1624),U_1625)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1626,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1625,U_1624))
| ~ sP104(U_1624,U_1625,U_1626) ),
inference(clausify,[status(thm)],[f_597_3]) ).
cnf(f_597_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1626,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1625,U_1624))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1626,U_1624),U_1625)
| ~ sP104(U_1624,U_1625,U_1626) ),
inference(clausify,[status(thm)],[f_597_3]) ).
fof(f_598_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_598_2,plain,
! [U_1629,U_1628,U_1627] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1629,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1628,U_1627)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1629,U_1628),U_1627)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1627,U_1628) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
fof(f_598_3,plain,
! [U_1629,U_1627,U_1628] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1629,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1628,U_1627)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1629,U_1628),U_1627)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1627,U_1628) ),
inference(definitional_conversion,[status(esa)],[f_598_2]) ).
cnf(f_598_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1629,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1628,U_1627)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1629,U_1628),U_1627)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1627,U_1628) ),
inference(clausify,[status(thm)],[f_598_3]) ).
fof(f_599_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_599_2,plain,
! [U_1631,U_1630] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1630,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1631,U_1630)) = U_1631
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1630,U_1631) ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
fof(f_599_3,plain,
! [U_1631,U_1630] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1630,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1631,U_1630)) = U_1631
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1630,U_1631) ),
inference(definitional_conversion,[status(esa)],[f_599_2]) ).
cnf(f_599_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1630,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1631,U_1630)) = U_1631
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1630,U_1631) ),
inference(clausify,[status(thm)],[f_599_3]) ).
fof(f_600_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_600_2,plain,
! [U_1634,U_1633,U_1632] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1634,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1633,U_1634),U_1632))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1632,U_1633) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
fof(f_600_3,plain,
! [U_1633,U_1632,U_1634] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1634,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1633,U_1634),U_1632))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1632,U_1633) ),
inference(definitional_conversion,[status(esa)],[f_600_2]) ).
cnf(f_600_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1634,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1633,U_1634),U_1632))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1632,U_1633) ),
inference(clausify,[status(thm)],[f_600_3]) ).
fof(f_601_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_601_2,plain,
! [U_1637,U_1636,U_1635] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1635,U_1636),U_1637)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1635,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1637,U_1636)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1635,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1637,U_1636))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1635,U_1636),U_1637) ) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
fof(f_601_3,plain,
( ! [U_1643,U_1641,U_1639] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1639,U_1641),U_1643)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1639,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1643,U_1641)) )
& ! [U_1642,U_1640,U_1638] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1638,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1642,U_1640))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1638,U_1640),U_1642) ) ),
inference(miniscope,[status(thm)],[f_601_2]) ).
fof(f_601_4,plain,
( ! [U_1643,U_1641,U_1639] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1639,U_1641),U_1643)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1639,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1643,U_1641)) )
& ! [U_1638,U_1640,U_1642] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1638,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1642,U_1640))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1638,U_1640),U_1642) ) ),
inference(definitional_conversion,[status(esa)],[f_601_3]) ).
cnf(f_601_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1638,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1642,U_1640))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1638,U_1640),U_1642) ),
inference(clausify,[status(thm)],[f_601_4]) ).
cnf(f_601_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1639,U_1641),U_1643)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1639,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1643,U_1641)) ),
inference(clausify,[status(thm)],[f_601_4]) ).
fof(f_602_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_602_2,plain,
! [U_1646,U_1645,U_1644] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1646,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1645,U_1644)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1646,U_1644),U_1645)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1644,U_1645) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
fof(f_602_3,plain,
! [U_1646,U_1645,U_1644] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1646,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1645,U_1644)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1646,U_1644),U_1645)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1644,U_1645) ),
inference(definitional_conversion,[status(esa)],[f_602_2]) ).
cnf(f_602_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1646,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1645,U_1644)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1646,U_1644),U_1645)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1644,U_1645) ),
inference(clausify,[status(thm)],[f_602_3]) ).
fof(f_603_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_603_2,plain,
! [U_1647] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1647),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1647,
inference(variable_rename,[status(thm)],[f_603_1]) ).
fof(f_603_3,plain,
! [U_1647] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1647),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1647,
inference(definitional_conversion,[status(esa)],[f_603_2]) ).
cnf(f_603_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1647),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1647,
inference(clausify,[status(thm)],[f_603_3]) ).
fof(f_604_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).
fof(f_604_2,plain,
! [U_1649,U_1648] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1648),U_1649))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1649)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1648) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1649)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1648) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1648),U_1649)) ) ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
fof(f_604_3,plain,
( ! [U_1653,U_1651] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1651),U_1653))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1653)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1651) )
& ! [U_1652,U_1650] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1652)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1650) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1650),U_1652)) ) ),
inference(miniscope,[status(thm)],[f_604_2]) ).
fof(f_604_4,plain,
( ! [U_1652,U_1650] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1652)
| ~ sP105(U_1652,U_1650) )
& ! [U_1652,U_1650] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1650)
| ~ sP105(U_1652,U_1650) )
& ! [U_1653,U_1651] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1651),U_1653))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1653)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1651) )
& ! [U_1652,U_1650] :
( sP105(U_1652,U_1650)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1650),U_1652)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_604_3]) ).
cnf(f_604_5,plain,
( sP105(U_1652,U_1650)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1650),U_1652)) ),
inference(clausify,[status(thm)],[f_604_4]) ).
cnf(f_604_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1651),U_1653))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1653)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1651) ),
inference(clausify,[status(thm)],[f_604_4]) ).
cnf(f_604_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1650)
| ~ sP105(U_1652,U_1650) ),
inference(clausify,[status(thm)],[f_604_4]) ).
cnf(f_604_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1652)
| ~ sP105(U_1652,U_1650) ),
inference(clausify,[status(thm)],[f_604_4]) ).
fof(f_605_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]) ).
fof(f_605_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(definitional_conversion,[status(esa)],[f_605_1]) ).
cnf(f_605_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_OPls)),
inference(clausify,[status(thm)],[f_605_2]) ).
fof(f_606_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_606_2,plain,
! [U_1656,U_1655,U_1654] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1655,U_1654)),U_1656) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1655),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1654,U_1656))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1654,U_1655) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
fof(f_606_3,plain,
! [U_1654,U_1656,U_1655] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1655,U_1654)),U_1656) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1655),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1654,U_1656))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1654,U_1655) ),
inference(definitional_conversion,[status(esa)],[f_606_2]) ).
cnf(f_606_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1655,U_1654)),U_1656) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_1655),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1654,U_1656))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1654,U_1655) ),
inference(clausify,[status(thm)],[f_606_3]) ).
fof(f_607_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_607_2,plain,
! [U_1659,U_1658,U_1657] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1659,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1658,U_1657))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1659,U_1657),c_Nat_OSuc(U_1658))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1657,U_1658) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
fof(f_607_3,plain,
! [U_1657,U_1658,U_1659] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1659,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1658,U_1657))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1659,U_1657),c_Nat_OSuc(U_1658))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1657,U_1658) ),
inference(definitional_conversion,[status(esa)],[f_607_2]) ).
cnf(f_607_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1659,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1658,U_1657))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1659,U_1657),c_Nat_OSuc(U_1658))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1657,U_1658) ),
inference(clausify,[status(thm)],[f_607_3]) ).
fof(f_608_1,plain,
! [V_y,V_x,V_c] :
( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_c),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_c,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_nnf,[status(thm)],[fact_rabs__ratiotest__lemma]) ).
fof(f_608_2,plain,
! [U_1662,U_1661,U_1660] :
( U_1661 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1660),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1662)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1660,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
fof(f_608_3,plain,
! [U_1660,U_1661,U_1662] :
( U_1661 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1660),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1662)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1660,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(definitional_conversion,[status(esa)],[f_608_2]) ).
cnf(f_608_4,plain,
( U_1661 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1660),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1662)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1660,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_608_3]) ).
fof(f_609_1,plain,
! [V_real2,V_real1] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_complex_Osize_I1_J]) ).
fof(f_609_2,plain,
! [U_1664,U_1663] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(U_1663,U_1664)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_609_1]) ).
fof(f_609_3,plain,
! [U_1664,U_1663] : c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(U_1663,U_1664)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_609_2]) ).
cnf(f_609_4,plain,
c_Complex_Ocomplex_Ocomplex__size(c_Complex_Ocomplex_OComplex(U_1663,U_1664)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_609_3]) ).
fof(f_610_1,plain,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2),V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff1]) ).
fof(f_610_2,plain,
! [U_1669,U_1668,U_1667,U_1666,U_1665] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1666),U_1667),U_1668),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1665),U_1667),U_1669))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1666,U_1665)),U_1667),U_1668),U_1669) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1666,U_1665)),U_1667),U_1668),U_1669)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1666),U_1667),U_1668),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1665),U_1667),U_1669)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1665,U_1666) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
fof(f_610_3,plain,
( ! [U_1665,U_1666,U_1667,U_1668,U_1669] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1666),U_1667),U_1668),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1665),U_1667),U_1669))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1666,U_1665)),U_1667),U_1668),U_1669)
| ~ sP106(U_1665,U_1666,U_1667,U_1668,U_1669) )
& ! [U_1665,U_1666,U_1667,U_1668,U_1669] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1666,U_1665)),U_1667),U_1668),U_1669)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1666),U_1667),U_1668),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1665),U_1667),U_1669))
| ~ sP106(U_1665,U_1666,U_1667,U_1668,U_1669) )
& ! [U_1665,U_1666,U_1667,U_1668,U_1669] :
( sP106(U_1665,U_1666,U_1667,U_1668,U_1669)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1665,U_1666) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106])],[f_610_2]) ).
cnf(f_610_4,plain,
( sP106(U_1665,U_1666,U_1667,U_1668,U_1669)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1665,U_1666) ),
inference(clausify,[status(thm)],[f_610_3]) ).
cnf(f_610_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1666,U_1665)),U_1667),U_1668),U_1669)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1666),U_1667),U_1668),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1665),U_1667),U_1669))
| ~ sP106(U_1665,U_1666,U_1667,U_1668,U_1669) ),
inference(clausify,[status(thm)],[f_610_3]) ).
cnf(f_610_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1666),U_1667),U_1668),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1665),U_1667),U_1669))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1666,U_1665)),U_1667),U_1668),U_1669)
| ~ sP106(U_1665,U_1666,U_1667,U_1668,U_1669) ),
inference(clausify,[status(thm)],[f_610_3]) ).
fof(f_611_1,plain,
! [V_n,V_m,V_u,V_i,V_j] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i,V_j)),V_u),V_m),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j,V_i) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq1]) ).
fof(f_611_2,plain,
! [U_1674,U_1673,U_1672,U_1671,U_1670] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1671),U_1672),U_1673),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1670),U_1672),U_1674)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1671,U_1670)),U_1672),U_1673),U_1674)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1670,U_1671) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
! [U_1672,U_1673,U_1671,U_1670,U_1674] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1671),U_1672),U_1673),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1670),U_1672),U_1674)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1671,U_1670)),U_1672),U_1673),U_1674)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1670,U_1671) ),
inference(definitional_conversion,[status(esa)],[f_611_2]) ).
cnf(f_611_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1671),U_1672),U_1673),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1670),U_1672),U_1674)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1671,U_1670)),U_1672),U_1673),U_1674)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1670,U_1671) ),
inference(clausify,[status(thm)],[f_611_3]) ).
fof(f_612_1,plain,
! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) != V_n_2 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_i_2,V_j_2)),V_u_2),V_m_2) = V_n_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j_2,V_i_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff1]) ).
fof(f_612_2,plain,
! [U_1679,U_1678,U_1677,U_1676,U_1675] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1676),U_1677),U_1678) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1675),U_1677),U_1679)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1676,U_1675)),U_1677),U_1678) != U_1679 )
& ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1676,U_1675)),U_1677),U_1678) = U_1679
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1676),U_1677),U_1678) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1675),U_1677),U_1679) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1675,U_1676) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
fof(f_612_3,plain,
( ! [U_1675,U_1676,U_1677,U_1678,U_1679] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1676),U_1677),U_1678) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1675),U_1677),U_1679)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1676,U_1675)),U_1677),U_1678) != U_1679
| ~ sP107(U_1675,U_1676,U_1677,U_1678,U_1679) )
& ! [U_1675,U_1676,U_1677,U_1678,U_1679] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1676,U_1675)),U_1677),U_1678) = U_1679
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1676),U_1677),U_1678) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1675),U_1677),U_1679)
| ~ sP107(U_1675,U_1676,U_1677,U_1678,U_1679) )
& ! [U_1675,U_1676,U_1677,U_1678,U_1679] :
( sP107(U_1675,U_1676,U_1677,U_1678,U_1679)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1675,U_1676) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP107])],[f_612_2]) ).
cnf(f_612_4,plain,
( sP107(U_1675,U_1676,U_1677,U_1678,U_1679)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1675,U_1676) ),
inference(clausify,[status(thm)],[f_612_3]) ).
cnf(f_612_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1676,U_1675)),U_1677),U_1678) = U_1679
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1676),U_1677),U_1678) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1675),U_1677),U_1679)
| ~ sP107(U_1675,U_1676,U_1677,U_1678,U_1679) ),
inference(clausify,[status(thm)],[f_612_3]) ).
cnf(f_612_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1676),U_1677),U_1678) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1675),U_1677),U_1679)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1676,U_1675)),U_1677),U_1678) != U_1679
| ~ sP107(U_1675,U_1676,U_1677,U_1678,U_1679) ),
inference(clausify,[status(thm)],[f_612_3]) ).
fof(f_613_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| ( V_m_2 != V_n_2
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_m_2 = V_n_2
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel__disj]) ).
fof(f_613_2,plain,
! [U_1682,U_1681,U_1680] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1680),U_1681) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1680),U_1682)
| ( U_1681 != U_1682
& U_1680 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1681 = U_1682
| U_1680 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1680),U_1681) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1680),U_1682) ) ),
inference(variable_rename,[status(thm)],[f_613_1]) ).
fof(f_613_3,plain,
( ! [U_1688,U_1686,U_1684] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1684),U_1686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1684),U_1688)
| ( U_1686 != U_1688
& U_1684 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1687,U_1685,U_1683] :
( U_1685 = U_1687
| U_1683 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1683),U_1685) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1683),U_1687) ) ),
inference(miniscope,[status(thm)],[f_613_2]) ).
fof(f_613_4,plain,
( ! [U_1688,U_1686,U_1684] :
( U_1686 != U_1688
| ~ sP108(U_1688,U_1686,U_1684) )
& ! [U_1688,U_1686,U_1684] :
( U_1684 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP108(U_1688,U_1686,U_1684) )
& ! [U_1688,U_1686,U_1684] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1684),U_1686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1684),U_1688)
| sP108(U_1688,U_1686,U_1684) )
& ! [U_1683,U_1687,U_1685] :
( U_1685 = U_1687
| U_1683 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1683),U_1685) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1683),U_1687) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP108])],[f_613_3]) ).
cnf(f_613_5,plain,
( U_1685 = U_1687
| U_1683 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1683),U_1685) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1683),U_1687) ),
inference(clausify,[status(thm)],[f_613_4]) ).
cnf(f_613_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1684),U_1686) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1684),U_1688)
| sP108(U_1688,U_1686,U_1684) ),
inference(clausify,[status(thm)],[f_613_4]) ).
cnf(f_613_7,plain,
( U_1684 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP108(U_1688,U_1686,U_1684) ),
inference(clausify,[status(thm)],[f_613_4]) ).
cnf(f_613_8,plain,
( U_1686 != U_1688
| ~ sP108(U_1688,U_1686,U_1684) ),
inference(clausify,[status(thm)],[f_613_4]) ).
fof(f_614_1,plain,
! [V_k,V_j,V_u,V_i] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_k)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_j)),V_u),V_k),
inference(fof_nnf,[status(thm)],[fact_left__add__mult__distrib]) ).
fof(f_614_2,plain,
! [U_1692,U_1691,U_1690,U_1689] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1689),U_1690),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1691),U_1690),U_1692)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1689,U_1691)),U_1690),U_1692),
inference(variable_rename,[status(thm)],[f_614_1]) ).
fof(f_614_3,plain,
! [U_1690,U_1691,U_1689,U_1692] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1689),U_1690),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1691),U_1690),U_1692)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1689,U_1691)),U_1690),U_1692),
inference(definitional_conversion,[status(esa)],[f_614_2]) ).
cnf(f_614_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1689),U_1690),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1691),U_1690),U_1692)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1689,U_1691)),U_1690),U_1692),
inference(clausify,[status(thm)],[f_614_3]) ).
fof(f_615_1,plain,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)
| V_m_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2) )
& ( V_m_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__eq__add__iff2]) ).
fof(f_615_2,plain,
! [U_1697,U_1696,U_1695,U_1694,U_1693] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1693),U_1695),U_1696) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1694),U_1695),U_1697)
| U_1696 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1693)),U_1695),U_1697) )
& ( U_1696 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1693)),U_1695),U_1697)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1693),U_1695),U_1696) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1694),U_1695),U_1697) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1693,U_1694) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
fof(f_615_3,plain,
( ! [U_1693,U_1694,U_1695,U_1696,U_1697] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1693),U_1695),U_1696) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1694),U_1695),U_1697)
| U_1696 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1693)),U_1695),U_1697)
| ~ sP109(U_1693,U_1694,U_1695,U_1696,U_1697) )
& ! [U_1693,U_1694,U_1695,U_1696,U_1697] :
( U_1696 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1693)),U_1695),U_1697)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1693),U_1695),U_1696) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1694),U_1695),U_1697)
| ~ sP109(U_1693,U_1694,U_1695,U_1696,U_1697) )
& ! [U_1693,U_1694,U_1695,U_1696,U_1697] :
( sP109(U_1693,U_1694,U_1695,U_1696,U_1697)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1693,U_1694) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_615_2]) ).
cnf(f_615_4,plain,
( sP109(U_1693,U_1694,U_1695,U_1696,U_1697)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1693,U_1694) ),
inference(clausify,[status(thm)],[f_615_3]) ).
cnf(f_615_5,plain,
( U_1696 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1693)),U_1695),U_1697)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1693),U_1695),U_1696) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1694),U_1695),U_1697)
| ~ sP109(U_1693,U_1694,U_1695,U_1696,U_1697) ),
inference(clausify,[status(thm)],[f_615_3]) ).
cnf(f_615_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1693),U_1695),U_1696) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1694),U_1695),U_1697)
| U_1696 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1694,U_1693)),U_1695),U_1697)
| ~ sP109(U_1693,U_1694,U_1695,U_1696,U_1697) ),
inference(clausify,[status(thm)],[f_615_3]) ).
fof(f_616_1,plain,
! [V_n,V_m,V_u,V_j,V_i] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_u),V_m),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_u),V_n)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_i)),V_u),V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__add__eq2]) ).
fof(f_616_2,plain,
! [U_1702,U_1701,U_1700,U_1699,U_1698] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1698),U_1700),U_1701),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1699),U_1700),U_1702)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1701,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1699,U_1698)),U_1700),U_1702))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1698,U_1699) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
fof(f_616_3,plain,
! [U_1699,U_1698,U_1701,U_1700,U_1702] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1698),U_1700),U_1701),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1699),U_1700),U_1702)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1701,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1699,U_1698)),U_1700),U_1702))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1698,U_1699) ),
inference(definitional_conversion,[status(esa)],[f_616_2]) ).
cnf(f_616_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1698),U_1700),U_1701),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1699),U_1700),U_1702)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1701,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1699,U_1698)),U_1700),U_1702))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1698,U_1699) ),
inference(clausify,[status(thm)],[f_616_3]) ).
fof(f_617_1,plain,
! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_i_2)),V_u_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2),V_m_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2),V_n_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i_2,V_j_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__add__iff2]) ).
fof(f_617_2,plain,
! [U_1707,U_1706,U_1705,U_1704,U_1703] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1703),U_1705),U_1706),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1704),U_1705),U_1707))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1706,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1704,U_1703)),U_1705),U_1707)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1706,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1704,U_1703)),U_1705),U_1707))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1703),U_1705),U_1706),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1704),U_1705),U_1707)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1703,U_1704) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
fof(f_617_3,plain,
( ! [U_1703,U_1705,U_1704,U_1706,U_1707] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1703),U_1705),U_1706),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1704),U_1705),U_1707))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1706,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1704,U_1703)),U_1705),U_1707))
| ~ sP110(U_1703,U_1705,U_1704,U_1706,U_1707) )
& ! [U_1703,U_1705,U_1704,U_1706,U_1707] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1706,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1704,U_1703)),U_1705),U_1707))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1703),U_1705),U_1706),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1704),U_1705),U_1707))
| ~ sP110(U_1703,U_1705,U_1704,U_1706,U_1707) )
& ! [U_1703,U_1705,U_1704,U_1706,U_1707] :
( sP110(U_1703,U_1705,U_1704,U_1706,U_1707)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1703,U_1704) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_617_2]) ).
cnf(f_617_4,plain,
( sP110(U_1703,U_1705,U_1704,U_1706,U_1707)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1703,U_1704) ),
inference(clausify,[status(thm)],[f_617_3]) ).
cnf(f_617_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1706,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1704,U_1703)),U_1705),U_1707))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1703),U_1705),U_1706),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1704),U_1705),U_1707))
| ~ sP110(U_1703,U_1705,U_1704,U_1706,U_1707) ),
inference(clausify,[status(thm)],[f_617_3]) ).
cnf(f_617_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1703),U_1705),U_1706),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1704),U_1705),U_1707))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1706,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1704,U_1703)),U_1705),U_1707))
| ~ sP110(U_1703,U_1705,U_1704,U_1706,U_1707) ),
inference(clausify,[status(thm)],[f_617_3]) ).
fof(f_618_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,hAPP(hAPP(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)))),hAPP(hAPP(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_618_2,plain,
! [U_1709,U_1708] : 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_1708,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1708),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1709),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_618_1]) ).
fof(f_618_3,plain,
! [U_1709,U_1708] : 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_1708,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1708),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1709),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(definitional_conversion,[status(esa)],[f_618_2]) ).
cnf(f_618_4,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_1708,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1708),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1709),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_618_3]) ).
fof(f_619_1,plain,
! [V_real2,V_real1] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(V_real1,V_real2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_complex_Osize_I2_J]) ).
fof(f_619_2,plain,
! [U_1711,U_1710] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_1710,U_1711)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_619_1]) ).
fof(f_619_3,plain,
! [U_1711,U_1710] : c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_1710,U_1711)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_619_2]) ).
cnf(f_619_4,plain,
c_Nat_Osize__class_Osize(tc_Complex_Ocomplex,c_Complex_Ocomplex_OComplex(U_1710,U_1711)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_619_3]) ).
fof(f_620_1,plain,
! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__case(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2),
inference(fof_nnf,[status(thm)],[fact_complex_Osimps_I2_J]) ).
fof(f_620_2,plain,
! [U_1715,U_1714,U_1713,U_1712] : c_Complex_Ocomplex_Ocomplex__case(U_1712,U_1713,c_Complex_Ocomplex_OComplex(U_1714,U_1715)) = hAPP(hAPP(U_1713,U_1714),U_1715),
inference(variable_rename,[status(thm)],[f_620_1]) ).
fof(f_620_3,plain,
! [U_1713,U_1712,U_1714,U_1715] : c_Complex_Ocomplex_Ocomplex__case(U_1712,U_1713,c_Complex_Ocomplex_OComplex(U_1714,U_1715)) = hAPP(hAPP(U_1713,U_1714),U_1715),
inference(definitional_conversion,[status(esa)],[f_620_2]) ).
cnf(f_620_4,plain,
c_Complex_Ocomplex_Ocomplex__case(U_1712,U_1713,c_Complex_Ocomplex_OComplex(U_1714,U_1715)) = hAPP(hAPP(U_1713,U_1714),U_1715),
inference(clausify,[status(thm)],[f_620_3]) ).
fof(f_621_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_621_2,plain,
! [U_1717,U_1716] :
( c_Rings_Oinverse__class_Odivide(U_1716,c_Groups_Ozero__class_Ozero(U_1716),U_1717) = c_Groups_Ozero__class_Ozero(U_1716)
| ~ class_Rings_Odivision__ring(U_1716) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
fof(f_621_3,plain,
! [U_1716,U_1717] :
( c_Rings_Oinverse__class_Odivide(U_1716,c_Groups_Ozero__class_Ozero(U_1716),U_1717) = c_Groups_Ozero__class_Ozero(U_1716)
| ~ class_Rings_Odivision__ring(U_1716) ),
inference(definitional_conversion,[status(esa)],[f_621_2]) ).
cnf(f_621_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1716,c_Groups_Ozero__class_Ozero(U_1716),U_1717) = c_Groups_Ozero__class_Ozero(U_1716)
| ~ class_Rings_Odivision__ring(U_1716) ),
inference(clausify,[status(thm)],[f_621_3]) ).
fof(f_622_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_622_2,plain,
! [U_1719,U_1718] :
( c_Rings_Oinverse__class_Odivide(U_1718,c_Groups_Ozero__class_Ozero(U_1718),U_1719) = c_Groups_Ozero__class_Ozero(U_1718)
| ~ class_RealVector_Oreal__normed__field(U_1718) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
fof(f_622_3,plain,
! [U_1718,U_1719] :
( c_Rings_Oinverse__class_Odivide(U_1718,c_Groups_Ozero__class_Ozero(U_1718),U_1719) = c_Groups_Ozero__class_Ozero(U_1718)
| ~ class_RealVector_Oreal__normed__field(U_1718) ),
inference(definitional_conversion,[status(esa)],[f_622_2]) ).
cnf(f_622_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1718,c_Groups_Ozero__class_Ozero(U_1718),U_1719) = c_Groups_Ozero__class_Ozero(U_1718)
| ~ class_RealVector_Oreal__normed__field(U_1718) ),
inference(clausify,[status(thm)],[f_622_3]) ).
fof(f_623_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_623_2,plain,
! [U_1721,U_1720] :
( c_Rings_Oinverse__class_Odivide(U_1720,U_1721,c_Groups_Ozero__class_Ozero(U_1720)) = c_Groups_Ozero__class_Ozero(U_1720)
| ~ class_Rings_Odivision__ring__inverse__zero(U_1720) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
fof(f_623_3,plain,
! [U_1720,U_1721] :
( c_Rings_Oinverse__class_Odivide(U_1720,U_1721,c_Groups_Ozero__class_Ozero(U_1720)) = c_Groups_Ozero__class_Ozero(U_1720)
| ~ class_Rings_Odivision__ring__inverse__zero(U_1720) ),
inference(definitional_conversion,[status(esa)],[f_623_2]) ).
cnf(f_623_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1720,U_1721,c_Groups_Ozero__class_Ozero(U_1720)) = c_Groups_Ozero__class_Ozero(U_1720)
| ~ class_Rings_Odivision__ring__inverse__zero(U_1720) ),
inference(clausify,[status(thm)],[f_623_3]) ).
fof(f_624_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_624_2,plain,
! [U_1725,U_1724,U_1723,U_1722] :
( c_Rings_Oinverse__class_Odivide(U_1722,c_Groups_Ominus__class_Ominus(U_1722,U_1723,U_1724),U_1725) = c_Groups_Ominus__class_Ominus(U_1722,c_Rings_Oinverse__class_Odivide(U_1722,U_1723,U_1725),c_Rings_Oinverse__class_Odivide(U_1722,U_1724,U_1725))
| ~ class_Rings_Odivision__ring(U_1722) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
fof(f_624_3,plain,
! [U_1722,U_1723,U_1724,U_1725] :
( c_Rings_Oinverse__class_Odivide(U_1722,c_Groups_Ominus__class_Ominus(U_1722,U_1723,U_1724),U_1725) = c_Groups_Ominus__class_Ominus(U_1722,c_Rings_Oinverse__class_Odivide(U_1722,U_1723,U_1725),c_Rings_Oinverse__class_Odivide(U_1722,U_1724,U_1725))
| ~ class_Rings_Odivision__ring(U_1722) ),
inference(definitional_conversion,[status(esa)],[f_624_2]) ).
cnf(f_624_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1722,c_Groups_Ominus__class_Ominus(U_1722,U_1723,U_1724),U_1725) = c_Groups_Ominus__class_Ominus(U_1722,c_Rings_Oinverse__class_Odivide(U_1722,U_1723,U_1725),c_Rings_Oinverse__class_Odivide(U_1722,U_1724,U_1725))
| ~ class_Rings_Odivision__ring(U_1722) ),
inference(clausify,[status(thm)],[f_624_3]) ).
fof(f_625_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_625_2,plain,
! [U_1729,U_1728,U_1727,U_1726] :
( c_Rings_Oinverse__class_Odivide(U_1726,c_Groups_Ominus__class_Ominus(U_1726,U_1727,U_1728),U_1729) = c_Groups_Ominus__class_Ominus(U_1726,c_Rings_Oinverse__class_Odivide(U_1726,U_1727,U_1729),c_Rings_Oinverse__class_Odivide(U_1726,U_1728,U_1729))
| ~ class_RealVector_Oreal__normed__field(U_1726) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
fof(f_625_3,plain,
! [U_1726,U_1727,U_1728,U_1729] :
( c_Rings_Oinverse__class_Odivide(U_1726,c_Groups_Ominus__class_Ominus(U_1726,U_1727,U_1728),U_1729) = c_Groups_Ominus__class_Ominus(U_1726,c_Rings_Oinverse__class_Odivide(U_1726,U_1727,U_1729),c_Rings_Oinverse__class_Odivide(U_1726,U_1728,U_1729))
| ~ class_RealVector_Oreal__normed__field(U_1726) ),
inference(definitional_conversion,[status(esa)],[f_625_2]) ).
cnf(f_625_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1726,c_Groups_Ominus__class_Ominus(U_1726,U_1727,U_1728),U_1729) = c_Groups_Ominus__class_Ominus(U_1726,c_Rings_Oinverse__class_Odivide(U_1726,U_1727,U_1729),c_Rings_Oinverse__class_Odivide(U_1726,U_1728,U_1729))
| ~ class_RealVector_Oreal__normed__field(U_1726) ),
inference(clausify,[status(thm)],[f_625_3]) ).
fof(f_626_1,plain,
! [V_c,V_b,V_a,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(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_626_2,plain,
! [U_1733,U_1732,U_1731,U_1730] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1730),U_1731),c_Rings_Oinverse__class_Odivide(U_1730,U_1732,U_1733)) = c_Rings_Oinverse__class_Odivide(U_1730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1730),U_1731),U_1732),U_1733)
| ~ class_Rings_Odivision__ring(U_1730) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
fof(f_626_3,plain,
! [U_1733,U_1730,U_1731,U_1732] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1730),U_1731),c_Rings_Oinverse__class_Odivide(U_1730,U_1732,U_1733)) = c_Rings_Oinverse__class_Odivide(U_1730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1730),U_1731),U_1732),U_1733)
| ~ class_Rings_Odivision__ring(U_1730) ),
inference(definitional_conversion,[status(esa)],[f_626_2]) ).
cnf(f_626_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1730),U_1731),c_Rings_Oinverse__class_Odivide(U_1730,U_1732,U_1733)) = c_Rings_Oinverse__class_Odivide(U_1730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1730),U_1731),U_1732),U_1733)
| ~ class_Rings_Odivision__ring(U_1730) ),
inference(clausify,[status(thm)],[f_626_3]) ).
fof(f_627_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_627_2,plain,
! [U_1737,U_1736,U_1735,U_1734] :
( c_Rings_Oinverse__class_Odivide(U_1734,c_Groups_Oplus__class_Oplus(U_1734,U_1735,U_1736),U_1737) = c_Groups_Oplus__class_Oplus(U_1734,c_Rings_Oinverse__class_Odivide(U_1734,U_1735,U_1737),c_Rings_Oinverse__class_Odivide(U_1734,U_1736,U_1737))
| ~ class_Rings_Odivision__ring(U_1734) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
fof(f_627_3,plain,
! [U_1735,U_1734,U_1736,U_1737] :
( c_Rings_Oinverse__class_Odivide(U_1734,c_Groups_Oplus__class_Oplus(U_1734,U_1735,U_1736),U_1737) = c_Groups_Oplus__class_Oplus(U_1734,c_Rings_Oinverse__class_Odivide(U_1734,U_1735,U_1737),c_Rings_Oinverse__class_Odivide(U_1734,U_1736,U_1737))
| ~ class_Rings_Odivision__ring(U_1734) ),
inference(definitional_conversion,[status(esa)],[f_627_2]) ).
cnf(f_627_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1734,c_Groups_Oplus__class_Oplus(U_1734,U_1735,U_1736),U_1737) = c_Groups_Oplus__class_Oplus(U_1734,c_Rings_Oinverse__class_Odivide(U_1734,U_1735,U_1737),c_Rings_Oinverse__class_Odivide(U_1734,U_1736,U_1737))
| ~ class_Rings_Odivision__ring(U_1734) ),
inference(clausify,[status(thm)],[f_627_3]) ).
fof(f_628_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_628_2,plain,
! [U_1741,U_1740,U_1739,U_1738] :
( c_Rings_Oinverse__class_Odivide(U_1738,c_Groups_Oplus__class_Oplus(U_1738,U_1739,U_1740),U_1741) = c_Groups_Oplus__class_Oplus(U_1738,c_Rings_Oinverse__class_Odivide(U_1738,U_1739,U_1741),c_Rings_Oinverse__class_Odivide(U_1738,U_1740,U_1741))
| ~ class_RealVector_Oreal__normed__field(U_1738) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
fof(f_628_3,plain,
! [U_1738,U_1739,U_1740,U_1741] :
( c_Rings_Oinverse__class_Odivide(U_1738,c_Groups_Oplus__class_Oplus(U_1738,U_1739,U_1740),U_1741) = c_Groups_Oplus__class_Oplus(U_1738,c_Rings_Oinverse__class_Odivide(U_1738,U_1739,U_1741),c_Rings_Oinverse__class_Odivide(U_1738,U_1740,U_1741))
| ~ class_RealVector_Oreal__normed__field(U_1738) ),
inference(definitional_conversion,[status(esa)],[f_628_2]) ).
cnf(f_628_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1738,c_Groups_Oplus__class_Oplus(U_1738,U_1739,U_1740),U_1741) = c_Groups_Oplus__class_Oplus(U_1738,c_Rings_Oinverse__class_Odivide(U_1738,U_1739,U_1741),c_Rings_Oinverse__class_Odivide(U_1738,U_1740,U_1741))
| ~ class_RealVector_Oreal__normed__field(U_1738) ),
inference(clausify,[status(thm)],[f_628_3]) ).
fof(f_629_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_629_2,plain,
! [U_1743,U_1742] :
( c_Rings_Oinverse__class_Odivide(U_1742,U_1743,c_Groups_Oone__class_Oone(U_1742)) = U_1743
| ~ class_Rings_Odivision__ring(U_1742) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
fof(f_629_3,plain,
! [U_1743,U_1742] :
( c_Rings_Oinverse__class_Odivide(U_1742,U_1743,c_Groups_Oone__class_Oone(U_1742)) = U_1743
| ~ class_Rings_Odivision__ring(U_1742) ),
inference(definitional_conversion,[status(esa)],[f_629_2]) ).
cnf(f_629_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1742,U_1743,c_Groups_Oone__class_Oone(U_1742)) = U_1743
| ~ class_Rings_Odivision__ring(U_1742) ),
inference(clausify,[status(thm)],[f_629_3]) ).
fof(f_630_1,plain,
! [V_n,V_b,V_a,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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_630_2,plain,
! [U_1747,U_1746,U_1745,U_1744] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1744),c_Rings_Oinverse__class_Odivide(U_1744,U_1745,U_1746)),U_1747) = c_Rings_Oinverse__class_Odivide(U_1744,hAPP(hAPP(c_Power_Opower__class_Opower(U_1744),U_1745),U_1747),hAPP(hAPP(c_Power_Opower__class_Opower(U_1744),U_1746),U_1747))
| ~ class_Fields_Ofield__inverse__zero(U_1744) ),
inference(variable_rename,[status(thm)],[f_630_1]) ).
fof(f_630_3,plain,
! [U_1744,U_1745,U_1746,U_1747] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1744),c_Rings_Oinverse__class_Odivide(U_1744,U_1745,U_1746)),U_1747) = c_Rings_Oinverse__class_Odivide(U_1744,hAPP(hAPP(c_Power_Opower__class_Opower(U_1744),U_1745),U_1747),hAPP(hAPP(c_Power_Opower__class_Opower(U_1744),U_1746),U_1747))
| ~ class_Fields_Ofield__inverse__zero(U_1744) ),
inference(definitional_conversion,[status(esa)],[f_630_2]) ).
cnf(f_630_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1744),c_Rings_Oinverse__class_Odivide(U_1744,U_1745,U_1746)),U_1747) = c_Rings_Oinverse__class_Odivide(U_1744,hAPP(hAPP(c_Power_Opower__class_Opower(U_1744),U_1745),U_1747),hAPP(hAPP(c_Power_Opower__class_Opower(U_1744),U_1746),U_1747))
| ~ class_Fields_Ofield__inverse__zero(U_1744) ),
inference(clausify,[status(thm)],[f_630_3]) ).
fof(f_631_1,plain,
! [V_a,V_r] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_r),V_a),hAPP(hAPP(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_631_2,plain,
! [U_1749,U_1748] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1748),U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1748),U_1748)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1749,U_1748),
inference(variable_rename,[status(thm)],[f_631_1]) ).
fof(f_631_3,plain,
! [U_1749,U_1748] : c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1748),U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1748),U_1748)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1749,U_1748),
inference(definitional_conversion,[status(esa)],[f_631_2]) ).
cnf(f_631_4,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1748),U_1749),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1748),U_1748)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1749,U_1748),
inference(clausify,[status(thm)],[f_631_3]) ).
fof(f_632_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_632_2,plain,
! [U_1751,U_1750] : c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1750,U_1751)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1750),c_NthRoot_Osqrt(U_1751)),
inference(variable_rename,[status(thm)],[f_632_1]) ).
fof(f_632_3,plain,
! [U_1750,U_1751] : c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1750,U_1751)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1750),c_NthRoot_Osqrt(U_1751)),
inference(definitional_conversion,[status(esa)],[f_632_2]) ).
cnf(f_632_4,plain,
c_NthRoot_Osqrt(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1750,U_1751)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_1750),c_NthRoot_Osqrt(U_1751)),
inference(clausify,[status(thm)],[f_632_3]) ).
fof(f_633_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_633_2,plain,
! [U_1754,U_1753,U_1752] :
( c_RealVector_Onorm__class_Onorm(U_1752,c_Rings_Oinverse__class_Odivide(U_1752,U_1754,U_1753)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1752,U_1754),c_RealVector_Onorm__class_Onorm(U_1752,U_1753))
| U_1753 = c_Groups_Ozero__class_Ozero(U_1752)
| ~ class_RealVector_Oreal__normed__field(U_1752) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
fof(f_633_3,plain,
! [U_1752,U_1753,U_1754] :
( c_RealVector_Onorm__class_Onorm(U_1752,c_Rings_Oinverse__class_Odivide(U_1752,U_1754,U_1753)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1752,U_1754),c_RealVector_Onorm__class_Onorm(U_1752,U_1753))
| U_1753 = c_Groups_Ozero__class_Ozero(U_1752)
| ~ class_RealVector_Oreal__normed__field(U_1752) ),
inference(definitional_conversion,[status(esa)],[f_633_2]) ).
cnf(f_633_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1752,c_Rings_Oinverse__class_Odivide(U_1752,U_1754,U_1753)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1752,U_1754),c_RealVector_Onorm__class_Onorm(U_1752,U_1753))
| U_1753 = c_Groups_Ozero__class_Ozero(U_1752)
| ~ class_RealVector_Oreal__normed__field(U_1752) ),
inference(clausify,[status(thm)],[f_633_3]) ).
fof(f_634_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_634_2,plain,
! [U_1757,U_1756,U_1755] :
( c_RealVector_Onorm__class_Onorm(U_1755,c_Rings_Oinverse__class_Odivide(U_1755,U_1756,U_1757)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1755,U_1756),c_RealVector_Onorm__class_Onorm(U_1755,U_1757))
| ~ class_RealVector_Oreal__normed__field(U_1755)
| ~ class_Fields_Ofield__inverse__zero(U_1755) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
fof(f_634_3,plain,
! [U_1755,U_1756,U_1757] :
( c_RealVector_Onorm__class_Onorm(U_1755,c_Rings_Oinverse__class_Odivide(U_1755,U_1756,U_1757)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1755,U_1756),c_RealVector_Onorm__class_Onorm(U_1755,U_1757))
| ~ class_RealVector_Oreal__normed__field(U_1755)
| ~ class_Fields_Ofield__inverse__zero(U_1755) ),
inference(definitional_conversion,[status(esa)],[f_634_2]) ).
cnf(f_634_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1755,c_Rings_Oinverse__class_Odivide(U_1755,U_1756,U_1757)) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1755,U_1756),c_RealVector_Onorm__class_Onorm(U_1755,U_1757))
| ~ class_RealVector_Oreal__normed__field(U_1755)
| ~ class_Fields_Ofield__inverse__zero(U_1755) ),
inference(clausify,[status(thm)],[f_634_3]) ).
fof(f_635_1,plain,
! [V_b,V_a,V_c,T_a] :
( V_a = c_Rings_Oinverse__class_Odivide(T_a,V_b,V_c)
| hAPP(hAPP(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_635_2,plain,
! [U_1761,U_1760,U_1759,U_1758] :
( U_1760 = c_Rings_Oinverse__class_Odivide(U_1758,U_1761,U_1759)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1760),U_1759) != U_1761
| U_1759 = c_Groups_Ozero__class_Ozero(U_1758)
| ~ class_Rings_Odivision__ring(U_1758) ),
inference(variable_rename,[status(thm)],[f_635_1]) ).
fof(f_635_3,plain,
! [U_1758,U_1759,U_1760,U_1761] :
( U_1760 = c_Rings_Oinverse__class_Odivide(U_1758,U_1761,U_1759)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1760),U_1759) != U_1761
| U_1759 = c_Groups_Ozero__class_Ozero(U_1758)
| ~ class_Rings_Odivision__ring(U_1758) ),
inference(definitional_conversion,[status(esa)],[f_635_2]) ).
cnf(f_635_4,plain,
( U_1760 = c_Rings_Oinverse__class_Odivide(U_1758,U_1761,U_1759)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1760),U_1759) != U_1761
| U_1759 = c_Groups_Ozero__class_Ozero(U_1758)
| ~ class_Rings_Odivision__ring(U_1758) ),
inference(clausify,[status(thm)],[f_635_3]) ).
fof(f_636_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 != hAPP(hAPP(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_636_2,plain,
! [U_1765,U_1764,U_1763,U_1762] :
( c_Rings_Oinverse__class_Odivide(U_1762,U_1764,U_1763) = U_1765
| U_1764 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1762),U_1765),U_1763)
| U_1763 = c_Groups_Ozero__class_Ozero(U_1762)
| ~ class_Rings_Odivision__ring(U_1762) ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
fof(f_636_3,plain,
! [U_1762,U_1763,U_1764,U_1765] :
( c_Rings_Oinverse__class_Odivide(U_1762,U_1764,U_1763) = U_1765
| U_1764 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1762),U_1765),U_1763)
| U_1763 = c_Groups_Ozero__class_Ozero(U_1762)
| ~ class_Rings_Odivision__ring(U_1762) ),
inference(definitional_conversion,[status(esa)],[f_636_2]) ).
cnf(f_636_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1762,U_1764,U_1763) = U_1765
| U_1764 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1762),U_1765),U_1763)
| U_1763 = c_Groups_Ozero__class_Ozero(U_1762)
| ~ class_Rings_Odivision__ring(U_1762) ),
inference(clausify,[status(thm)],[f_636_3]) ).
fof(f_637_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 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) )
& ( V_b_2 = hAPP(hAPP(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_637_2,plain,
! [U_1769,U_1768,U_1767,U_1766] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1766,U_1768,U_1767) = U_1769
| U_1768 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1769),U_1767) )
& ( U_1768 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1769),U_1767)
| c_Rings_Oinverse__class_Odivide(U_1766,U_1768,U_1767) != U_1769 ) )
| U_1767 = c_Groups_Ozero__class_Ozero(U_1766)
| ~ class_Rings_Odivision__ring(U_1766) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
( ! [U_1766,U_1767,U_1768,U_1769] :
( c_Rings_Oinverse__class_Odivide(U_1766,U_1768,U_1767) = U_1769
| U_1768 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1769),U_1767)
| ~ sP111(U_1766,U_1767,U_1768,U_1769) )
& ! [U_1766,U_1767,U_1768,U_1769] :
( U_1768 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1769),U_1767)
| c_Rings_Oinverse__class_Odivide(U_1766,U_1768,U_1767) != U_1769
| ~ sP111(U_1766,U_1767,U_1768,U_1769) )
& ! [U_1766,U_1767,U_1768,U_1769] :
( sP111(U_1766,U_1767,U_1768,U_1769)
| U_1767 = c_Groups_Ozero__class_Ozero(U_1766)
| ~ class_Rings_Odivision__ring(U_1766) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111])],[f_637_2]) ).
cnf(f_637_4,plain,
( sP111(U_1766,U_1767,U_1768,U_1769)
| U_1767 = c_Groups_Ozero__class_Ozero(U_1766)
| ~ class_Rings_Odivision__ring(U_1766) ),
inference(clausify,[status(thm)],[f_637_3]) ).
cnf(f_637_5,plain,
( U_1768 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1769),U_1767)
| c_Rings_Oinverse__class_Odivide(U_1766,U_1768,U_1767) != U_1769
| ~ sP111(U_1766,U_1767,U_1768,U_1769) ),
inference(clausify,[status(thm)],[f_637_3]) ).
cnf(f_637_6,plain,
( c_Rings_Oinverse__class_Odivide(U_1766,U_1768,U_1767) = U_1769
| U_1768 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1769),U_1767)
| ~ sP111(U_1766,U_1767,U_1768,U_1769) ),
inference(clausify,[status(thm)],[f_637_3]) ).
fof(f_638_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)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) != V_b_2 )
& ( hAPP(hAPP(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_638_2,plain,
! [U_1773,U_1772,U_1771,U_1770] :
( ( ( U_1772 = c_Rings_Oinverse__class_Odivide(U_1770,U_1773,U_1771)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1771) != U_1773 )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1771) = U_1773
| U_1772 != c_Rings_Oinverse__class_Odivide(U_1770,U_1773,U_1771) ) )
| U_1771 = c_Groups_Ozero__class_Ozero(U_1770)
| ~ class_Rings_Odivision__ring(U_1770) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
fof(f_638_3,plain,
( ! [U_1773,U_1771,U_1770,U_1772] :
( U_1772 = c_Rings_Oinverse__class_Odivide(U_1770,U_1773,U_1771)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1771) != U_1773
| ~ sP112(U_1773,U_1771,U_1770,U_1772) )
& ! [U_1773,U_1771,U_1770,U_1772] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1771) = U_1773
| U_1772 != c_Rings_Oinverse__class_Odivide(U_1770,U_1773,U_1771)
| ~ sP112(U_1773,U_1771,U_1770,U_1772) )
& ! [U_1773,U_1771,U_1770,U_1772] :
( sP112(U_1773,U_1771,U_1770,U_1772)
| U_1771 = c_Groups_Ozero__class_Ozero(U_1770)
| ~ class_Rings_Odivision__ring(U_1770) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_638_2]) ).
cnf(f_638_4,plain,
( sP112(U_1773,U_1771,U_1770,U_1772)
| U_1771 = c_Groups_Ozero__class_Ozero(U_1770)
| ~ class_Rings_Odivision__ring(U_1770) ),
inference(clausify,[status(thm)],[f_638_3]) ).
cnf(f_638_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1771) = U_1773
| U_1772 != c_Rings_Oinverse__class_Odivide(U_1770,U_1773,U_1771)
| ~ sP112(U_1773,U_1771,U_1770,U_1772) ),
inference(clausify,[status(thm)],[f_638_3]) ).
cnf(f_638_6,plain,
( U_1772 = c_Rings_Oinverse__class_Odivide(U_1770,U_1773,U_1771)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1770),U_1772),U_1771) != U_1773
| ~ sP112(U_1773,U_1771,U_1770,U_1772) ),
inference(clausify,[status(thm)],[f_638_3]) ).
fof(f_639_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_639_2,plain,
! [U_1775,U_1774] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1774,U_1775,U_1775) = c_Groups_Oone__class_Oone(U_1774)
| U_1775 = c_Groups_Ozero__class_Ozero(U_1774) )
& ( c_Rings_Oinverse__class_Odivide(U_1774,U_1775,U_1775) = c_Groups_Ozero__class_Ozero(U_1774)
| U_1775 != c_Groups_Ozero__class_Ozero(U_1774) ) )
| ~ class_Rings_Odivision__ring__inverse__zero(U_1774) ),
inference(variable_rename,[status(thm)],[f_639_1]) ).
fof(f_639_3,plain,
( ! [U_1774,U_1775] :
( c_Rings_Oinverse__class_Odivide(U_1774,U_1775,U_1775) = c_Groups_Oone__class_Oone(U_1774)
| U_1775 = c_Groups_Ozero__class_Ozero(U_1774)
| ~ sP113(U_1774,U_1775) )
& ! [U_1774,U_1775] :
( c_Rings_Oinverse__class_Odivide(U_1774,U_1775,U_1775) = c_Groups_Ozero__class_Ozero(U_1774)
| U_1775 != c_Groups_Ozero__class_Ozero(U_1774)
| ~ sP113(U_1774,U_1775) )
& ! [U_1774,U_1775] :
( sP113(U_1774,U_1775)
| ~ class_Rings_Odivision__ring__inverse__zero(U_1774) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113])],[f_639_2]) ).
cnf(f_639_4,plain,
( sP113(U_1774,U_1775)
| ~ class_Rings_Odivision__ring__inverse__zero(U_1774) ),
inference(clausify,[status(thm)],[f_639_3]) ).
cnf(f_639_5,plain,
( c_Rings_Oinverse__class_Odivide(U_1774,U_1775,U_1775) = c_Groups_Ozero__class_Ozero(U_1774)
| U_1775 != c_Groups_Ozero__class_Ozero(U_1774)
| ~ sP113(U_1774,U_1775) ),
inference(clausify,[status(thm)],[f_639_3]) ).
cnf(f_639_6,plain,
( c_Rings_Oinverse__class_Odivide(U_1774,U_1775,U_1775) = c_Groups_Oone__class_Oone(U_1774)
| U_1775 = c_Groups_Ozero__class_Ozero(U_1774)
| ~ sP113(U_1774,U_1775) ),
inference(clausify,[status(thm)],[f_639_3]) ).
fof(f_640_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_640_2,plain,
! [U_1777,U_1776] :
( c_Rings_Oinverse__class_Odivide(U_1776,U_1777,U_1777) = c_Groups_Oone__class_Oone(U_1776)
| U_1777 = c_Groups_Ozero__class_Ozero(U_1776)
| ~ class_Rings_Odivision__ring(U_1776) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
fof(f_640_3,plain,
! [U_1777,U_1776] :
( c_Rings_Oinverse__class_Odivide(U_1776,U_1777,U_1777) = c_Groups_Oone__class_Oone(U_1776)
| U_1777 = c_Groups_Ozero__class_Ozero(U_1776)
| ~ class_Rings_Odivision__ring(U_1776) ),
inference(definitional_conversion,[status(esa)],[f_640_2]) ).
cnf(f_640_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1776,U_1777,U_1777) = c_Groups_Oone__class_Oone(U_1776)
| U_1777 = c_Groups_Ozero__class_Ozero(U_1776)
| ~ class_Rings_Odivision__ring(U_1776) ),
inference(clausify,[status(thm)],[f_640_3]) ).
fof(f_641_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_641_2,plain,
! [U_1780,U_1779,U_1778] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1778,U_1780,U_1779) = c_Groups_Oone__class_Oone(U_1778)
| U_1780 != U_1779 )
& ( U_1780 = U_1779
| c_Rings_Oinverse__class_Odivide(U_1778,U_1780,U_1779) != c_Groups_Oone__class_Oone(U_1778) ) )
| U_1779 = c_Groups_Ozero__class_Ozero(U_1778)
| ~ class_Rings_Odivision__ring(U_1778) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
fof(f_641_3,plain,
( ! [U_1778,U_1779,U_1780] :
( c_Rings_Oinverse__class_Odivide(U_1778,U_1780,U_1779) = c_Groups_Oone__class_Oone(U_1778)
| U_1780 != U_1779
| ~ sP114(U_1778,U_1779,U_1780) )
& ! [U_1778,U_1779,U_1780] :
( U_1780 = U_1779
| c_Rings_Oinverse__class_Odivide(U_1778,U_1780,U_1779) != c_Groups_Oone__class_Oone(U_1778)
| ~ sP114(U_1778,U_1779,U_1780) )
& ! [U_1778,U_1779,U_1780] :
( sP114(U_1778,U_1779,U_1780)
| U_1779 = c_Groups_Ozero__class_Ozero(U_1778)
| ~ class_Rings_Odivision__ring(U_1778) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_641_2]) ).
cnf(f_641_4,plain,
( sP114(U_1778,U_1779,U_1780)
| U_1779 = c_Groups_Ozero__class_Ozero(U_1778)
| ~ class_Rings_Odivision__ring(U_1778) ),
inference(clausify,[status(thm)],[f_641_3]) ).
cnf(f_641_5,plain,
( U_1780 = U_1779
| c_Rings_Oinverse__class_Odivide(U_1778,U_1780,U_1779) != c_Groups_Oone__class_Oone(U_1778)
| ~ sP114(U_1778,U_1779,U_1780) ),
inference(clausify,[status(thm)],[f_641_3]) ).
cnf(f_641_6,plain,
( c_Rings_Oinverse__class_Odivide(U_1778,U_1780,U_1779) = c_Groups_Oone__class_Oone(U_1778)
| U_1780 != U_1779
| ~ sP114(U_1778,U_1779,U_1780) ),
inference(clausify,[status(thm)],[f_641_3]) ).
fof(f_642_1,plain,
! [V_n,V_a,V_b,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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_642_2,plain,
! [U_1784,U_1783,U_1782,U_1781] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1781),c_Rings_Oinverse__class_Odivide(U_1781,U_1783,U_1782)),U_1784) = c_Rings_Oinverse__class_Odivide(U_1781,hAPP(hAPP(c_Power_Opower__class_Opower(U_1781),U_1783),U_1784),hAPP(hAPP(c_Power_Opower__class_Opower(U_1781),U_1782),U_1784))
| U_1782 = c_Groups_Ozero__class_Ozero(U_1781)
| ~ class_Fields_Ofield(U_1781) ),
inference(variable_rename,[status(thm)],[f_642_1]) ).
fof(f_642_3,plain,
! [U_1782,U_1783,U_1784,U_1781] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1781),c_Rings_Oinverse__class_Odivide(U_1781,U_1783,U_1782)),U_1784) = c_Rings_Oinverse__class_Odivide(U_1781,hAPP(hAPP(c_Power_Opower__class_Opower(U_1781),U_1783),U_1784),hAPP(hAPP(c_Power_Opower__class_Opower(U_1781),U_1782),U_1784))
| U_1782 = c_Groups_Ozero__class_Ozero(U_1781)
| ~ class_Fields_Ofield(U_1781) ),
inference(definitional_conversion,[status(esa)],[f_642_2]) ).
cnf(f_642_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1781),c_Rings_Oinverse__class_Odivide(U_1781,U_1783,U_1782)),U_1784) = c_Rings_Oinverse__class_Odivide(U_1781,hAPP(hAPP(c_Power_Opower__class_Opower(U_1781),U_1783),U_1784),hAPP(hAPP(c_Power_Opower__class_Opower(U_1781),U_1782),U_1784))
| U_1782 = c_Groups_Ozero__class_Ozero(U_1781)
| ~ class_Fields_Ofield(U_1781) ),
inference(clausify,[status(thm)],[f_642_3]) ).
fof(f_643_1,plain,
! [V_n,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) = hAPP(hAPP(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_643_2,plain,
! [U_1787,U_1786,U_1785] :
( c_Rings_Oinverse__class_Odivide(U_1785,c_Groups_Oone__class_Oone(U_1785),hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),U_1786),U_1787)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),c_Rings_Oinverse__class_Odivide(U_1785,c_Groups_Oone__class_Oone(U_1785),U_1786)),U_1787)
| ~ class_Fields_Ofield__inverse__zero(U_1785) ),
inference(variable_rename,[status(thm)],[f_643_1]) ).
fof(f_643_3,plain,
! [U_1785,U_1786,U_1787] :
( c_Rings_Oinverse__class_Odivide(U_1785,c_Groups_Oone__class_Oone(U_1785),hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),U_1786),U_1787)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),c_Rings_Oinverse__class_Odivide(U_1785,c_Groups_Oone__class_Oone(U_1785),U_1786)),U_1787)
| ~ class_Fields_Ofield__inverse__zero(U_1785) ),
inference(definitional_conversion,[status(esa)],[f_643_2]) ).
cnf(f_643_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1785,c_Groups_Oone__class_Oone(U_1785),hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),U_1786),U_1787)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1785),c_Rings_Oinverse__class_Odivide(U_1785,c_Groups_Oone__class_Oone(U_1785),U_1786)),U_1787)
| ~ class_Fields_Ofield__inverse__zero(U_1785) ),
inference(clausify,[status(thm)],[f_643_3]) ).
fof(f_644_1,plain,
! [V_ya_2,V_xa_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_xa_2,V_ya_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_ya_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_xa_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_ya_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_xa_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_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_xa_2,V_ya_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__le__divide__iff]) ).
fof(f_644_2,plain,
! [U_1789,U_1788] :
( ( 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_1788,U_1789))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1789,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_1788) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1789)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1788,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1789,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_1788) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1789)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1788,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_1788,U_1789)) ) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
fof(f_644_3,plain,
( ! [U_1793,U_1791] :
( 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_1791,U_1793))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1793,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_1791) )
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1793)
& ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1791,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
& ! [U_1792,U_1790] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1792,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_1790) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1792)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1790,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_1790,U_1792)) ) ),
inference(miniscope,[status(thm)],[f_644_2]) ).
fof(f_644_4,plain,
( ! [U_1791,U_1793] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1793,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP117(U_1791,U_1793) )
& ! [U_1791,U_1793] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1791)
| ~ sP117(U_1791,U_1793) )
& ! [U_1791,U_1793] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1793)
| ~ sP116(U_1791,U_1793) )
& ! [U_1791,U_1793] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1791,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP116(U_1791,U_1793) )
& ! [U_1792,U_1790] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1792,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_1790)
| ~ sP115(U_1792,U_1790) )
& ! [U_1792,U_1790] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1792)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1790,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP115(U_1792,U_1790) )
& ! [U_1791,U_1793] :
( 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_1791,U_1793))
| sP117(U_1791,U_1793)
| sP116(U_1791,U_1793) )
& ! [U_1792,U_1790] :
( sP115(U_1792,U_1790)
| ~ 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_1790,U_1792)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115,sP116,sP117])],[f_644_3]) ).
cnf(f_644_5,plain,
( sP115(U_1792,U_1790)
| ~ 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_1790,U_1792)) ),
inference(clausify,[status(thm)],[f_644_4]) ).
cnf(f_644_6,plain,
( 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_1791,U_1793))
| sP117(U_1791,U_1793)
| sP116(U_1791,U_1793) ),
inference(clausify,[status(thm)],[f_644_4]) ).
cnf(f_644_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1792)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1790,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP115(U_1792,U_1790) ),
inference(clausify,[status(thm)],[f_644_4]) ).
cnf(f_644_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1792,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_1790)
| ~ sP115(U_1792,U_1790) ),
inference(clausify,[status(thm)],[f_644_4]) ).
cnf(f_644_9,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1791,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP116(U_1791,U_1793) ),
inference(clausify,[status(thm)],[f_644_4]) ).
cnf(f_644_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1793)
| ~ sP116(U_1791,U_1793) ),
inference(clausify,[status(thm)],[f_644_4]) ).
cnf(f_644_11,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1791)
| ~ sP117(U_1791,U_1793) ),
inference(clausify,[status(thm)],[f_644_4]) ).
cnf(f_644_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1793,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP117(U_1791,U_1793) ),
inference(clausify,[status(thm)],[f_644_4]) ).
fof(f_645_1,plain,
! [V_a_2,V_w_2,V_b_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_a_2
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
& c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
& c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
| c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) )
| c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) != V_a_2 ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of1]) ).
fof(f_645_2,plain,
! [U_1797,U_1796,U_1795,U_1794] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1794,U_1795,c_Int_Onumber__class_Onumber__of(U_1794,U_1796)) = U_1797
| ( U_1797 != c_Groups_Ozero__class_Ozero(U_1794)
& c_Int_Onumber__class_Onumber__of(U_1794,U_1796) = c_Groups_Ozero__class_Ozero(U_1794) )
| ( U_1795 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1797),c_Int_Onumber__class_Onumber__of(U_1794,U_1796))
& c_Int_Onumber__class_Onumber__of(U_1794,U_1796) != c_Groups_Ozero__class_Ozero(U_1794) ) )
& ( ( ( U_1797 = c_Groups_Ozero__class_Ozero(U_1794)
| c_Int_Onumber__class_Onumber__of(U_1794,U_1796) != c_Groups_Ozero__class_Ozero(U_1794) )
& ( U_1795 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1797),c_Int_Onumber__class_Onumber__of(U_1794,U_1796))
| c_Int_Onumber__class_Onumber__of(U_1794,U_1796) = c_Groups_Ozero__class_Ozero(U_1794) ) )
| c_Rings_Oinverse__class_Odivide(U_1794,U_1795,c_Int_Onumber__class_Onumber__of(U_1794,U_1796)) != U_1797 ) )
| ~ class_Int_Onumber(U_1794)
| ~ class_Fields_Ofield__inverse__zero(U_1794) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
fof(f_645_3,plain,
( ! [U_1794,U_1796,U_1797] :
( U_1797 != c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP120(U_1794,U_1796,U_1797) )
& ! [U_1794,U_1796,U_1797] :
( c_Int_Onumber__class_Onumber__of(U_1794,U_1796) = c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP120(U_1794,U_1796,U_1797) )
& ! [U_1794,U_1795,U_1796,U_1797] :
( U_1795 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1797),c_Int_Onumber__class_Onumber__of(U_1794,U_1796))
| ~ sP119(U_1794,U_1795,U_1796,U_1797) )
& ! [U_1794,U_1795,U_1796,U_1797] :
( c_Int_Onumber__class_Onumber__of(U_1794,U_1796) != c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP119(U_1794,U_1795,U_1796,U_1797) )
& ! [U_1794,U_1795,U_1796,U_1797] :
( U_1797 = c_Groups_Ozero__class_Ozero(U_1794)
| c_Int_Onumber__class_Onumber__of(U_1794,U_1796) != c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP118(U_1794,U_1795,U_1796,U_1797) )
& ! [U_1794,U_1795,U_1796,U_1797] :
( U_1795 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1797),c_Int_Onumber__class_Onumber__of(U_1794,U_1796))
| c_Int_Onumber__class_Onumber__of(U_1794,U_1796) = c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP118(U_1794,U_1795,U_1796,U_1797) )
& ! [U_1794,U_1795,U_1796,U_1797] :
( c_Rings_Oinverse__class_Odivide(U_1794,U_1795,c_Int_Onumber__class_Onumber__of(U_1794,U_1796)) = U_1797
| sP120(U_1794,U_1796,U_1797)
| sP119(U_1794,U_1795,U_1796,U_1797)
| ~ sP121(U_1794,U_1795,U_1796,U_1797) )
& ! [U_1794,U_1795,U_1796,U_1797] :
( sP118(U_1794,U_1795,U_1796,U_1797)
| c_Rings_Oinverse__class_Odivide(U_1794,U_1795,c_Int_Onumber__class_Onumber__of(U_1794,U_1796)) != U_1797
| ~ sP121(U_1794,U_1795,U_1796,U_1797) )
& ! [U_1794,U_1795,U_1796,U_1797] :
( sP121(U_1794,U_1795,U_1796,U_1797)
| ~ class_Int_Onumber(U_1794)
| ~ class_Fields_Ofield__inverse__zero(U_1794) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118,sP119,sP120,sP121])],[f_645_2]) ).
cnf(f_645_4,plain,
( sP121(U_1794,U_1795,U_1796,U_1797)
| ~ class_Int_Onumber(U_1794)
| ~ class_Fields_Ofield__inverse__zero(U_1794) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_5,plain,
( sP118(U_1794,U_1795,U_1796,U_1797)
| c_Rings_Oinverse__class_Odivide(U_1794,U_1795,c_Int_Onumber__class_Onumber__of(U_1794,U_1796)) != U_1797
| ~ sP121(U_1794,U_1795,U_1796,U_1797) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_6,plain,
( c_Rings_Oinverse__class_Odivide(U_1794,U_1795,c_Int_Onumber__class_Onumber__of(U_1794,U_1796)) = U_1797
| sP120(U_1794,U_1796,U_1797)
| sP119(U_1794,U_1795,U_1796,U_1797)
| ~ sP121(U_1794,U_1795,U_1796,U_1797) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_7,plain,
( U_1795 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1797),c_Int_Onumber__class_Onumber__of(U_1794,U_1796))
| c_Int_Onumber__class_Onumber__of(U_1794,U_1796) = c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP118(U_1794,U_1795,U_1796,U_1797) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_8,plain,
( U_1797 = c_Groups_Ozero__class_Ozero(U_1794)
| c_Int_Onumber__class_Onumber__of(U_1794,U_1796) != c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP118(U_1794,U_1795,U_1796,U_1797) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_9,plain,
( c_Int_Onumber__class_Onumber__of(U_1794,U_1796) != c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP119(U_1794,U_1795,U_1796,U_1797) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_10,plain,
( U_1795 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1797),c_Int_Onumber__class_Onumber__of(U_1794,U_1796))
| ~ sP119(U_1794,U_1795,U_1796,U_1797) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_11,plain,
( c_Int_Onumber__class_Onumber__of(U_1794,U_1796) = c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP120(U_1794,U_1796,U_1797) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_12,plain,
( U_1797 != c_Groups_Ozero__class_Ozero(U_1794)
| ~ sP120(U_1794,U_1796,U_1797) ),
inference(clausify,[status(thm)],[f_645_3]) ).
fof(f_646_1,plain,
! [V_w_2,V_c_2,V_b_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) = c_Int_Onumber__class_Onumber__of(T_a,V_w_2)
| ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( V_b_2 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2)
& V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_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) != c_Int_Onumber__class_Onumber__of(T_a,V_w_2) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__eq__eq__number__of]) ).
fof(f_646_2,plain,
! [U_1801,U_1800,U_1799,U_1798] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1798,U_1799,U_1800) = c_Int_Onumber__class_Onumber__of(U_1798,U_1801)
| ( c_Int_Onumber__class_Onumber__of(U_1798,U_1801) != c_Groups_Ozero__class_Ozero(U_1798)
& U_1800 = c_Groups_Ozero__class_Ozero(U_1798) )
| ( U_1799 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),c_Int_Onumber__class_Onumber__of(U_1798,U_1801)),U_1800)
& U_1800 != c_Groups_Ozero__class_Ozero(U_1798) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of(U_1798,U_1801) = c_Groups_Ozero__class_Ozero(U_1798)
| U_1800 != c_Groups_Ozero__class_Ozero(U_1798) )
& ( U_1799 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),c_Int_Onumber__class_Onumber__of(U_1798,U_1801)),U_1800)
| U_1800 = c_Groups_Ozero__class_Ozero(U_1798) ) )
| c_Rings_Oinverse__class_Odivide(U_1798,U_1799,U_1800) != c_Int_Onumber__class_Onumber__of(U_1798,U_1801) ) )
| ~ class_Int_Onumber(U_1798)
| ~ class_Fields_Ofield__inverse__zero(U_1798) ),
inference(variable_rename,[status(thm)],[f_646_1]) ).
fof(f_646_3,plain,
( ! [U_1798,U_1801,U_1800] :
( c_Int_Onumber__class_Onumber__of(U_1798,U_1801) != c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP124(U_1798,U_1801,U_1800) )
& ! [U_1798,U_1801,U_1800] :
( U_1800 = c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP124(U_1798,U_1801,U_1800) )
& ! [U_1798,U_1801,U_1799,U_1800] :
( U_1799 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),c_Int_Onumber__class_Onumber__of(U_1798,U_1801)),U_1800)
| ~ sP123(U_1798,U_1801,U_1799,U_1800) )
& ! [U_1798,U_1801,U_1799,U_1800] :
( U_1800 != c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP123(U_1798,U_1801,U_1799,U_1800) )
& ! [U_1798,U_1801,U_1799,U_1800] :
( c_Int_Onumber__class_Onumber__of(U_1798,U_1801) = c_Groups_Ozero__class_Ozero(U_1798)
| U_1800 != c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP122(U_1798,U_1801,U_1799,U_1800) )
& ! [U_1798,U_1801,U_1799,U_1800] :
( U_1799 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),c_Int_Onumber__class_Onumber__of(U_1798,U_1801)),U_1800)
| U_1800 = c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP122(U_1798,U_1801,U_1799,U_1800) )
& ! [U_1798,U_1801,U_1799,U_1800] :
( c_Rings_Oinverse__class_Odivide(U_1798,U_1799,U_1800) = c_Int_Onumber__class_Onumber__of(U_1798,U_1801)
| sP124(U_1798,U_1801,U_1800)
| sP123(U_1798,U_1801,U_1799,U_1800)
| ~ sP125(U_1798,U_1801,U_1799,U_1800) )
& ! [U_1798,U_1801,U_1799,U_1800] :
( sP122(U_1798,U_1801,U_1799,U_1800)
| c_Rings_Oinverse__class_Odivide(U_1798,U_1799,U_1800) != c_Int_Onumber__class_Onumber__of(U_1798,U_1801)
| ~ sP125(U_1798,U_1801,U_1799,U_1800) )
& ! [U_1798,U_1801,U_1799,U_1800] :
( sP125(U_1798,U_1801,U_1799,U_1800)
| ~ class_Int_Onumber(U_1798)
| ~ class_Fields_Ofield__inverse__zero(U_1798) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122,sP123,sP124,sP125])],[f_646_2]) ).
cnf(f_646_4,plain,
( sP125(U_1798,U_1801,U_1799,U_1800)
| ~ class_Int_Onumber(U_1798)
| ~ class_Fields_Ofield__inverse__zero(U_1798) ),
inference(clausify,[status(thm)],[f_646_3]) ).
cnf(f_646_5,plain,
( sP122(U_1798,U_1801,U_1799,U_1800)
| c_Rings_Oinverse__class_Odivide(U_1798,U_1799,U_1800) != c_Int_Onumber__class_Onumber__of(U_1798,U_1801)
| ~ sP125(U_1798,U_1801,U_1799,U_1800) ),
inference(clausify,[status(thm)],[f_646_3]) ).
cnf(f_646_6,plain,
( c_Rings_Oinverse__class_Odivide(U_1798,U_1799,U_1800) = c_Int_Onumber__class_Onumber__of(U_1798,U_1801)
| sP124(U_1798,U_1801,U_1800)
| sP123(U_1798,U_1801,U_1799,U_1800)
| ~ sP125(U_1798,U_1801,U_1799,U_1800) ),
inference(clausify,[status(thm)],[f_646_3]) ).
cnf(f_646_7,plain,
( U_1799 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),c_Int_Onumber__class_Onumber__of(U_1798,U_1801)),U_1800)
| U_1800 = c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP122(U_1798,U_1801,U_1799,U_1800) ),
inference(clausify,[status(thm)],[f_646_3]) ).
cnf(f_646_8,plain,
( c_Int_Onumber__class_Onumber__of(U_1798,U_1801) = c_Groups_Ozero__class_Ozero(U_1798)
| U_1800 != c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP122(U_1798,U_1801,U_1799,U_1800) ),
inference(clausify,[status(thm)],[f_646_3]) ).
cnf(f_646_9,plain,
( U_1800 != c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP123(U_1798,U_1801,U_1799,U_1800) ),
inference(clausify,[status(thm)],[f_646_3]) ).
cnf(f_646_10,plain,
( U_1799 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1798),c_Int_Onumber__class_Onumber__of(U_1798,U_1801)),U_1800)
| ~ sP123(U_1798,U_1801,U_1799,U_1800) ),
inference(clausify,[status(thm)],[f_646_3]) ).
cnf(f_646_11,plain,
( U_1800 = c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP124(U_1798,U_1801,U_1800) ),
inference(clausify,[status(thm)],[f_646_3]) ).
cnf(f_646_12,plain,
( c_Int_Onumber__class_Onumber__of(U_1798,U_1801) != c_Groups_Ozero__class_Ozero(U_1798)
| ~ sP124(U_1798,U_1801,U_1800) ),
inference(clausify,[status(thm)],[f_646_3]) ).
fof(f_647_1,plain,
! [V_c_2,V_b_2,V_w_2,T_a] :
( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)
| ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a)
& V_c_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2) != V_b_2
& V_c_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_c_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2) = V_b_2
| V_c_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
| c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of]) ).
fof(f_647_2,plain,
! [U_1805,U_1804,U_1803,U_1802] :
( ( ( c_Int_Onumber__class_Onumber__of(U_1802,U_1803) = c_Rings_Oinverse__class_Odivide(U_1802,U_1804,U_1805)
| ( c_Int_Onumber__class_Onumber__of(U_1802,U_1803) != c_Groups_Ozero__class_Ozero(U_1802)
& U_1805 = c_Groups_Ozero__class_Ozero(U_1802) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1802),c_Int_Onumber__class_Onumber__of(U_1802,U_1803)),U_1805) != U_1804
& U_1805 != c_Groups_Ozero__class_Ozero(U_1802) ) )
& ( ( ( c_Int_Onumber__class_Onumber__of(U_1802,U_1803) = c_Groups_Ozero__class_Ozero(U_1802)
| U_1805 != c_Groups_Ozero__class_Ozero(U_1802) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1802),c_Int_Onumber__class_Onumber__of(U_1802,U_1803)),U_1805) = U_1804
| U_1805 = c_Groups_Ozero__class_Ozero(U_1802) ) )
| c_Int_Onumber__class_Onumber__of(U_1802,U_1803) != c_Rings_Oinverse__class_Odivide(U_1802,U_1804,U_1805) ) )
| ~ class_Int_Onumber(U_1802)
| ~ class_Fields_Ofield__inverse__zero(U_1802) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
fof(f_647_3,plain,
( ! [U_1802,U_1805,U_1803] :
( c_Int_Onumber__class_Onumber__of(U_1802,U_1803) != c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP128(U_1802,U_1805,U_1803) )
& ! [U_1802,U_1805,U_1803] :
( U_1805 = c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP128(U_1802,U_1805,U_1803) )
& ! [U_1802,U_1805,U_1804,U_1803] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1802),c_Int_Onumber__class_Onumber__of(U_1802,U_1803)),U_1805) != U_1804
| ~ sP127(U_1802,U_1805,U_1804,U_1803) )
& ! [U_1802,U_1805,U_1804,U_1803] :
( U_1805 != c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP127(U_1802,U_1805,U_1804,U_1803) )
& ! [U_1802,U_1805,U_1804,U_1803] :
( c_Int_Onumber__class_Onumber__of(U_1802,U_1803) = c_Groups_Ozero__class_Ozero(U_1802)
| U_1805 != c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP126(U_1802,U_1805,U_1804,U_1803) )
& ! [U_1802,U_1805,U_1804,U_1803] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1802),c_Int_Onumber__class_Onumber__of(U_1802,U_1803)),U_1805) = U_1804
| U_1805 = c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP126(U_1802,U_1805,U_1804,U_1803) )
& ! [U_1802,U_1805,U_1804,U_1803] :
( c_Int_Onumber__class_Onumber__of(U_1802,U_1803) = c_Rings_Oinverse__class_Odivide(U_1802,U_1804,U_1805)
| sP128(U_1802,U_1805,U_1803)
| sP127(U_1802,U_1805,U_1804,U_1803)
| ~ sP129(U_1802,U_1805,U_1804,U_1803) )
& ! [U_1802,U_1805,U_1804,U_1803] :
( sP126(U_1802,U_1805,U_1804,U_1803)
| c_Int_Onumber__class_Onumber__of(U_1802,U_1803) != c_Rings_Oinverse__class_Odivide(U_1802,U_1804,U_1805)
| ~ sP129(U_1802,U_1805,U_1804,U_1803) )
& ! [U_1802,U_1805,U_1804,U_1803] :
( sP129(U_1802,U_1805,U_1804,U_1803)
| ~ class_Int_Onumber(U_1802)
| ~ class_Fields_Ofield__inverse__zero(U_1802) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126,sP127,sP128,sP129])],[f_647_2]) ).
cnf(f_647_4,plain,
( sP129(U_1802,U_1805,U_1804,U_1803)
| ~ class_Int_Onumber(U_1802)
| ~ class_Fields_Ofield__inverse__zero(U_1802) ),
inference(clausify,[status(thm)],[f_647_3]) ).
cnf(f_647_5,plain,
( sP126(U_1802,U_1805,U_1804,U_1803)
| c_Int_Onumber__class_Onumber__of(U_1802,U_1803) != c_Rings_Oinverse__class_Odivide(U_1802,U_1804,U_1805)
| ~ sP129(U_1802,U_1805,U_1804,U_1803) ),
inference(clausify,[status(thm)],[f_647_3]) ).
cnf(f_647_6,plain,
( c_Int_Onumber__class_Onumber__of(U_1802,U_1803) = c_Rings_Oinverse__class_Odivide(U_1802,U_1804,U_1805)
| sP128(U_1802,U_1805,U_1803)
| sP127(U_1802,U_1805,U_1804,U_1803)
| ~ sP129(U_1802,U_1805,U_1804,U_1803) ),
inference(clausify,[status(thm)],[f_647_3]) ).
cnf(f_647_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1802),c_Int_Onumber__class_Onumber__of(U_1802,U_1803)),U_1805) = U_1804
| U_1805 = c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP126(U_1802,U_1805,U_1804,U_1803) ),
inference(clausify,[status(thm)],[f_647_3]) ).
cnf(f_647_8,plain,
( c_Int_Onumber__class_Onumber__of(U_1802,U_1803) = c_Groups_Ozero__class_Ozero(U_1802)
| U_1805 != c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP126(U_1802,U_1805,U_1804,U_1803) ),
inference(clausify,[status(thm)],[f_647_3]) ).
cnf(f_647_9,plain,
( U_1805 != c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP127(U_1802,U_1805,U_1804,U_1803) ),
inference(clausify,[status(thm)],[f_647_3]) ).
cnf(f_647_10,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1802),c_Int_Onumber__class_Onumber__of(U_1802,U_1803)),U_1805) != U_1804
| ~ sP127(U_1802,U_1805,U_1804,U_1803) ),
inference(clausify,[status(thm)],[f_647_3]) ).
cnf(f_647_11,plain,
( U_1805 = c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP128(U_1802,U_1805,U_1803) ),
inference(clausify,[status(thm)],[f_647_3]) ).
cnf(f_647_12,plain,
( c_Int_Onumber__class_Onumber__of(U_1802,U_1803) != c_Groups_Ozero__class_Ozero(U_1802)
| ~ sP128(U_1802,U_1805,U_1803) ),
inference(clausify,[status(thm)],[f_647_3]) ).
fof(f_648_1,plain,
! [V_w_2,V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
| ( V_a_2 != c_Groups_Ozero__class_Ozero(T_a)
& c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) != V_b_2
& c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Int_Onumber__class_Onumber__of(T_a,V_w_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) = V_b_2
| c_Int_Onumber__class_Onumber__of(T_a,V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) )
| V_a_2 != c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__eq__number__of1]) ).
fof(f_648_2,plain,
! [U_1809,U_1808,U_1807,U_1806] :
( ( ( U_1807 = c_Rings_Oinverse__class_Odivide(U_1806,U_1808,c_Int_Onumber__class_Onumber__of(U_1806,U_1809))
| ( U_1807 != c_Groups_Ozero__class_Ozero(U_1806)
& c_Int_Onumber__class_Onumber__of(U_1806,U_1809) = c_Groups_Ozero__class_Ozero(U_1806) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1806),U_1807),c_Int_Onumber__class_Onumber__of(U_1806,U_1809)) != U_1808
& c_Int_Onumber__class_Onumber__of(U_1806,U_1809) != c_Groups_Ozero__class_Ozero(U_1806) ) )
& ( ( ( U_1807 = c_Groups_Ozero__class_Ozero(U_1806)
| c_Int_Onumber__class_Onumber__of(U_1806,U_1809) != c_Groups_Ozero__class_Ozero(U_1806) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1806),U_1807),c_Int_Onumber__class_Onumber__of(U_1806,U_1809)) = U_1808
| c_Int_Onumber__class_Onumber__of(U_1806,U_1809) = c_Groups_Ozero__class_Ozero(U_1806) ) )
| U_1807 != c_Rings_Oinverse__class_Odivide(U_1806,U_1808,c_Int_Onumber__class_Onumber__of(U_1806,U_1809)) ) )
| ~ class_Int_Onumber(U_1806)
| ~ class_Fields_Ofield__inverse__zero(U_1806) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
fof(f_648_3,plain,
( ! [U_1809,U_1806,U_1807] :
( U_1807 != c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP132(U_1809,U_1806,U_1807) )
& ! [U_1809,U_1806,U_1807] :
( c_Int_Onumber__class_Onumber__of(U_1806,U_1809) = c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP132(U_1809,U_1806,U_1807) )
& ! [U_1809,U_1808,U_1806,U_1807] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1806),U_1807),c_Int_Onumber__class_Onumber__of(U_1806,U_1809)) != U_1808
| ~ sP131(U_1809,U_1808,U_1806,U_1807) )
& ! [U_1809,U_1808,U_1806,U_1807] :
( c_Int_Onumber__class_Onumber__of(U_1806,U_1809) != c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP131(U_1809,U_1808,U_1806,U_1807) )
& ! [U_1809,U_1808,U_1806,U_1807] :
( U_1807 = c_Groups_Ozero__class_Ozero(U_1806)
| c_Int_Onumber__class_Onumber__of(U_1806,U_1809) != c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP130(U_1809,U_1808,U_1806,U_1807) )
& ! [U_1809,U_1808,U_1806,U_1807] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1806),U_1807),c_Int_Onumber__class_Onumber__of(U_1806,U_1809)) = U_1808
| c_Int_Onumber__class_Onumber__of(U_1806,U_1809) = c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP130(U_1809,U_1808,U_1806,U_1807) )
& ! [U_1809,U_1808,U_1806,U_1807] :
( U_1807 = c_Rings_Oinverse__class_Odivide(U_1806,U_1808,c_Int_Onumber__class_Onumber__of(U_1806,U_1809))
| sP132(U_1809,U_1806,U_1807)
| sP131(U_1809,U_1808,U_1806,U_1807)
| ~ sP133(U_1809,U_1808,U_1806,U_1807) )
& ! [U_1809,U_1808,U_1806,U_1807] :
( sP130(U_1809,U_1808,U_1806,U_1807)
| U_1807 != c_Rings_Oinverse__class_Odivide(U_1806,U_1808,c_Int_Onumber__class_Onumber__of(U_1806,U_1809))
| ~ sP133(U_1809,U_1808,U_1806,U_1807) )
& ! [U_1809,U_1808,U_1806,U_1807] :
( sP133(U_1809,U_1808,U_1806,U_1807)
| ~ class_Int_Onumber(U_1806)
| ~ class_Fields_Ofield__inverse__zero(U_1806) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130,sP131,sP132,sP133])],[f_648_2]) ).
cnf(f_648_4,plain,
( sP133(U_1809,U_1808,U_1806,U_1807)
| ~ class_Int_Onumber(U_1806)
| ~ class_Fields_Ofield__inverse__zero(U_1806) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_5,plain,
( sP130(U_1809,U_1808,U_1806,U_1807)
| U_1807 != c_Rings_Oinverse__class_Odivide(U_1806,U_1808,c_Int_Onumber__class_Onumber__of(U_1806,U_1809))
| ~ sP133(U_1809,U_1808,U_1806,U_1807) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_6,plain,
( U_1807 = c_Rings_Oinverse__class_Odivide(U_1806,U_1808,c_Int_Onumber__class_Onumber__of(U_1806,U_1809))
| sP132(U_1809,U_1806,U_1807)
| sP131(U_1809,U_1808,U_1806,U_1807)
| ~ sP133(U_1809,U_1808,U_1806,U_1807) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1806),U_1807),c_Int_Onumber__class_Onumber__of(U_1806,U_1809)) = U_1808
| c_Int_Onumber__class_Onumber__of(U_1806,U_1809) = c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP130(U_1809,U_1808,U_1806,U_1807) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_8,plain,
( U_1807 = c_Groups_Ozero__class_Ozero(U_1806)
| c_Int_Onumber__class_Onumber__of(U_1806,U_1809) != c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP130(U_1809,U_1808,U_1806,U_1807) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_9,plain,
( c_Int_Onumber__class_Onumber__of(U_1806,U_1809) != c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP131(U_1809,U_1808,U_1806,U_1807) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_10,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1806),U_1807),c_Int_Onumber__class_Onumber__of(U_1806,U_1809)) != U_1808
| ~ sP131(U_1809,U_1808,U_1806,U_1807) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_11,plain,
( c_Int_Onumber__class_Onumber__of(U_1806,U_1809) = c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP132(U_1809,U_1806,U_1807) ),
inference(clausify,[status(thm)],[f_648_3]) ).
cnf(f_648_12,plain,
( U_1807 != c_Groups_Ozero__class_Ozero(U_1806)
| ~ sP132(U_1809,U_1806,U_1807) ),
inference(clausify,[status(thm)],[f_648_3]) ).
fof(f_649_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_649_2,plain,
! [U_1811,U_1810] :
( c_Rings_Oinverse__class_Odivide(U_1810,U_1811,c_Int_Onumber__class_Onumber__of(U_1810,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_1810)
| ~ class_Int_Onumber__ring(U_1810)
| ~ class_Fields_Ofield__inverse__zero(U_1810) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
fof(f_649_3,plain,
! [U_1811,U_1810] :
( c_Rings_Oinverse__class_Odivide(U_1810,U_1811,c_Int_Onumber__class_Onumber__of(U_1810,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_1810)
| ~ class_Int_Onumber__ring(U_1810)
| ~ class_Fields_Ofield__inverse__zero(U_1810) ),
inference(definitional_conversion,[status(esa)],[f_649_2]) ).
cnf(f_649_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1810,U_1811,c_Int_Onumber__class_Onumber__of(U_1810,c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_1810)
| ~ class_Int_Onumber__ring(U_1810)
| ~ class_Fields_Ofield__inverse__zero(U_1810) ),
inference(clausify,[status(thm)],[f_649_3]) ).
fof(f_650_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_650_2,plain,
! [U_1813,U_1812] :
( c_Rings_Oinverse__class_Odivide(U_1812,U_1813,c_Int_Onumber__class_Onumber__of(U_1812,c_Int_OBit1(c_Int_OPls))) = U_1813
| ~ class_Int_Onumber__ring(U_1812)
| ~ class_Fields_Ofield(U_1812) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
fof(f_650_3,plain,
! [U_1813,U_1812] :
( c_Rings_Oinverse__class_Odivide(U_1812,U_1813,c_Int_Onumber__class_Onumber__of(U_1812,c_Int_OBit1(c_Int_OPls))) = U_1813
| ~ class_Int_Onumber__ring(U_1812)
| ~ class_Fields_Ofield(U_1812) ),
inference(definitional_conversion,[status(esa)],[f_650_2]) ).
cnf(f_650_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1812,U_1813,c_Int_Onumber__class_Onumber__of(U_1812,c_Int_OBit1(c_Int_OPls))) = U_1813
| ~ class_Int_Onumber__ring(U_1812)
| ~ class_Fields_Ofield(U_1812) ),
inference(clausify,[status(thm)],[f_650_3]) ).
fof(f_651_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_651_2,plain,
! [U_1815,U_1814] :
( c_Rings_Oinverse__class_Odivide(U_1814,U_1815,c_Int_Onumber__class_Onumber__of(U_1814,c_Int_OBit1(c_Int_OPls))) = U_1815
| ~ class_Int_Onumber__ring(U_1814)
| ~ class_Fields_Ofield(U_1814) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
fof(f_651_3,plain,
! [U_1814,U_1815] :
( c_Rings_Oinverse__class_Odivide(U_1814,U_1815,c_Int_Onumber__class_Onumber__of(U_1814,c_Int_OBit1(c_Int_OPls))) = U_1815
| ~ class_Int_Onumber__ring(U_1814)
| ~ class_Fields_Ofield(U_1814) ),
inference(definitional_conversion,[status(esa)],[f_651_2]) ).
cnf(f_651_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1814,U_1815,c_Int_Onumber__class_Onumber__of(U_1814,c_Int_OBit1(c_Int_OPls))) = U_1815
| ~ class_Int_Onumber__ring(U_1814)
| ~ class_Fields_Ofield(U_1814) ),
inference(clausify,[status(thm)],[f_651_3]) ).
fof(f_652_1,plain,
! [V_m,V_n,V_a,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(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_652_2,plain,
! [U_1819,U_1818,U_1817,U_1816] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1816),U_1817),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1819,U_1818)) = c_Rings_Oinverse__class_Odivide(U_1816,hAPP(hAPP(c_Power_Opower__class_Opower(U_1816),U_1817),U_1819),hAPP(hAPP(c_Power_Opower__class_Opower(U_1816),U_1817),U_1818))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1818,U_1819)
| U_1817 = c_Groups_Ozero__class_Ozero(U_1816)
| ~ class_Fields_Ofield(U_1816) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
fof(f_652_3,plain,
! [U_1816,U_1817,U_1819,U_1818] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1816),U_1817),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1819,U_1818)) = c_Rings_Oinverse__class_Odivide(U_1816,hAPP(hAPP(c_Power_Opower__class_Opower(U_1816),U_1817),U_1819),hAPP(hAPP(c_Power_Opower__class_Opower(U_1816),U_1817),U_1818))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1818,U_1819)
| U_1817 = c_Groups_Ozero__class_Ozero(U_1816)
| ~ class_Fields_Ofield(U_1816) ),
inference(definitional_conversion,[status(esa)],[f_652_2]) ).
cnf(f_652_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1816),U_1817),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_1819,U_1818)) = c_Rings_Oinverse__class_Odivide(U_1816,hAPP(hAPP(c_Power_Opower__class_Opower(U_1816),U_1817),U_1819),hAPP(hAPP(c_Power_Opower__class_Opower(U_1816),U_1817),U_1818))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1818,U_1819)
| U_1817 = c_Groups_Ozero__class_Ozero(U_1816)
| ~ class_Fields_Ofield(U_1816) ),
inference(clausify,[status(thm)],[f_652_3]) ).
fof(f_653_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_653_2,plain,
! [U_1821,U_1820] : 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_1820,U_1821),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1821) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1820,U_1821),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[f_653_1]) ).
fof(f_653_3,plain,
! [U_1821,U_1820] : 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_1820,U_1821),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1821) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1820,U_1821),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(definitional_conversion,[status(esa)],[f_653_2]) ).
cnf(f_653_4,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_1820,U_1821),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1821) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1820,U_1821),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_653_3]) ).
fof(f_654_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_654_2,plain,
! [U_1823,U_1822] : 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_1822,U_1823),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1822) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1823,U_1822),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(variable_rename,[status(thm)],[f_654_1]) ).
fof(f_654_3,plain,
! [U_1822,U_1823] : 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_1822,U_1823),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1822) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1823,U_1822),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(definitional_conversion,[status(esa)],[f_654_2]) ).
cnf(f_654_4,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_1822,U_1823),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1822) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1823,U_1822),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
inference(clausify,[status(thm)],[f_654_3]) ).
fof(f_655_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_655_2,plain,
! [U_1824] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1824,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_1824,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = U_1824,
inference(variable_rename,[status(thm)],[f_655_1]) ).
fof(f_655_3,plain,
! [U_1824] : c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1824,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_1824,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = U_1824,
inference(definitional_conversion,[status(esa)],[f_655_2]) ).
cnf(f_655_4,plain,
c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1824,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_1824,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = U_1824,
inference(clausify,[status(thm)],[f_655_3]) ).
fof(f_656_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_656_2,plain,
! [U_1829,U_1828,U_1827,U_1826,U_1825] :
( c_Groups_Ominus__class_Ominus(U_1825,c_Groups_Oplus__class_Oplus(U_1825,U_1826,U_1827),c_Groups_Oplus__class_Oplus(U_1825,U_1828,U_1829)) = c_Groups_Oplus__class_Oplus(U_1825,c_Groups_Ominus__class_Ominus(U_1825,U_1826,U_1828),c_Groups_Ominus__class_Ominus(U_1825,U_1827,U_1829))
| ~ class_Groups_Oab__group__add(U_1825) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
fof(f_656_3,plain,
! [U_1825,U_1826,U_1827,U_1828,U_1829] :
( c_Groups_Ominus__class_Ominus(U_1825,c_Groups_Oplus__class_Oplus(U_1825,U_1826,U_1827),c_Groups_Oplus__class_Oplus(U_1825,U_1828,U_1829)) = c_Groups_Oplus__class_Oplus(U_1825,c_Groups_Ominus__class_Ominus(U_1825,U_1826,U_1828),c_Groups_Ominus__class_Ominus(U_1825,U_1827,U_1829))
| ~ class_Groups_Oab__group__add(U_1825) ),
inference(definitional_conversion,[status(esa)],[f_656_2]) ).
cnf(f_656_4,plain,
( c_Groups_Ominus__class_Ominus(U_1825,c_Groups_Oplus__class_Oplus(U_1825,U_1826,U_1827),c_Groups_Oplus__class_Oplus(U_1825,U_1828,U_1829)) = c_Groups_Oplus__class_Oplus(U_1825,c_Groups_Ominus__class_Ominus(U_1825,U_1826,U_1828),c_Groups_Ominus__class_Ominus(U_1825,U_1827,U_1829))
| ~ class_Groups_Oab__group__add(U_1825) ),
inference(clausify,[status(thm)],[f_656_3]) ).
fof(f_657_1,plain,
! [V_b_2,V_a_2,V_f_2] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(V_f_2,V_a_2),hAPP(hAPP(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_f_2,V_b_2),hAPP(V_f_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_f_2,V_b_2),hAPP(hAPP(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_f_2,V_b_2),hAPP(V_f_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_657_2,plain,
! [U_1832,U_1831,U_1830] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_1830,U_1831),hAPP(hAPP(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_1830,U_1832),hAPP(U_1830,U_1831)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1832,U_1831))),U_1831)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_1830,U_1832),hAPP(hAPP(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_1830,U_1832),hAPP(U_1830,U_1831)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1832,U_1831))),U_1832)),
inference(variable_rename,[status(thm)],[f_657_1]) ).
fof(f_657_3,plain,
! [U_1830,U_1831,U_1832] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_1830,U_1831),hAPP(hAPP(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_1830,U_1832),hAPP(U_1830,U_1831)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1832,U_1831))),U_1831)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_1830,U_1832),hAPP(hAPP(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_1830,U_1832),hAPP(U_1830,U_1831)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1832,U_1831))),U_1832)),
inference(definitional_conversion,[status(esa)],[f_657_2]) ).
cnf(f_657_4,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_1830,U_1831),hAPP(hAPP(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_1830,U_1832),hAPP(U_1830,U_1831)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1832,U_1831))),U_1831)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(U_1830,U_1832),hAPP(hAPP(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_1830,U_1832),hAPP(U_1830,U_1831)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_1832,U_1831))),U_1832)),
inference(clausify,[status(thm)],[f_657_3]) ).
fof(f_658_1,plain,
! [V_h,V_d,V_c,V_b,V_a,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d)),V_h) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_b,V_d),V_h)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_c),V_h)),V_d))
| ~ class_RealVector_Oreal__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_DERIV__mult__lemma]) ).
fof(f_658_2,plain,
! [U_1838,U_1837,U_1836,U_1835,U_1834,U_1833] :
( c_Rings_Oinverse__class_Odivide(U_1833,c_Groups_Ominus__class_Ominus(U_1833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),U_1835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1836),U_1837)),U_1838) = c_Groups_Oplus__class_Oplus(U_1833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),c_Rings_Oinverse__class_Odivide(U_1833,c_Groups_Ominus__class_Ominus(U_1833,U_1835,U_1837),U_1838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),c_Rings_Oinverse__class_Odivide(U_1833,c_Groups_Ominus__class_Ominus(U_1833,U_1834,U_1836),U_1838)),U_1837))
| ~ class_RealVector_Oreal__field(U_1833) ),
inference(variable_rename,[status(thm)],[f_658_1]) ).
fof(f_658_3,plain,
! [U_1833,U_1834,U_1835,U_1836,U_1837,U_1838] :
( c_Rings_Oinverse__class_Odivide(U_1833,c_Groups_Ominus__class_Ominus(U_1833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),U_1835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1836),U_1837)),U_1838) = c_Groups_Oplus__class_Oplus(U_1833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),c_Rings_Oinverse__class_Odivide(U_1833,c_Groups_Ominus__class_Ominus(U_1833,U_1835,U_1837),U_1838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),c_Rings_Oinverse__class_Odivide(U_1833,c_Groups_Ominus__class_Ominus(U_1833,U_1834,U_1836),U_1838)),U_1837))
| ~ class_RealVector_Oreal__field(U_1833) ),
inference(definitional_conversion,[status(esa)],[f_658_2]) ).
cnf(f_658_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1833,c_Groups_Ominus__class_Ominus(U_1833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),U_1835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1836),U_1837)),U_1838) = c_Groups_Oplus__class_Oplus(U_1833,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),U_1834),c_Rings_Oinverse__class_Odivide(U_1833,c_Groups_Ominus__class_Ominus(U_1833,U_1835,U_1837),U_1838)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1833),c_Rings_Oinverse__class_Odivide(U_1833,c_Groups_Ominus__class_Ominus(U_1833,U_1834,U_1836),U_1838)),U_1837))
| ~ class_RealVector_Oreal__field(U_1833) ),
inference(clausify,[status(thm)],[f_658_3]) ).
fof(f_659_1,plain,
! [V_za_2,V_ya_2,V_xa_2] :
( ( V_xa_2 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_ya_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_xa_2) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_ya_2,V_za_2) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_xa_2) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_ya_2,V_za_2)
| V_xa_2 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_ya_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_za_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_eq__divide__2__times__iff]) ).
fof(f_659_2,plain,
! [U_1841,U_1840,U_1839] :
( ( U_1839 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1840,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1841))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1839) != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1840,U_1841) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1839) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1840,U_1841)
| U_1839 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1840,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1841)) ) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
( ! [U_1847,U_1845,U_1843] :
( U_1843 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1845,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1847))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),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,U_1845,U_1847) )
& ! [U_1846,U_1844,U_1842] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1842) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1844,U_1846)
| U_1842 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1844,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1846)) ) ),
inference(miniscope,[status(thm)],[f_659_2]) ).
fof(f_659_4,plain,
( ! [U_1845,U_1843,U_1847] :
( U_1843 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1845,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1847))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),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,U_1845,U_1847) )
& ! [U_1842,U_1844,U_1846] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1842) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1844,U_1846)
| U_1842 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1844,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1846)) ) ),
inference(definitional_conversion,[status(esa)],[f_659_3]) ).
cnf(f_659_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1842) = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1844,U_1846)
| U_1842 != c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1844,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1846)) ),
inference(clausify,[status(thm)],[f_659_4]) ).
cnf(f_659_6,plain,
( U_1843 = c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1845,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_1847))
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),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,U_1845,U_1847) ),
inference(clausify,[status(thm)],[f_659_4]) ).
fof(f_660_1,plain,
! [V_y,V_x,V_z,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__divide__eq__iff]) ).
fof(f_660_2,plain,
! [U_1851,U_1850,U_1849,U_1848] :
( c_Groups_Ominus__class_Ominus(U_1848,U_1850,c_Rings_Oinverse__class_Odivide(U_1848,U_1851,U_1849)) = c_Rings_Oinverse__class_Odivide(U_1848,c_Groups_Ominus__class_Ominus(U_1848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),U_1850),U_1851),U_1849)
| U_1849 = c_Groups_Ozero__class_Ozero(U_1848)
| ~ class_Fields_Ofield(U_1848) ),
inference(variable_rename,[status(thm)],[f_660_1]) ).
fof(f_660_3,plain,
! [U_1849,U_1850,U_1848,U_1851] :
( c_Groups_Ominus__class_Ominus(U_1848,U_1850,c_Rings_Oinverse__class_Odivide(U_1848,U_1851,U_1849)) = c_Rings_Oinverse__class_Odivide(U_1848,c_Groups_Ominus__class_Ominus(U_1848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),U_1850),U_1851),U_1849)
| U_1849 = c_Groups_Ozero__class_Ozero(U_1848)
| ~ class_Fields_Ofield(U_1848) ),
inference(definitional_conversion,[status(esa)],[f_660_2]) ).
cnf(f_660_4,plain,
( c_Groups_Ominus__class_Ominus(U_1848,U_1850,c_Rings_Oinverse__class_Odivide(U_1848,U_1851,U_1849)) = c_Rings_Oinverse__class_Odivide(U_1848,c_Groups_Ominus__class_Ominus(U_1848,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1848),U_1849),U_1850),U_1851),U_1849)
| U_1849 = c_Groups_Ozero__class_Ozero(U_1848)
| ~ class_Fields_Ofield(U_1848) ),
inference(clausify,[status(thm)],[f_660_3]) ).
fof(f_661_1,plain,
! [V_y,V_x,V_z,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__diff__eq__iff]) ).
fof(f_661_2,plain,
! [U_1855,U_1854,U_1853,U_1852] :
( c_Groups_Ominus__class_Ominus(U_1852,c_Rings_Oinverse__class_Odivide(U_1852,U_1854,U_1853),U_1855) = c_Rings_Oinverse__class_Odivide(U_1852,c_Groups_Ominus__class_Ominus(U_1852,U_1854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1852),U_1853),U_1855)),U_1853)
| U_1853 = c_Groups_Ozero__class_Ozero(U_1852)
| ~ class_Fields_Ofield(U_1852) ),
inference(variable_rename,[status(thm)],[f_661_1]) ).
fof(f_661_3,plain,
! [U_1852,U_1853,U_1854,U_1855] :
( c_Groups_Ominus__class_Ominus(U_1852,c_Rings_Oinverse__class_Odivide(U_1852,U_1854,U_1853),U_1855) = c_Rings_Oinverse__class_Odivide(U_1852,c_Groups_Ominus__class_Ominus(U_1852,U_1854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1852),U_1853),U_1855)),U_1853)
| U_1853 = c_Groups_Ozero__class_Ozero(U_1852)
| ~ class_Fields_Ofield(U_1852) ),
inference(definitional_conversion,[status(esa)],[f_661_2]) ).
cnf(f_661_4,plain,
( c_Groups_Ominus__class_Ominus(U_1852,c_Rings_Oinverse__class_Odivide(U_1852,U_1854,U_1853),U_1855) = c_Rings_Oinverse__class_Odivide(U_1852,c_Groups_Ominus__class_Ominus(U_1852,U_1854,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1852),U_1853),U_1855)),U_1853)
| U_1853 = c_Groups_Ozero__class_Ozero(U_1852)
| ~ class_Fields_Ofield(U_1852) ),
inference(clausify,[status(thm)],[f_661_3]) ).
fof(f_662_1,plain,
! [V_w,V_x,V_z,V_y,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Ominus__class_Ominus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__frac__eq]) ).
fof(f_662_2,plain,
! [U_1860,U_1859,U_1858,U_1857,U_1856] :
( c_Groups_Ominus__class_Ominus(U_1856,c_Rings_Oinverse__class_Odivide(U_1856,U_1859,U_1857),c_Rings_Oinverse__class_Odivide(U_1856,U_1860,U_1858)) = c_Rings_Oinverse__class_Odivide(U_1856,c_Groups_Ominus__class_Ominus(U_1856,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1859),U_1858),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1860),U_1857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1857),U_1858))
| U_1858 = c_Groups_Ozero__class_Ozero(U_1856)
| U_1857 = c_Groups_Ozero__class_Ozero(U_1856)
| ~ class_Fields_Ofield(U_1856) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
fof(f_662_3,plain,
! [U_1856,U_1857,U_1858,U_1859,U_1860] :
( c_Groups_Ominus__class_Ominus(U_1856,c_Rings_Oinverse__class_Odivide(U_1856,U_1859,U_1857),c_Rings_Oinverse__class_Odivide(U_1856,U_1860,U_1858)) = c_Rings_Oinverse__class_Odivide(U_1856,c_Groups_Ominus__class_Ominus(U_1856,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1859),U_1858),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1860),U_1857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1857),U_1858))
| U_1858 = c_Groups_Ozero__class_Ozero(U_1856)
| U_1857 = c_Groups_Ozero__class_Ozero(U_1856)
| ~ class_Fields_Ofield(U_1856) ),
inference(definitional_conversion,[status(esa)],[f_662_2]) ).
cnf(f_662_4,plain,
( c_Groups_Ominus__class_Ominus(U_1856,c_Rings_Oinverse__class_Odivide(U_1856,U_1859,U_1857),c_Rings_Oinverse__class_Odivide(U_1856,U_1860,U_1858)) = c_Rings_Oinverse__class_Odivide(U_1856,c_Groups_Ominus__class_Ominus(U_1856,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1859),U_1858),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1860),U_1857)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1856),U_1857),U_1858))
| U_1858 = c_Groups_Ozero__class_Ozero(U_1856)
| U_1857 = c_Groups_Ozero__class_Ozero(U_1856)
| ~ class_Fields_Ofield(U_1856) ),
inference(clausify,[status(thm)],[f_662_3]) ).
fof(f_663_1,plain,
! [V_w,V_z,V_y,V_x,T_a] :
( hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(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_663_2,plain,
! [U_1865,U_1864,U_1863,U_1862,U_1861] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1861),c_Rings_Oinverse__class_Odivide(U_1861,U_1862,U_1863)),c_Rings_Oinverse__class_Odivide(U_1861,U_1864,U_1865)) = c_Rings_Oinverse__class_Odivide(U_1861,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1861),U_1862),U_1864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1861),U_1863),U_1865))
| ~ class_Fields_Ofield__inverse__zero(U_1861) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
! [U_1861,U_1862,U_1863,U_1864,U_1865] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1861),c_Rings_Oinverse__class_Odivide(U_1861,U_1862,U_1863)),c_Rings_Oinverse__class_Odivide(U_1861,U_1864,U_1865)) = c_Rings_Oinverse__class_Odivide(U_1861,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1861),U_1862),U_1864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1861),U_1863),U_1865))
| ~ class_Fields_Ofield__inverse__zero(U_1861) ),
inference(definitional_conversion,[status(esa)],[f_663_2]) ).
cnf(f_663_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1861),c_Rings_Oinverse__class_Odivide(U_1861,U_1862,U_1863)),c_Rings_Oinverse__class_Odivide(U_1861,U_1864,U_1865)) = c_Rings_Oinverse__class_Odivide(U_1861,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1861),U_1862),U_1864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1861),U_1863),U_1865))
| ~ class_Fields_Ofield__inverse__zero(U_1861) ),
inference(clausify,[status(thm)],[f_663_3]) ).
fof(f_664_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_664_2,plain,
! [U_1868,U_1867,U_1866] :
( c_Groups_Oabs__class_Oabs(U_1866,c_Rings_Oinverse__class_Odivide(U_1866,U_1867,U_1868)) = c_Rings_Oinverse__class_Odivide(U_1866,c_Groups_Oabs__class_Oabs(U_1866,U_1867),c_Groups_Oabs__class_Oabs(U_1866,U_1868))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1866) ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
! [U_1866,U_1867,U_1868] :
( c_Groups_Oabs__class_Oabs(U_1866,c_Rings_Oinverse__class_Odivide(U_1866,U_1867,U_1868)) = c_Rings_Oinverse__class_Odivide(U_1866,c_Groups_Oabs__class_Oabs(U_1866,U_1867),c_Groups_Oabs__class_Oabs(U_1866,U_1868))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1866) ),
inference(definitional_conversion,[status(esa)],[f_664_2]) ).
cnf(f_664_4,plain,
( c_Groups_Oabs__class_Oabs(U_1866,c_Rings_Oinverse__class_Odivide(U_1866,U_1867,U_1868)) = c_Rings_Oinverse__class_Odivide(U_1866,c_Groups_Oabs__class_Oabs(U_1866,U_1867),c_Groups_Oabs__class_Oabs(U_1866,U_1868))
| ~ class_Fields_Olinordered__field__inverse__zero(U_1866) ),
inference(clausify,[status(thm)],[f_664_3]) ).
fof(f_665_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_665_2,plain,
! [U_1871,U_1870,U_1869] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),c_Rings_Oinverse__class_Odivide(U_1869,U_1870,U_1871))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1869,U_1871,c_Groups_Ozero__class_Ozero(U_1869))
| ~ c_Orderings_Oord__class_Oless__eq(U_1869,U_1870,c_Groups_Ozero__class_Ozero(U_1869)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1871)
| ~ c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1870) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_1869,U_1871,c_Groups_Ozero__class_Ozero(U_1869))
& c_Orderings_Oord__class_Oless__eq(U_1869,U_1870,c_Groups_Ozero__class_Ozero(U_1869)) )
| ( c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1871)
& c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1870) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),c_Rings_Oinverse__class_Odivide(U_1869,U_1870,U_1871)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1869) ),
inference(variable_rename,[status(thm)],[f_665_1]) ).
fof(f_665_3,plain,
( ! [U_1871,U_1870,U_1869] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1869,U_1871,c_Groups_Ozero__class_Ozero(U_1869))
| ~ c_Orderings_Oord__class_Oless__eq(U_1869,U_1870,c_Groups_Ozero__class_Ozero(U_1869))
| ~ sP136(U_1871,U_1870,U_1869) )
& ! [U_1871,U_1870,U_1869] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1871)
| ~ c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1870)
| ~ sP136(U_1871,U_1870,U_1869) )
& ! [U_1871,U_1870,U_1869] :
( c_Orderings_Oord__class_Oless__eq(U_1869,U_1871,c_Groups_Ozero__class_Ozero(U_1869))
| ~ sP135(U_1871,U_1870,U_1869) )
& ! [U_1871,U_1870,U_1869] :
( c_Orderings_Oord__class_Oless__eq(U_1869,U_1870,c_Groups_Ozero__class_Ozero(U_1869))
| ~ sP135(U_1871,U_1870,U_1869) )
& ! [U_1871,U_1870,U_1869] :
( c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1871)
| ~ sP134(U_1871,U_1870,U_1869) )
& ! [U_1871,U_1870,U_1869] :
( c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1870)
| ~ sP134(U_1871,U_1870,U_1869) )
& ! [U_1871,U_1870,U_1869] :
( c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),c_Rings_Oinverse__class_Odivide(U_1869,U_1870,U_1871))
| sP136(U_1871,U_1870,U_1869)
| ~ sP137(U_1871,U_1870,U_1869) )
& ! [U_1871,U_1870,U_1869] :
( sP135(U_1871,U_1870,U_1869)
| sP134(U_1871,U_1870,U_1869)
| ~ c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),c_Rings_Oinverse__class_Odivide(U_1869,U_1870,U_1871))
| ~ sP137(U_1871,U_1870,U_1869) )
& ! [U_1871,U_1870,U_1869] :
( sP137(U_1871,U_1870,U_1869)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1869) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134,sP135,sP136,sP137])],[f_665_2]) ).
cnf(f_665_4,plain,
( sP137(U_1871,U_1870,U_1869)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1869) ),
inference(clausify,[status(thm)],[f_665_3]) ).
cnf(f_665_5,plain,
( sP135(U_1871,U_1870,U_1869)
| sP134(U_1871,U_1870,U_1869)
| ~ c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),c_Rings_Oinverse__class_Odivide(U_1869,U_1870,U_1871))
| ~ sP137(U_1871,U_1870,U_1869) ),
inference(clausify,[status(thm)],[f_665_3]) ).
cnf(f_665_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),c_Rings_Oinverse__class_Odivide(U_1869,U_1870,U_1871))
| sP136(U_1871,U_1870,U_1869)
| ~ sP137(U_1871,U_1870,U_1869) ),
inference(clausify,[status(thm)],[f_665_3]) ).
cnf(f_665_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1870)
| ~ sP134(U_1871,U_1870,U_1869) ),
inference(clausify,[status(thm)],[f_665_3]) ).
cnf(f_665_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1871)
| ~ sP134(U_1871,U_1870,U_1869) ),
inference(clausify,[status(thm)],[f_665_3]) ).
cnf(f_665_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_1869,U_1870,c_Groups_Ozero__class_Ozero(U_1869))
| ~ sP135(U_1871,U_1870,U_1869) ),
inference(clausify,[status(thm)],[f_665_3]) ).
cnf(f_665_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_1869,U_1871,c_Groups_Ozero__class_Ozero(U_1869))
| ~ sP135(U_1871,U_1870,U_1869) ),
inference(clausify,[status(thm)],[f_665_3]) ).
cnf(f_665_11,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1871)
| ~ c_Orderings_Oord__class_Oless__eq(U_1869,c_Groups_Ozero__class_Ozero(U_1869),U_1870)
| ~ sP136(U_1871,U_1870,U_1869) ),
inference(clausify,[status(thm)],[f_665_3]) ).
cnf(f_665_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1869,U_1871,c_Groups_Ozero__class_Ozero(U_1869))
| ~ c_Orderings_Oord__class_Oless__eq(U_1869,U_1870,c_Groups_Ozero__class_Ozero(U_1869))
| ~ sP136(U_1871,U_1870,U_1869) ),
inference(clausify,[status(thm)],[f_665_3]) ).
fof(f_666_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_666_2,plain,
! [U_1874,U_1873,U_1872] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1872,c_Rings_Oinverse__class_Odivide(U_1872,U_1873,U_1874),c_Groups_Ozero__class_Ozero(U_1872))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1874)
| ~ c_Orderings_Oord__class_Oless__eq(U_1872,U_1873,c_Groups_Ozero__class_Ozero(U_1872)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_1872,U_1874,c_Groups_Ozero__class_Ozero(U_1872))
| ~ c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1873) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1874)
& c_Orderings_Oord__class_Oless__eq(U_1872,U_1873,c_Groups_Ozero__class_Ozero(U_1872)) )
| ( c_Orderings_Oord__class_Oless__eq(U_1872,U_1874,c_Groups_Ozero__class_Ozero(U_1872))
& c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1873) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1872,c_Rings_Oinverse__class_Odivide(U_1872,U_1873,U_1874),c_Groups_Ozero__class_Ozero(U_1872)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_1872) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
( ! [U_1873,U_1874,U_1872] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1874)
| ~ c_Orderings_Oord__class_Oless__eq(U_1872,U_1873,c_Groups_Ozero__class_Ozero(U_1872))
| ~ sP140(U_1873,U_1874,U_1872) )
& ! [U_1873,U_1874,U_1872] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1872,U_1874,c_Groups_Ozero__class_Ozero(U_1872))
| ~ c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1873)
| ~ sP140(U_1873,U_1874,U_1872) )
& ! [U_1873,U_1874,U_1872] :
( c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1874)
| ~ sP139(U_1873,U_1874,U_1872) )
& ! [U_1873,U_1874,U_1872] :
( c_Orderings_Oord__class_Oless__eq(U_1872,U_1873,c_Groups_Ozero__class_Ozero(U_1872))
| ~ sP139(U_1873,U_1874,U_1872) )
& ! [U_1873,U_1874,U_1872] :
( c_Orderings_Oord__class_Oless__eq(U_1872,U_1874,c_Groups_Ozero__class_Ozero(U_1872))
| ~ sP138(U_1873,U_1874,U_1872) )
& ! [U_1873,U_1874,U_1872] :
( c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1873)
| ~ sP138(U_1873,U_1874,U_1872) )
& ! [U_1873,U_1874,U_1872] :
( c_Orderings_Oord__class_Oless__eq(U_1872,c_Rings_Oinverse__class_Odivide(U_1872,U_1873,U_1874),c_Groups_Ozero__class_Ozero(U_1872))
| sP140(U_1873,U_1874,U_1872)
| ~ sP141(U_1873,U_1874,U_1872) )
& ! [U_1873,U_1874,U_1872] :
( sP139(U_1873,U_1874,U_1872)
| sP138(U_1873,U_1874,U_1872)
| ~ c_Orderings_Oord__class_Oless__eq(U_1872,c_Rings_Oinverse__class_Odivide(U_1872,U_1873,U_1874),c_Groups_Ozero__class_Ozero(U_1872))
| ~ sP141(U_1873,U_1874,U_1872) )
& ! [U_1873,U_1874,U_1872] :
( sP141(U_1873,U_1874,U_1872)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1872) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138,sP139,sP140,sP141])],[f_666_2]) ).
cnf(f_666_4,plain,
( sP141(U_1873,U_1874,U_1872)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1872) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_5,plain,
( sP139(U_1873,U_1874,U_1872)
| sP138(U_1873,U_1874,U_1872)
| ~ c_Orderings_Oord__class_Oless__eq(U_1872,c_Rings_Oinverse__class_Odivide(U_1872,U_1873,U_1874),c_Groups_Ozero__class_Ozero(U_1872))
| ~ sP141(U_1873,U_1874,U_1872) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1872,c_Rings_Oinverse__class_Odivide(U_1872,U_1873,U_1874),c_Groups_Ozero__class_Ozero(U_1872))
| sP140(U_1873,U_1874,U_1872)
| ~ sP141(U_1873,U_1874,U_1872) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1873)
| ~ sP138(U_1873,U_1874,U_1872) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_1872,U_1874,c_Groups_Ozero__class_Ozero(U_1872))
| ~ sP138(U_1873,U_1874,U_1872) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_1872,U_1873,c_Groups_Ozero__class_Ozero(U_1872))
| ~ sP139(U_1873,U_1874,U_1872) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1874)
| ~ sP139(U_1873,U_1874,U_1872) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_11,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1872,U_1874,c_Groups_Ozero__class_Ozero(U_1872))
| ~ c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1873)
| ~ sP140(U_1873,U_1874,U_1872) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1872,c_Groups_Ozero__class_Ozero(U_1872),U_1874)
| ~ c_Orderings_Oord__class_Oless__eq(U_1872,U_1873,c_Groups_Ozero__class_Ozero(U_1872))
| ~ sP140(U_1873,U_1874,U_1872) ),
inference(clausify,[status(thm)],[f_666_3]) ).
fof(f_667_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_667_2,plain,
! [U_1878,U_1877,U_1876,U_1875] :
( c_Orderings_Oord__class_Oless__eq(U_1875,c_Rings_Oinverse__class_Odivide(U_1875,U_1876,U_1878),c_Rings_Oinverse__class_Odivide(U_1875,U_1877,U_1878))
| ~ c_Orderings_Oord__class_Oless__eq(U_1875,c_Groups_Ozero__class_Ozero(U_1875),U_1878)
| ~ c_Orderings_Oord__class_Oless__eq(U_1875,U_1876,U_1877)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1875) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
! [U_1877,U_1878,U_1875,U_1876] :
( c_Orderings_Oord__class_Oless__eq(U_1875,c_Rings_Oinverse__class_Odivide(U_1875,U_1876,U_1878),c_Rings_Oinverse__class_Odivide(U_1875,U_1877,U_1878))
| ~ c_Orderings_Oord__class_Oless__eq(U_1875,c_Groups_Ozero__class_Ozero(U_1875),U_1878)
| ~ c_Orderings_Oord__class_Oless__eq(U_1875,U_1876,U_1877)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1875) ),
inference(definitional_conversion,[status(esa)],[f_667_2]) ).
cnf(f_667_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1875,c_Rings_Oinverse__class_Odivide(U_1875,U_1876,U_1878),c_Rings_Oinverse__class_Odivide(U_1875,U_1877,U_1878))
| ~ c_Orderings_Oord__class_Oless__eq(U_1875,c_Groups_Ozero__class_Ozero(U_1875),U_1878)
| ~ c_Orderings_Oord__class_Oless__eq(U_1875,U_1876,U_1877)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1875) ),
inference(clausify,[status(thm)],[f_667_3]) ).
fof(f_668_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_668_2,plain,
! [U_1882,U_1881,U_1880,U_1879] :
( c_Orderings_Oord__class_Oless__eq(U_1879,c_Rings_Oinverse__class_Odivide(U_1879,U_1881,U_1882),c_Rings_Oinverse__class_Odivide(U_1879,U_1880,U_1882))
| ~ c_Orderings_Oord__class_Oless__eq(U_1879,U_1882,c_Groups_Ozero__class_Ozero(U_1879))
| ~ c_Orderings_Oord__class_Oless__eq(U_1879,U_1880,U_1881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1879) ),
inference(variable_rename,[status(thm)],[f_668_1]) ).
fof(f_668_3,plain,
! [U_1879,U_1880,U_1881,U_1882] :
( c_Orderings_Oord__class_Oless__eq(U_1879,c_Rings_Oinverse__class_Odivide(U_1879,U_1881,U_1882),c_Rings_Oinverse__class_Odivide(U_1879,U_1880,U_1882))
| ~ c_Orderings_Oord__class_Oless__eq(U_1879,U_1882,c_Groups_Ozero__class_Ozero(U_1879))
| ~ c_Orderings_Oord__class_Oless__eq(U_1879,U_1880,U_1881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1879) ),
inference(definitional_conversion,[status(esa)],[f_668_2]) ).
cnf(f_668_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1879,c_Rings_Oinverse__class_Odivide(U_1879,U_1881,U_1882),c_Rings_Oinverse__class_Odivide(U_1879,U_1880,U_1882))
| ~ c_Orderings_Oord__class_Oless__eq(U_1879,U_1882,c_Groups_Ozero__class_Ozero(U_1879))
| ~ c_Orderings_Oord__class_Oless__eq(U_1879,U_1880,U_1881)
| ~ class_Fields_Olinordered__field__inverse__zero(U_1879) ),
inference(clausify,[status(thm)],[f_668_3]) ).
fof(f_669_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) )
| ( hAPP(hAPP(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) )
& ( hAPP(hAPP(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_669_2,plain,
! [U_1886,U_1885,U_1884,U_1883] :
( ( ( U_1884 = c_Rings_Oinverse__class_Odivide(U_1883,U_1885,U_1886)
| ( U_1884 != c_Groups_Ozero__class_Ozero(U_1883)
& U_1886 = c_Groups_Ozero__class_Ozero(U_1883) )
| ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1884),U_1886) != U_1885
& U_1886 != c_Groups_Ozero__class_Ozero(U_1883) ) )
& ( ( ( U_1884 = c_Groups_Ozero__class_Ozero(U_1883)
| U_1886 != c_Groups_Ozero__class_Ozero(U_1883) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1884),U_1886) = U_1885
| U_1886 = c_Groups_Ozero__class_Ozero(U_1883) ) )
| U_1884 != c_Rings_Oinverse__class_Odivide(U_1883,U_1885,U_1886) ) )
| ~ class_Fields_Ofield__inverse__zero(U_1883) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
fof(f_669_3,plain,
( ! [U_1884,U_1883,U_1886] :
( U_1884 != c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP144(U_1884,U_1883,U_1886) )
& ! [U_1884,U_1883,U_1886] :
( U_1886 = c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP144(U_1884,U_1883,U_1886) )
& ! [U_1885,U_1884,U_1883,U_1886] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1884),U_1886) != U_1885
| ~ sP143(U_1885,U_1884,U_1883,U_1886) )
& ! [U_1885,U_1884,U_1883,U_1886] :
( U_1886 != c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP143(U_1885,U_1884,U_1883,U_1886) )
& ! [U_1885,U_1884,U_1883,U_1886] :
( U_1884 = c_Groups_Ozero__class_Ozero(U_1883)
| U_1886 != c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP142(U_1885,U_1884,U_1883,U_1886) )
& ! [U_1885,U_1884,U_1883,U_1886] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1884),U_1886) = U_1885
| U_1886 = c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP142(U_1885,U_1884,U_1883,U_1886) )
& ! [U_1885,U_1884,U_1883,U_1886] :
( U_1884 = c_Rings_Oinverse__class_Odivide(U_1883,U_1885,U_1886)
| sP144(U_1884,U_1883,U_1886)
| sP143(U_1885,U_1884,U_1883,U_1886)
| ~ sP145(U_1885,U_1884,U_1883,U_1886) )
& ! [U_1885,U_1884,U_1883,U_1886] :
( sP142(U_1885,U_1884,U_1883,U_1886)
| U_1884 != c_Rings_Oinverse__class_Odivide(U_1883,U_1885,U_1886)
| ~ sP145(U_1885,U_1884,U_1883,U_1886) )
& ! [U_1885,U_1884,U_1883,U_1886] :
( sP145(U_1885,U_1884,U_1883,U_1886)
| ~ class_Fields_Ofield__inverse__zero(U_1883) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142,sP143,sP144,sP145])],[f_669_2]) ).
cnf(f_669_4,plain,
( sP145(U_1885,U_1884,U_1883,U_1886)
| ~ class_Fields_Ofield__inverse__zero(U_1883) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_5,plain,
( sP142(U_1885,U_1884,U_1883,U_1886)
| U_1884 != c_Rings_Oinverse__class_Odivide(U_1883,U_1885,U_1886)
| ~ sP145(U_1885,U_1884,U_1883,U_1886) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_6,plain,
( U_1884 = c_Rings_Oinverse__class_Odivide(U_1883,U_1885,U_1886)
| sP144(U_1884,U_1883,U_1886)
| sP143(U_1885,U_1884,U_1883,U_1886)
| ~ sP145(U_1885,U_1884,U_1883,U_1886) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_7,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1884),U_1886) = U_1885
| U_1886 = c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP142(U_1885,U_1884,U_1883,U_1886) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_8,plain,
( U_1884 = c_Groups_Ozero__class_Ozero(U_1883)
| U_1886 != c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP142(U_1885,U_1884,U_1883,U_1886) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_9,plain,
( U_1886 != c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP143(U_1885,U_1884,U_1883,U_1886) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_10,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1883),U_1884),U_1886) != U_1885
| ~ sP143(U_1885,U_1884,U_1883,U_1886) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_11,plain,
( U_1886 = c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP144(U_1884,U_1883,U_1886) ),
inference(clausify,[status(thm)],[f_669_3]) ).
cnf(f_669_12,plain,
( U_1884 != c_Groups_Ozero__class_Ozero(U_1883)
| ~ sP144(U_1884,U_1883,U_1886) ),
inference(clausify,[status(thm)],[f_669_3]) ).
fof(f_670_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 != hAPP(hAPP(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 = hAPP(hAPP(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_670_2,plain,
! [U_1890,U_1889,U_1888,U_1887] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1887,U_1888,U_1889) = U_1890
| ( U_1890 != c_Groups_Ozero__class_Ozero(U_1887)
& U_1889 = c_Groups_Ozero__class_Ozero(U_1887) )
| ( U_1888 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1889)
& U_1889 != c_Groups_Ozero__class_Ozero(U_1887) ) )
& ( ( ( U_1890 = c_Groups_Ozero__class_Ozero(U_1887)
| U_1889 != c_Groups_Ozero__class_Ozero(U_1887) )
& ( U_1888 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1889)
| U_1889 = c_Groups_Ozero__class_Ozero(U_1887) ) )
| c_Rings_Oinverse__class_Odivide(U_1887,U_1888,U_1889) != U_1890 ) )
| ~ class_Fields_Ofield__inverse__zero(U_1887) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
fof(f_670_3,plain,
( ! [U_1887,U_1890,U_1889] :
( U_1890 != c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP148(U_1887,U_1890,U_1889) )
& ! [U_1887,U_1890,U_1889] :
( U_1889 = c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP148(U_1887,U_1890,U_1889) )
& ! [U_1888,U_1887,U_1890,U_1889] :
( U_1888 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1889)
| ~ sP147(U_1888,U_1887,U_1890,U_1889) )
& ! [U_1888,U_1887,U_1890,U_1889] :
( U_1889 != c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP147(U_1888,U_1887,U_1890,U_1889) )
& ! [U_1888,U_1887,U_1890,U_1889] :
( U_1890 = c_Groups_Ozero__class_Ozero(U_1887)
| U_1889 != c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP146(U_1888,U_1887,U_1890,U_1889) )
& ! [U_1888,U_1887,U_1890,U_1889] :
( U_1888 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1889)
| U_1889 = c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP146(U_1888,U_1887,U_1890,U_1889) )
& ! [U_1888,U_1887,U_1890,U_1889] :
( c_Rings_Oinverse__class_Odivide(U_1887,U_1888,U_1889) = U_1890
| sP148(U_1887,U_1890,U_1889)
| sP147(U_1888,U_1887,U_1890,U_1889)
| ~ sP149(U_1888,U_1887,U_1890,U_1889) )
& ! [U_1888,U_1887,U_1890,U_1889] :
( sP146(U_1888,U_1887,U_1890,U_1889)
| c_Rings_Oinverse__class_Odivide(U_1887,U_1888,U_1889) != U_1890
| ~ sP149(U_1888,U_1887,U_1890,U_1889) )
& ! [U_1888,U_1887,U_1890,U_1889] :
( sP149(U_1888,U_1887,U_1890,U_1889)
| ~ class_Fields_Ofield__inverse__zero(U_1887) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146,sP147,sP148,sP149])],[f_670_2]) ).
cnf(f_670_4,plain,
( sP149(U_1888,U_1887,U_1890,U_1889)
| ~ class_Fields_Ofield__inverse__zero(U_1887) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_5,plain,
( sP146(U_1888,U_1887,U_1890,U_1889)
| c_Rings_Oinverse__class_Odivide(U_1887,U_1888,U_1889) != U_1890
| ~ sP149(U_1888,U_1887,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_6,plain,
( c_Rings_Oinverse__class_Odivide(U_1887,U_1888,U_1889) = U_1890
| sP148(U_1887,U_1890,U_1889)
| sP147(U_1888,U_1887,U_1890,U_1889)
| ~ sP149(U_1888,U_1887,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_7,plain,
( U_1888 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1889)
| U_1889 = c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP146(U_1888,U_1887,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_8,plain,
( U_1890 = c_Groups_Ozero__class_Ozero(U_1887)
| U_1889 != c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP146(U_1888,U_1887,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_9,plain,
( U_1889 != c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP147(U_1888,U_1887,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_10,plain,
( U_1888 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1887),U_1890),U_1889)
| ~ sP147(U_1888,U_1887,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_11,plain,
( U_1889 = c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP148(U_1887,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_670_3]) ).
cnf(f_670_12,plain,
( U_1890 != c_Groups_Ozero__class_Ozero(U_1887)
| ~ sP148(U_1887,U_1890,U_1889) ),
inference(clausify,[status(thm)],[f_670_3]) ).
fof(f_671_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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_671_2,plain,
! [U_1894,U_1893,U_1892,U_1891] :
( c_Rings_Oinverse__class_Odivide(U_1891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1893),U_1892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1894),U_1892)) = c_Rings_Oinverse__class_Odivide(U_1891,U_1893,U_1894)
| U_1892 = c_Groups_Ozero__class_Ozero(U_1891)
| ~ class_Fields_Ofield__inverse__zero(U_1891) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
fof(f_671_3,plain,
! [U_1894,U_1891,U_1892,U_1893] :
( c_Rings_Oinverse__class_Odivide(U_1891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1893),U_1892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1894),U_1892)) = c_Rings_Oinverse__class_Odivide(U_1891,U_1893,U_1894)
| U_1892 = c_Groups_Ozero__class_Ozero(U_1891)
| ~ class_Fields_Ofield__inverse__zero(U_1891) ),
inference(definitional_conversion,[status(esa)],[f_671_2]) ).
cnf(f_671_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1891,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1893),U_1892),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1891),U_1894),U_1892)) = c_Rings_Oinverse__class_Odivide(U_1891,U_1893,U_1894)
| U_1892 = c_Groups_Ozero__class_Ozero(U_1891)
| ~ class_Fields_Ofield__inverse__zero(U_1891) ),
inference(clausify,[status(thm)],[f_671_3]) ).
fof(f_672_1,plain,
! [V_b,V_a,V_c,T_a] :
( c_Rings_Oinverse__class_Odivide(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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_672_2,plain,
! [U_1898,U_1897,U_1896,U_1895] :
( c_Rings_Oinverse__class_Odivide(U_1895,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1895),U_1896),U_1897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1895),U_1896),U_1898)) = c_Rings_Oinverse__class_Odivide(U_1895,U_1897,U_1898)
| U_1896 = c_Groups_Ozero__class_Ozero(U_1895)
| ~ class_Fields_Ofield__inverse__zero(U_1895) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
fof(f_672_3,plain,
! [U_1895,U_1897,U_1896,U_1898] :
( c_Rings_Oinverse__class_Odivide(U_1895,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1895),U_1896),U_1897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1895),U_1896),U_1898)) = c_Rings_Oinverse__class_Odivide(U_1895,U_1897,U_1898)
| U_1896 = c_Groups_Ozero__class_Ozero(U_1895)
| ~ class_Fields_Ofield__inverse__zero(U_1895) ),
inference(definitional_conversion,[status(esa)],[f_672_2]) ).
cnf(f_672_4,plain,
( c_Rings_Oinverse__class_Odivide(U_1895,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1895),U_1896),U_1897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1895),U_1896),U_1898)) = c_Rings_Oinverse__class_Odivide(U_1895,U_1897,U_1898)
| U_1896 = c_Groups_Ozero__class_Ozero(U_1895)
| ~ class_Fields_Ofield__inverse__zero(U_1895) ),
inference(clausify,[status(thm)],[f_672_3]) ).
fof(f_673_1,plain,
! [V_w_2,V_xa_2,V_za_2,V_ya_2,T_a] :
( ( ( c_Rings_Oinverse__class_Odivide(T_a,V_xa_2,V_ya_2) = c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_za_2)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_za_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_za_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_ya_2)
| c_Rings_Oinverse__class_Odivide(T_a,V_xa_2,V_ya_2) != c_Rings_Oinverse__class_Odivide(T_a,V_w_2,V_za_2) ) )
| V_za_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_frac__eq__eq]) ).
fof(f_673_2,plain,
! [U_1903,U_1902,U_1901,U_1900,U_1899] :
( ( ( c_Rings_Oinverse__class_Odivide(U_1899,U_1902,U_1900) = c_Rings_Oinverse__class_Odivide(U_1899,U_1903,U_1901)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1902),U_1901) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1900) )
& ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1902),U_1901) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1900)
| c_Rings_Oinverse__class_Odivide(U_1899,U_1902,U_1900) != c_Rings_Oinverse__class_Odivide(U_1899,U_1903,U_1901) ) )
| U_1901 = c_Groups_Ozero__class_Ozero(U_1899)
| U_1900 = c_Groups_Ozero__class_Ozero(U_1899)
| ~ class_Fields_Ofield(U_1899) ),
inference(variable_rename,[status(thm)],[f_673_1]) ).
fof(f_673_3,plain,
( ! [U_1900,U_1899,U_1901,U_1902,U_1903] :
( c_Rings_Oinverse__class_Odivide(U_1899,U_1902,U_1900) = c_Rings_Oinverse__class_Odivide(U_1899,U_1903,U_1901)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1902),U_1901) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1900)
| ~ sP150(U_1900,U_1899,U_1901,U_1902,U_1903) )
& ! [U_1900,U_1899,U_1901,U_1902,U_1903] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1902),U_1901) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1900)
| c_Rings_Oinverse__class_Odivide(U_1899,U_1902,U_1900) != c_Rings_Oinverse__class_Odivide(U_1899,U_1903,U_1901)
| ~ sP150(U_1900,U_1899,U_1901,U_1902,U_1903) )
& ! [U_1900,U_1899,U_1901,U_1902,U_1903] :
( sP150(U_1900,U_1899,U_1901,U_1902,U_1903)
| U_1901 = c_Groups_Ozero__class_Ozero(U_1899)
| U_1900 = c_Groups_Ozero__class_Ozero(U_1899)
| ~ class_Fields_Ofield(U_1899) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150])],[f_673_2]) ).
cnf(f_673_4,plain,
( sP150(U_1900,U_1899,U_1901,U_1902,U_1903)
| U_1901 = c_Groups_Ozero__class_Ozero(U_1899)
| U_1900 = c_Groups_Ozero__class_Ozero(U_1899)
| ~ class_Fields_Ofield(U_1899) ),
inference(clausify,[status(thm)],[f_673_3]) ).
cnf(f_673_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1902),U_1901) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1900)
| c_Rings_Oinverse__class_Odivide(U_1899,U_1902,U_1900) != c_Rings_Oinverse__class_Odivide(U_1899,U_1903,U_1901)
| ~ sP150(U_1900,U_1899,U_1901,U_1902,U_1903) ),
inference(clausify,[status(thm)],[f_673_3]) ).
cnf(f_673_6,plain,
( c_Rings_Oinverse__class_Odivide(U_1899,U_1902,U_1900) = c_Rings_Oinverse__class_Odivide(U_1899,U_1903,U_1901)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1902),U_1901) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1899),U_1903),U_1900)
| ~ sP150(U_1900,U_1899,U_1901,U_1902,U_1903) ),
inference(clausify,[status(thm)],[f_673_3]) ).
fof(f_674_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_674_2,plain,
! [U_1906,U_1905,U_1904] :
( c_Groups_Oabs__class_Oabs(U_1904,c_Rings_Oinverse__class_Odivide(U_1904,U_1906,U_1905)) = c_Rings_Oinverse__class_Odivide(U_1904,c_Groups_Oabs__class_Oabs(U_1904,U_1906),c_Groups_Oabs__class_Oabs(U_1904,U_1905))
| U_1905 = c_Groups_Ozero__class_Ozero(U_1904)
| ~ class_Fields_Olinordered__field(U_1904) ),
inference(variable_rename,[status(thm)],[f_674_1]) ).
fof(f_674_3,plain,
! [U_1906,U_1904,U_1905] :
( c_Groups_Oabs__class_Oabs(U_1904,c_Rings_Oinverse__class_Odivide(U_1904,U_1906,U_1905)) = c_Rings_Oinverse__class_Odivide(U_1904,c_Groups_Oabs__class_Oabs(U_1904,U_1906),c_Groups_Oabs__class_Oabs(U_1904,U_1905))
| U_1905 = c_Groups_Ozero__class_Ozero(U_1904)
| ~ class_Fields_Olinordered__field(U_1904) ),
inference(definitional_conversion,[status(esa)],[f_674_2]) ).
cnf(f_674_4,plain,
( c_Groups_Oabs__class_Oabs(U_1904,c_Rings_Oinverse__class_Odivide(U_1904,U_1906,U_1905)) = c_Rings_Oinverse__class_Odivide(U_1904,c_Groups_Oabs__class_Oabs(U_1904,U_1906),c_Groups_Oabs__class_Oabs(U_1904,U_1905))
| U_1905 = c_Groups_Ozero__class_Ozero(U_1904)
| ~ class_Fields_Olinordered__field(U_1904) ),
inference(clausify,[status(thm)],[f_674_3]) ).
fof(f_675_1,plain,
! [V_w,V_x,V_z,V_y,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),c_Rings_Oinverse__class_Odivide(T_a,V_w,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z))
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__frac__eq]) ).
fof(f_675_2,plain,
! [U_1911,U_1910,U_1909,U_1908,U_1907] :
( c_Groups_Oplus__class_Oplus(U_1907,c_Rings_Oinverse__class_Odivide(U_1907,U_1910,U_1908),c_Rings_Oinverse__class_Odivide(U_1907,U_1911,U_1909)) = c_Rings_Oinverse__class_Odivide(U_1907,c_Groups_Oplus__class_Oplus(U_1907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1910),U_1909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1911),U_1908)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1908),U_1909))
| U_1909 = c_Groups_Ozero__class_Ozero(U_1907)
| U_1908 = c_Groups_Ozero__class_Ozero(U_1907)
| ~ class_Fields_Ofield(U_1907) ),
inference(variable_rename,[status(thm)],[f_675_1]) ).
fof(f_675_3,plain,
! [U_1907,U_1908,U_1909,U_1910,U_1911] :
( c_Groups_Oplus__class_Oplus(U_1907,c_Rings_Oinverse__class_Odivide(U_1907,U_1910,U_1908),c_Rings_Oinverse__class_Odivide(U_1907,U_1911,U_1909)) = c_Rings_Oinverse__class_Odivide(U_1907,c_Groups_Oplus__class_Oplus(U_1907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1910),U_1909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1911),U_1908)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1908),U_1909))
| U_1909 = c_Groups_Ozero__class_Ozero(U_1907)
| U_1908 = c_Groups_Ozero__class_Ozero(U_1907)
| ~ class_Fields_Ofield(U_1907) ),
inference(definitional_conversion,[status(esa)],[f_675_2]) ).
cnf(f_675_4,plain,
( c_Groups_Oplus__class_Oplus(U_1907,c_Rings_Oinverse__class_Odivide(U_1907,U_1910,U_1908),c_Rings_Oinverse__class_Odivide(U_1907,U_1911,U_1909)) = c_Rings_Oinverse__class_Odivide(U_1907,c_Groups_Oplus__class_Oplus(U_1907,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1910),U_1909),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1911),U_1908)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1907),U_1908),U_1909))
| U_1909 = c_Groups_Ozero__class_Ozero(U_1907)
| U_1908 = c_Groups_Ozero__class_Ozero(U_1907)
| ~ class_Fields_Ofield(U_1907) ),
inference(clausify,[status(thm)],[f_675_3]) ).
fof(f_676_1,plain,
! [V_y,V_x,V_z,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_z),V_y) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_z)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__add__eq__iff]) ).
fof(f_676_2,plain,
! [U_1915,U_1914,U_1913,U_1912] :
( c_Groups_Oplus__class_Oplus(U_1912,c_Rings_Oinverse__class_Odivide(U_1912,U_1914,U_1913),U_1915) = c_Rings_Oinverse__class_Odivide(U_1912,c_Groups_Oplus__class_Oplus(U_1912,U_1914,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1912),U_1913),U_1915)),U_1913)
| U_1913 = c_Groups_Ozero__class_Ozero(U_1912)
| ~ class_Fields_Ofield(U_1912) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
fof(f_676_3,plain,
! [U_1913,U_1912,U_1914,U_1915] :
( c_Groups_Oplus__class_Oplus(U_1912,c_Rings_Oinverse__class_Odivide(U_1912,U_1914,U_1913),U_1915) = c_Rings_Oinverse__class_Odivide(U_1912,c_Groups_Oplus__class_Oplus(U_1912,U_1914,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1912),U_1913),U_1915)),U_1913)
| U_1913 = c_Groups_Ozero__class_Ozero(U_1912)
| ~ class_Fields_Ofield(U_1912) ),
inference(definitional_conversion,[status(esa)],[f_676_2]) ).
cnf(f_676_4,plain,
( c_Groups_Oplus__class_Oplus(U_1912,c_Rings_Oinverse__class_Odivide(U_1912,U_1914,U_1913),U_1915) = c_Rings_Oinverse__class_Odivide(U_1912,c_Groups_Oplus__class_Oplus(U_1912,U_1914,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1912),U_1913),U_1915)),U_1913)
| U_1913 = c_Groups_Ozero__class_Ozero(U_1912)
| ~ class_Fields_Ofield(U_1912) ),
inference(clausify,[status(thm)],[f_676_3]) ).
fof(f_677_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__frac__num]) ).
fof(f_677_2,plain,
! [U_1919,U_1918,U_1917,U_1916] :
( c_Groups_Oplus__class_Oplus(U_1916,c_Rings_Oinverse__class_Odivide(U_1916,U_1918,U_1917),U_1919) = c_Rings_Oinverse__class_Odivide(U_1916,c_Groups_Oplus__class_Oplus(U_1916,U_1918,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1916),U_1919),U_1917)),U_1917)
| U_1917 = c_Groups_Ozero__class_Ozero(U_1916)
| ~ class_Fields_Ofield__inverse__zero(U_1916) ),
inference(variable_rename,[status(thm)],[f_677_1]) ).
fof(f_677_3,plain,
! [U_1916,U_1917,U_1918,U_1919] :
( c_Groups_Oplus__class_Oplus(U_1916,c_Rings_Oinverse__class_Odivide(U_1916,U_1918,U_1917),U_1919) = c_Rings_Oinverse__class_Odivide(U_1916,c_Groups_Oplus__class_Oplus(U_1916,U_1918,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1916),U_1919),U_1917)),U_1917)
| U_1917 = c_Groups_Ozero__class_Ozero(U_1916)
| ~ class_Fields_Ofield__inverse__zero(U_1916) ),
inference(definitional_conversion,[status(esa)],[f_677_2]) ).
cnf(f_677_4,plain,
( c_Groups_Oplus__class_Oplus(U_1916,c_Rings_Oinverse__class_Odivide(U_1916,U_1918,U_1917),U_1919) = c_Rings_Oinverse__class_Odivide(U_1916,c_Groups_Oplus__class_Oplus(U_1916,U_1918,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1916),U_1919),U_1917)),U_1917)
| U_1917 = c_Groups_Ozero__class_Ozero(U_1916)
| ~ class_Fields_Ofield__inverse__zero(U_1916) ),
inference(clausify,[status(thm)],[f_677_3]) ).
fof(f_678_1,plain,
! [V_y,V_x,V_z,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_x,c_Rings_Oinverse__class_Odivide(T_a,V_y,V_z)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x),V_y),V_z)
| V_z = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__divide__eq__iff]) ).
fof(f_678_2,plain,
! [U_1923,U_1922,U_1921,U_1920] :
( c_Groups_Oplus__class_Oplus(U_1920,U_1922,c_Rings_Oinverse__class_Odivide(U_1920,U_1923,U_1921)) = c_Rings_Oinverse__class_Odivide(U_1920,c_Groups_Oplus__class_Oplus(U_1920,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),U_1921),U_1922),U_1923),U_1921)
| U_1921 = c_Groups_Ozero__class_Ozero(U_1920)
| ~ class_Fields_Ofield(U_1920) ),
inference(variable_rename,[status(thm)],[f_678_1]) ).
fof(f_678_3,plain,
! [U_1920,U_1921,U_1922,U_1923] :
( c_Groups_Oplus__class_Oplus(U_1920,U_1922,c_Rings_Oinverse__class_Odivide(U_1920,U_1923,U_1921)) = c_Rings_Oinverse__class_Odivide(U_1920,c_Groups_Oplus__class_Oplus(U_1920,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),U_1921),U_1922),U_1923),U_1921)
| U_1921 = c_Groups_Ozero__class_Ozero(U_1920)
| ~ class_Fields_Ofield(U_1920) ),
inference(definitional_conversion,[status(esa)],[f_678_2]) ).
cnf(f_678_4,plain,
( c_Groups_Oplus__class_Oplus(U_1920,U_1922,c_Rings_Oinverse__class_Odivide(U_1920,U_1923,U_1921)) = c_Rings_Oinverse__class_Odivide(U_1920,c_Groups_Oplus__class_Oplus(U_1920,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1920),U_1921),U_1922),U_1923),U_1921)
| U_1921 = c_Groups_Ozero__class_Ozero(U_1920)
| ~ class_Fields_Ofield(U_1920) ),
inference(clausify,[status(thm)],[f_678_3]) ).
fof(f_679_1,plain,
! [V_x,V_z,V_y,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y)) = c_Rings_Oinverse__class_Odivide(T_a,c_Groups_Oplus__class_Oplus(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y)),V_y)
| V_y = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Fields_Ofield__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__num__frac]) ).
fof(f_679_2,plain,
! [U_1927,U_1926,U_1925,U_1924] :
( c_Groups_Oplus__class_Oplus(U_1924,U_1926,c_Rings_Oinverse__class_Odivide(U_1924,U_1927,U_1925)) = c_Rings_Oinverse__class_Odivide(U_1924,c_Groups_Oplus__class_Oplus(U_1924,U_1927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1926),U_1925)),U_1925)
| U_1925 = c_Groups_Ozero__class_Ozero(U_1924)
| ~ class_Fields_Ofield__inverse__zero(U_1924) ),
inference(variable_rename,[status(thm)],[f_679_1]) ).
fof(f_679_3,plain,
! [U_1924,U_1925,U_1926,U_1927] :
( c_Groups_Oplus__class_Oplus(U_1924,U_1926,c_Rings_Oinverse__class_Odivide(U_1924,U_1927,U_1925)) = c_Rings_Oinverse__class_Odivide(U_1924,c_Groups_Oplus__class_Oplus(U_1924,U_1927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1926),U_1925)),U_1925)
| U_1925 = c_Groups_Ozero__class_Ozero(U_1924)
| ~ class_Fields_Ofield__inverse__zero(U_1924) ),
inference(definitional_conversion,[status(esa)],[f_679_2]) ).
cnf(f_679_4,plain,
( c_Groups_Oplus__class_Oplus(U_1924,U_1926,c_Rings_Oinverse__class_Odivide(U_1924,U_1927,U_1925)) = c_Rings_Oinverse__class_Odivide(U_1924,c_Groups_Oplus__class_Oplus(U_1924,U_1927,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1924),U_1926),U_1925)),U_1925)
| U_1925 = c_Groups_Ozero__class_Ozero(U_1924)
| ~ class_Fields_Ofield__inverse__zero(U_1924) ),
inference(clausify,[status(thm)],[f_679_3]) ).
fof(f_680_1,plain,
! [V_x] : c_Transcendental_Oarctan(V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(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_arctan__half]) ).
fof(f_680_2,plain,
! [U_1928] : c_Transcendental_Oarctan(U_1928) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1928,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1928),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))),
inference(variable_rename,[status(thm)],[f_680_1]) ).
fof(f_680_3,plain,
! [U_1928] : c_Transcendental_Oarctan(U_1928) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1928,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1928),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))),
inference(definitional_conversion,[status(esa)],[f_680_2]) ).
cnf(f_680_4,plain,
c_Transcendental_Oarctan(U_1928) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1928,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1928),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))))),
inference(clausify,[status(thm)],[f_680_3]) ).
fof(f_681_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,hAPP(hAPP(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)))),hAPP(hAPP(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_681_2,plain,
! [U_1931,U_1930,U_1929] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1930),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1931),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1929)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1931)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1930)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1931,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1929,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_1930,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1929,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_1929) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
fof(f_681_3,plain,
! [U_1929,U_1930,U_1931] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1930),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1931),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1929)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1931)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1930)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1931,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1929,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_1930,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1929,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_1929) ),
inference(definitional_conversion,[status(esa)],[f_681_2]) ).
cnf(f_681_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1930),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1931),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1929)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1931)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1930)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1931,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1929,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_1930,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1929,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_1929) ),
inference(clausify,[status(thm)],[f_681_3]) ).
fof(f_682_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,hAPP(hAPP(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)))),hAPP(hAPP(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_682_2,plain,
! [U_1934,U_1933,U_1932] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1932),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1934),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1933)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1934),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1933,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_1932),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1933,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_682_1]) ).
fof(f_682_3,plain,
! [U_1933,U_1934,U_1932] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1932),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1934),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1933)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1934),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1933,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_1932),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1933,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
inference(definitional_conversion,[status(esa)],[f_682_2]) ).
cnf(f_682_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1932),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_1934),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),U_1933)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1934),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1933,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_1932),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_1933,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_682_3]) ).
fof(f_683_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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_683_2,plain,
! [U_1938,U_1937,U_1936,U_1935] :
( c_Orderings_Oord__class_Oless(U_1935,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1938),U_1937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1938),U_1936))
| ~ c_Orderings_Oord__class_Oless(U_1935,U_1938,c_Groups_Ozero__class_Ozero(U_1935))
| ~ c_Orderings_Oord__class_Oless(U_1935,U_1936,U_1937)
| ~ class_Rings_Olinordered__ring__strict(U_1935) ),
inference(variable_rename,[status(thm)],[f_683_1]) ).
fof(f_683_3,plain,
! [U_1937,U_1935,U_1936,U_1938] :
( c_Orderings_Oord__class_Oless(U_1935,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1938),U_1937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1938),U_1936))
| ~ c_Orderings_Oord__class_Oless(U_1935,U_1938,c_Groups_Ozero__class_Ozero(U_1935))
| ~ c_Orderings_Oord__class_Oless(U_1935,U_1936,U_1937)
| ~ class_Rings_Olinordered__ring__strict(U_1935) ),
inference(definitional_conversion,[status(esa)],[f_683_2]) ).
cnf(f_683_4,plain,
( c_Orderings_Oord__class_Oless(U_1935,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1938),U_1937),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1935),U_1938),U_1936))
| ~ c_Orderings_Oord__class_Oless(U_1935,U_1938,c_Groups_Ozero__class_Ozero(U_1935))
| ~ c_Orderings_Oord__class_Oless(U_1935,U_1936,U_1937)
| ~ class_Rings_Olinordered__ring__strict(U_1935) ),
inference(clausify,[status(thm)],[f_683_3]) ).
fof(f_684_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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_684_2,plain,
! [U_1942,U_1941,U_1940,U_1939] :
( c_Orderings_Oord__class_Oless(U_1939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1939),U_1941),U_1942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1939),U_1940),U_1942))
| ~ c_Orderings_Oord__class_Oless(U_1939,U_1942,c_Groups_Ozero__class_Ozero(U_1939))
| ~ c_Orderings_Oord__class_Oless(U_1939,U_1940,U_1941)
| ~ class_Rings_Olinordered__ring__strict(U_1939) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
fof(f_684_3,plain,
! [U_1939,U_1940,U_1941,U_1942] :
( c_Orderings_Oord__class_Oless(U_1939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1939),U_1941),U_1942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1939),U_1940),U_1942))
| ~ c_Orderings_Oord__class_Oless(U_1939,U_1942,c_Groups_Ozero__class_Ozero(U_1939))
| ~ c_Orderings_Oord__class_Oless(U_1939,U_1940,U_1941)
| ~ class_Rings_Olinordered__ring__strict(U_1939) ),
inference(definitional_conversion,[status(esa)],[f_684_2]) ).
cnf(f_684_4,plain,
( c_Orderings_Oord__class_Oless(U_1939,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1939),U_1941),U_1942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1939),U_1940),U_1942))
| ~ c_Orderings_Oord__class_Oless(U_1939,U_1942,c_Groups_Ozero__class_Ozero(U_1939))
| ~ c_Orderings_Oord__class_Oless(U_1939,U_1940,U_1941)
| ~ class_Rings_Olinordered__ring__strict(U_1939) ),
inference(clausify,[status(thm)],[f_684_3]) ).
fof(f_685_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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_685_2,plain,
! [U_1946,U_1945,U_1944,U_1943] :
( c_Orderings_Oord__class_Oless(U_1943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1946),U_1944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1946),U_1945))
| ~ c_Orderings_Oord__class_Oless(U_1943,c_Groups_Ozero__class_Ozero(U_1943),U_1946)
| ~ c_Orderings_Oord__class_Oless(U_1943,U_1944,U_1945)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_1943) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
fof(f_685_3,plain,
! [U_1943,U_1944,U_1945,U_1946] :
( c_Orderings_Oord__class_Oless(U_1943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1946),U_1944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1946),U_1945))
| ~ c_Orderings_Oord__class_Oless(U_1943,c_Groups_Ozero__class_Ozero(U_1943),U_1946)
| ~ c_Orderings_Oord__class_Oless(U_1943,U_1944,U_1945)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_1943) ),
inference(definitional_conversion,[status(esa)],[f_685_2]) ).
cnf(f_685_4,plain,
( c_Orderings_Oord__class_Oless(U_1943,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1946),U_1944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1943),U_1946),U_1945))
| ~ c_Orderings_Oord__class_Oless(U_1943,c_Groups_Ozero__class_Ozero(U_1943),U_1946)
| ~ c_Orderings_Oord__class_Oless(U_1943,U_1944,U_1945)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_1943) ),
inference(clausify,[status(thm)],[f_685_3]) ).
fof(f_686_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(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_686_2,plain,
! [U_1950,U_1949,U_1948,U_1947] :
( c_Orderings_Oord__class_Oless(U_1947,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1949))
| ~ c_Orderings_Oord__class_Oless(U_1947,c_Groups_Ozero__class_Ozero(U_1947),U_1950)
| ~ c_Orderings_Oord__class_Oless(U_1947,U_1948,U_1949)
| ~ class_Rings_Olinordered__semiring__strict(U_1947) ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
fof(f_686_3,plain,
! [U_1948,U_1947,U_1950,U_1949] :
( c_Orderings_Oord__class_Oless(U_1947,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1949))
| ~ c_Orderings_Oord__class_Oless(U_1947,c_Groups_Ozero__class_Ozero(U_1947),U_1950)
| ~ c_Orderings_Oord__class_Oless(U_1947,U_1948,U_1949)
| ~ class_Rings_Olinordered__semiring__strict(U_1947) ),
inference(definitional_conversion,[status(esa)],[f_686_2]) ).
cnf(f_686_4,plain,
( c_Orderings_Oord__class_Oless(U_1947,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1948),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1947),U_1950),U_1949))
| ~ c_Orderings_Oord__class_Oless(U_1947,c_Groups_Ozero__class_Ozero(U_1947),U_1950)
| ~ c_Orderings_Oord__class_Oless(U_1947,U_1948,U_1949)
| ~ class_Rings_Olinordered__semiring__strict(U_1947) ),
inference(clausify,[status(thm)],[f_686_3]) ).
fof(f_687_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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_687_2,plain,
! [U_1954,U_1953,U_1952,U_1951] :
( c_Orderings_Oord__class_Oless(U_1951,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1951),U_1952),U_1954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1951),U_1953),U_1954))
| ~ c_Orderings_Oord__class_Oless(U_1951,c_Groups_Ozero__class_Ozero(U_1951),U_1954)
| ~ c_Orderings_Oord__class_Oless(U_1951,U_1952,U_1953)
| ~ class_Rings_Olinordered__semiring__strict(U_1951) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
fof(f_687_3,plain,
! [U_1951,U_1952,U_1953,U_1954] :
( c_Orderings_Oord__class_Oless(U_1951,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1951),U_1952),U_1954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1951),U_1953),U_1954))
| ~ c_Orderings_Oord__class_Oless(U_1951,c_Groups_Ozero__class_Ozero(U_1951),U_1954)
| ~ c_Orderings_Oord__class_Oless(U_1951,U_1952,U_1953)
| ~ class_Rings_Olinordered__semiring__strict(U_1951) ),
inference(definitional_conversion,[status(esa)],[f_687_2]) ).
cnf(f_687_4,plain,
( c_Orderings_Oord__class_Oless(U_1951,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1951),U_1952),U_1954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1951),U_1953),U_1954))
| ~ c_Orderings_Oord__class_Oless(U_1951,c_Groups_Ozero__class_Ozero(U_1951),U_1954)
| ~ c_Orderings_Oord__class_Oless(U_1951,U_1952,U_1953)
| ~ class_Rings_Olinordered__semiring__strict(U_1951) ),
inference(clausify,[status(thm)],[f_687_3]) ).
fof(f_688_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_688_2,plain,
! [U_1957,U_1956,U_1955] :
( c_Orderings_Oord__class_Oless(U_1955,c_Groups_Ozero__class_Ozero(U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1956),U_1957))
| ~ c_Orderings_Oord__class_Oless(U_1955,U_1957,c_Groups_Ozero__class_Ozero(U_1955))
| ~ c_Orderings_Oord__class_Oless(U_1955,U_1956,c_Groups_Ozero__class_Ozero(U_1955))
| ~ class_Rings_Olinordered__ring__strict(U_1955) ),
inference(variable_rename,[status(thm)],[f_688_1]) ).
fof(f_688_3,plain,
! [U_1955,U_1956,U_1957] :
( c_Orderings_Oord__class_Oless(U_1955,c_Groups_Ozero__class_Ozero(U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1956),U_1957))
| ~ c_Orderings_Oord__class_Oless(U_1955,U_1957,c_Groups_Ozero__class_Ozero(U_1955))
| ~ c_Orderings_Oord__class_Oless(U_1955,U_1956,c_Groups_Ozero__class_Ozero(U_1955))
| ~ class_Rings_Olinordered__ring__strict(U_1955) ),
inference(definitional_conversion,[status(esa)],[f_688_2]) ).
cnf(f_688_4,plain,
( c_Orderings_Oord__class_Oless(U_1955,c_Groups_Ozero__class_Ozero(U_1955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1955),U_1956),U_1957))
| ~ c_Orderings_Oord__class_Oless(U_1955,U_1957,c_Groups_Ozero__class_Ozero(U_1955))
| ~ c_Orderings_Oord__class_Oless(U_1955,U_1956,c_Groups_Ozero__class_Ozero(U_1955))
| ~ class_Rings_Olinordered__ring__strict(U_1955) ),
inference(clausify,[status(thm)],[f_688_3]) ).
fof(f_689_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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_689_2,plain,
! [U_1960,U_1959,U_1958] :
( c_Orderings_Oord__class_Oless(U_1958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1958),U_1959),U_1960),c_Groups_Ozero__class_Ozero(U_1958))
| ~ c_Orderings_Oord__class_Oless(U_1958,c_Groups_Ozero__class_Ozero(U_1958),U_1960)
| ~ c_Orderings_Oord__class_Oless(U_1958,U_1959,c_Groups_Ozero__class_Ozero(U_1958))
| ~ class_Rings_Olinordered__semiring__strict(U_1958) ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
fof(f_689_3,plain,
! [U_1958,U_1959,U_1960] :
( c_Orderings_Oord__class_Oless(U_1958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1958),U_1959),U_1960),c_Groups_Ozero__class_Ozero(U_1958))
| ~ c_Orderings_Oord__class_Oless(U_1958,c_Groups_Ozero__class_Ozero(U_1958),U_1960)
| ~ c_Orderings_Oord__class_Oless(U_1958,U_1959,c_Groups_Ozero__class_Ozero(U_1958))
| ~ class_Rings_Olinordered__semiring__strict(U_1958) ),
inference(definitional_conversion,[status(esa)],[f_689_2]) ).
cnf(f_689_4,plain,
( c_Orderings_Oord__class_Oless(U_1958,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1958),U_1959),U_1960),c_Groups_Ozero__class_Ozero(U_1958))
| ~ c_Orderings_Oord__class_Oless(U_1958,c_Groups_Ozero__class_Ozero(U_1958),U_1960)
| ~ c_Orderings_Oord__class_Oless(U_1958,U_1959,c_Groups_Ozero__class_Ozero(U_1958))
| ~ class_Rings_Olinordered__semiring__strict(U_1958) ),
inference(clausify,[status(thm)],[f_689_3]) ).
fof(f_690_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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_690_2,plain,
! [U_1964,U_1963,U_1962,U_1961] :
( ( ( c_Orderings_Oord__class_Oless(U_1961,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1964))
| ~ c_Orderings_Oord__class_Oless(U_1961,U_1964,U_1963) )
& ( c_Orderings_Oord__class_Oless(U_1961,U_1964,U_1963)
| ~ c_Orderings_Oord__class_Oless(U_1961,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1964)) ) )
| ~ c_Orderings_Oord__class_Oless(U_1961,U_1962,c_Groups_Ozero__class_Ozero(U_1961))
| ~ class_Rings_Olinordered__ring__strict(U_1961) ),
inference(variable_rename,[status(thm)],[f_690_1]) ).
fof(f_690_3,plain,
( ! [U_1961,U_1962,U_1963,U_1964] :
( c_Orderings_Oord__class_Oless(U_1961,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1964))
| ~ c_Orderings_Oord__class_Oless(U_1961,U_1964,U_1963)
| ~ sP151(U_1961,U_1962,U_1963,U_1964) )
& ! [U_1961,U_1962,U_1963,U_1964] :
( c_Orderings_Oord__class_Oless(U_1961,U_1964,U_1963)
| ~ c_Orderings_Oord__class_Oless(U_1961,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1964))
| ~ sP151(U_1961,U_1962,U_1963,U_1964) )
& ! [U_1961,U_1962,U_1963,U_1964] :
( sP151(U_1961,U_1962,U_1963,U_1964)
| ~ c_Orderings_Oord__class_Oless(U_1961,U_1962,c_Groups_Ozero__class_Ozero(U_1961))
| ~ class_Rings_Olinordered__ring__strict(U_1961) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151])],[f_690_2]) ).
cnf(f_690_4,plain,
( sP151(U_1961,U_1962,U_1963,U_1964)
| ~ c_Orderings_Oord__class_Oless(U_1961,U_1962,c_Groups_Ozero__class_Ozero(U_1961))
| ~ class_Rings_Olinordered__ring__strict(U_1961) ),
inference(clausify,[status(thm)],[f_690_3]) ).
cnf(f_690_5,plain,
( c_Orderings_Oord__class_Oless(U_1961,U_1964,U_1963)
| ~ c_Orderings_Oord__class_Oless(U_1961,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1964))
| ~ sP151(U_1961,U_1962,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_690_3]) ).
cnf(f_690_6,plain,
( c_Orderings_Oord__class_Oless(U_1961,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1963),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1961),U_1962),U_1964))
| ~ c_Orderings_Oord__class_Oless(U_1961,U_1964,U_1963)
| ~ sP151(U_1961,U_1962,U_1963,U_1964) ),
inference(clausify,[status(thm)],[f_690_3]) ).
fof(f_691_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),hAPP(hAPP(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_691_2,plain,
! [U_1967,U_1966,U_1965] :
( c_Orderings_Oord__class_Oless(U_1965,c_Groups_Ozero__class_Ozero(U_1965),U_1966)
| ~ c_Orderings_Oord__class_Oless(U_1965,c_Groups_Ozero__class_Ozero(U_1965),U_1967)
| ~ c_Orderings_Oord__class_Oless(U_1965,c_Groups_Ozero__class_Ozero(U_1965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),U_1967))
| ~ class_Rings_Olinordered__semiring__strict(U_1965) ),
inference(variable_rename,[status(thm)],[f_691_1]) ).
fof(f_691_3,plain,
! [U_1967,U_1965,U_1966] :
( c_Orderings_Oord__class_Oless(U_1965,c_Groups_Ozero__class_Ozero(U_1965),U_1966)
| ~ c_Orderings_Oord__class_Oless(U_1965,c_Groups_Ozero__class_Ozero(U_1965),U_1967)
| ~ c_Orderings_Oord__class_Oless(U_1965,c_Groups_Ozero__class_Ozero(U_1965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),U_1967))
| ~ class_Rings_Olinordered__semiring__strict(U_1965) ),
inference(definitional_conversion,[status(esa)],[f_691_2]) ).
cnf(f_691_4,plain,
( c_Orderings_Oord__class_Oless(U_1965,c_Groups_Ozero__class_Ozero(U_1965),U_1966)
| ~ c_Orderings_Oord__class_Oless(U_1965,c_Groups_Ozero__class_Ozero(U_1965),U_1967)
| ~ c_Orderings_Oord__class_Oless(U_1965,c_Groups_Ozero__class_Ozero(U_1965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1965),U_1966),U_1967))
| ~ class_Rings_Olinordered__semiring__strict(U_1965) ),
inference(clausify,[status(thm)],[f_691_3]) ).
fof(f_692_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),hAPP(hAPP(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_692_2,plain,
! [U_1970,U_1969,U_1968] :
( c_Orderings_Oord__class_Oless(U_1968,c_Groups_Ozero__class_Ozero(U_1968),U_1970)
| ~ c_Orderings_Oord__class_Oless(U_1968,c_Groups_Ozero__class_Ozero(U_1968),U_1969)
| ~ c_Orderings_Oord__class_Oless(U_1968,c_Groups_Ozero__class_Ozero(U_1968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1968),U_1969),U_1970))
| ~ class_Rings_Olinordered__semiring__strict(U_1968) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
fof(f_692_3,plain,
! [U_1969,U_1970,U_1968] :
( c_Orderings_Oord__class_Oless(U_1968,c_Groups_Ozero__class_Ozero(U_1968),U_1970)
| ~ c_Orderings_Oord__class_Oless(U_1968,c_Groups_Ozero__class_Ozero(U_1968),U_1969)
| ~ c_Orderings_Oord__class_Oless(U_1968,c_Groups_Ozero__class_Ozero(U_1968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1968),U_1969),U_1970))
| ~ class_Rings_Olinordered__semiring__strict(U_1968) ),
inference(definitional_conversion,[status(esa)],[f_692_2]) ).
cnf(f_692_4,plain,
( c_Orderings_Oord__class_Oless(U_1968,c_Groups_Ozero__class_Ozero(U_1968),U_1970)
| ~ c_Orderings_Oord__class_Oless(U_1968,c_Groups_Ozero__class_Ozero(U_1968),U_1969)
| ~ c_Orderings_Oord__class_Oless(U_1968,c_Groups_Ozero__class_Ozero(U_1968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1968),U_1969),U_1970))
| ~ class_Rings_Olinordered__semiring__strict(U_1968) ),
inference(clausify,[status(thm)],[f_692_3]) ).
fof(f_693_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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_693_2,plain,
! [U_1973,U_1972,U_1971] :
( c_Orderings_Oord__class_Oless(U_1971,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1971),U_1973),U_1972),c_Groups_Ozero__class_Ozero(U_1971))
| ~ c_Orderings_Oord__class_Oless(U_1971,U_1973,c_Groups_Ozero__class_Ozero(U_1971))
| ~ c_Orderings_Oord__class_Oless(U_1971,c_Groups_Ozero__class_Ozero(U_1971),U_1972)
| ~ class_Rings_Olinordered__semiring__strict(U_1971) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
fof(f_693_3,plain,
! [U_1972,U_1973,U_1971] :
( c_Orderings_Oord__class_Oless(U_1971,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1971),U_1973),U_1972),c_Groups_Ozero__class_Ozero(U_1971))
| ~ c_Orderings_Oord__class_Oless(U_1971,U_1973,c_Groups_Ozero__class_Ozero(U_1971))
| ~ c_Orderings_Oord__class_Oless(U_1971,c_Groups_Ozero__class_Ozero(U_1971),U_1972)
| ~ class_Rings_Olinordered__semiring__strict(U_1971) ),
inference(definitional_conversion,[status(esa)],[f_693_2]) ).
cnf(f_693_4,plain,
( c_Orderings_Oord__class_Oless(U_1971,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1971),U_1973),U_1972),c_Groups_Ozero__class_Ozero(U_1971))
| ~ c_Orderings_Oord__class_Oless(U_1971,U_1973,c_Groups_Ozero__class_Ozero(U_1971))
| ~ c_Orderings_Oord__class_Oless(U_1971,c_Groups_Ozero__class_Ozero(U_1971),U_1972)
| ~ class_Rings_Olinordered__semiring__strict(U_1971) ),
inference(clausify,[status(thm)],[f_693_3]) ).
fof(f_694_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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_694_2,plain,
! [U_1976,U_1975,U_1974] :
( c_Orderings_Oord__class_Oless(U_1974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1976),c_Groups_Ozero__class_Ozero(U_1974))
| ~ c_Orderings_Oord__class_Oless(U_1974,U_1976,c_Groups_Ozero__class_Ozero(U_1974))
| ~ c_Orderings_Oord__class_Oless(U_1974,c_Groups_Ozero__class_Ozero(U_1974),U_1975)
| ~ class_Rings_Olinordered__semiring__strict(U_1974) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
fof(f_694_3,plain,
! [U_1975,U_1976,U_1974] :
( c_Orderings_Oord__class_Oless(U_1974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1976),c_Groups_Ozero__class_Ozero(U_1974))
| ~ c_Orderings_Oord__class_Oless(U_1974,U_1976,c_Groups_Ozero__class_Ozero(U_1974))
| ~ c_Orderings_Oord__class_Oless(U_1974,c_Groups_Ozero__class_Ozero(U_1974),U_1975)
| ~ class_Rings_Olinordered__semiring__strict(U_1974) ),
inference(definitional_conversion,[status(esa)],[f_694_2]) ).
cnf(f_694_4,plain,
( c_Orderings_Oord__class_Oless(U_1974,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1974),U_1975),U_1976),c_Groups_Ozero__class_Ozero(U_1974))
| ~ c_Orderings_Oord__class_Oless(U_1974,U_1976,c_Groups_Ozero__class_Ozero(U_1974))
| ~ c_Orderings_Oord__class_Oless(U_1974,c_Groups_Ozero__class_Ozero(U_1974),U_1975)
| ~ class_Rings_Olinordered__semiring__strict(U_1974) ),
inference(clausify,[status(thm)],[f_694_3]) ).
fof(f_695_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_695_2,plain,
! [U_1979,U_1978,U_1977] :
( c_Orderings_Oord__class_Oless(U_1977,c_Groups_Ozero__class_Ozero(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1977),U_1978),U_1979))
| ~ c_Orderings_Oord__class_Oless(U_1977,c_Groups_Ozero__class_Ozero(U_1977),U_1979)
| ~ c_Orderings_Oord__class_Oless(U_1977,c_Groups_Ozero__class_Ozero(U_1977),U_1978)
| ~ class_Rings_Olinordered__semiring__strict(U_1977) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
fof(f_695_3,plain,
! [U_1977,U_1978,U_1979] :
( c_Orderings_Oord__class_Oless(U_1977,c_Groups_Ozero__class_Ozero(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1977),U_1978),U_1979))
| ~ c_Orderings_Oord__class_Oless(U_1977,c_Groups_Ozero__class_Ozero(U_1977),U_1979)
| ~ c_Orderings_Oord__class_Oless(U_1977,c_Groups_Ozero__class_Ozero(U_1977),U_1978)
| ~ class_Rings_Olinordered__semiring__strict(U_1977) ),
inference(definitional_conversion,[status(esa)],[f_695_2]) ).
cnf(f_695_4,plain,
( c_Orderings_Oord__class_Oless(U_1977,c_Groups_Ozero__class_Ozero(U_1977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1977),U_1978),U_1979))
| ~ c_Orderings_Oord__class_Oless(U_1977,c_Groups_Ozero__class_Ozero(U_1977),U_1979)
| ~ c_Orderings_Oord__class_Oless(U_1977,c_Groups_Ozero__class_Ozero(U_1977),U_1978)
| ~ class_Rings_Olinordered__semiring__strict(U_1977) ),
inference(clausify,[status(thm)],[f_695_3]) ).
fof(f_696_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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_696_2,plain,
! [U_1983,U_1982,U_1981,U_1980] :
( ( ( c_Orderings_Oord__class_Oless(U_1980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1983))
| ~ c_Orderings_Oord__class_Oless(U_1980,U_1982,U_1983) )
& ( c_Orderings_Oord__class_Oless(U_1980,U_1982,U_1983)
| ~ c_Orderings_Oord__class_Oless(U_1980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1983)) ) )
| ~ c_Orderings_Oord__class_Oless(U_1980,c_Groups_Ozero__class_Ozero(U_1980),U_1981)
| ~ class_Rings_Olinordered__ring__strict(U_1980) ),
inference(variable_rename,[status(thm)],[f_696_1]) ).
fof(f_696_3,plain,
( ! [U_1980,U_1981,U_1982,U_1983] :
( c_Orderings_Oord__class_Oless(U_1980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1983))
| ~ c_Orderings_Oord__class_Oless(U_1980,U_1982,U_1983)
| ~ sP152(U_1980,U_1981,U_1982,U_1983) )
& ! [U_1980,U_1981,U_1982,U_1983] :
( c_Orderings_Oord__class_Oless(U_1980,U_1982,U_1983)
| ~ c_Orderings_Oord__class_Oless(U_1980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1983))
| ~ sP152(U_1980,U_1981,U_1982,U_1983) )
& ! [U_1980,U_1981,U_1982,U_1983] :
( sP152(U_1980,U_1981,U_1982,U_1983)
| ~ c_Orderings_Oord__class_Oless(U_1980,c_Groups_Ozero__class_Ozero(U_1980),U_1981)
| ~ class_Rings_Olinordered__ring__strict(U_1980) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_696_2]) ).
cnf(f_696_4,plain,
( sP152(U_1980,U_1981,U_1982,U_1983)
| ~ c_Orderings_Oord__class_Oless(U_1980,c_Groups_Ozero__class_Ozero(U_1980),U_1981)
| ~ class_Rings_Olinordered__ring__strict(U_1980) ),
inference(clausify,[status(thm)],[f_696_3]) ).
cnf(f_696_5,plain,
( c_Orderings_Oord__class_Oless(U_1980,U_1982,U_1983)
| ~ c_Orderings_Oord__class_Oless(U_1980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1983))
| ~ sP152(U_1980,U_1981,U_1982,U_1983) ),
inference(clausify,[status(thm)],[f_696_3]) ).
cnf(f_696_6,plain,
( c_Orderings_Oord__class_Oless(U_1980,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1982),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1980),U_1981),U_1983))
| ~ c_Orderings_Oord__class_Oless(U_1980,U_1982,U_1983)
| ~ sP152(U_1980,U_1981,U_1982,U_1983) ),
inference(clausify,[status(thm)],[f_696_3]) ).
fof(f_697_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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_697_2,plain,
! [U_1987,U_1986,U_1985,U_1984] :
( ( ( c_Orderings_Oord__class_Oless(U_1984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1987))
| ( ( ~ c_Orderings_Oord__class_Oless(U_1984,U_1987,U_1986)
| ~ c_Orderings_Oord__class_Oless(U_1984,U_1985,c_Groups_Ozero__class_Ozero(U_1984)) )
& ( ~ c_Orderings_Oord__class_Oless(U_1984,U_1986,U_1987)
| ~ c_Orderings_Oord__class_Oless(U_1984,c_Groups_Ozero__class_Ozero(U_1984),U_1985) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_1984,U_1987,U_1986)
& c_Orderings_Oord__class_Oless(U_1984,U_1985,c_Groups_Ozero__class_Ozero(U_1984)) )
| ( c_Orderings_Oord__class_Oless(U_1984,U_1986,U_1987)
& c_Orderings_Oord__class_Oless(U_1984,c_Groups_Ozero__class_Ozero(U_1984),U_1985) )
| ~ c_Orderings_Oord__class_Oless(U_1984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1987)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1984) ),
inference(variable_rename,[status(thm)],[f_697_1]) ).
fof(f_697_3,plain,
( ! [U_1985,U_1984,U_1986,U_1987] :
( ~ c_Orderings_Oord__class_Oless(U_1984,U_1987,U_1986)
| ~ c_Orderings_Oord__class_Oless(U_1984,U_1985,c_Groups_Ozero__class_Ozero(U_1984))
| ~ sP155(U_1985,U_1984,U_1986,U_1987) )
& ! [U_1985,U_1984,U_1986,U_1987] :
( ~ c_Orderings_Oord__class_Oless(U_1984,U_1986,U_1987)
| ~ c_Orderings_Oord__class_Oless(U_1984,c_Groups_Ozero__class_Ozero(U_1984),U_1985)
| ~ sP155(U_1985,U_1984,U_1986,U_1987) )
& ! [U_1985,U_1984,U_1986,U_1987] :
( c_Orderings_Oord__class_Oless(U_1984,U_1987,U_1986)
| ~ sP154(U_1985,U_1984,U_1986,U_1987) )
& ! [U_1985,U_1984,U_1986,U_1987] :
( c_Orderings_Oord__class_Oless(U_1984,U_1985,c_Groups_Ozero__class_Ozero(U_1984))
| ~ sP154(U_1985,U_1984,U_1986,U_1987) )
& ! [U_1985,U_1984,U_1986,U_1987] :
( c_Orderings_Oord__class_Oless(U_1984,U_1986,U_1987)
| ~ sP153(U_1985,U_1984,U_1986,U_1987) )
& ! [U_1985,U_1984,U_1986,U_1987] :
( c_Orderings_Oord__class_Oless(U_1984,c_Groups_Ozero__class_Ozero(U_1984),U_1985)
| ~ sP153(U_1985,U_1984,U_1986,U_1987) )
& ! [U_1985,U_1984,U_1986,U_1987] :
( c_Orderings_Oord__class_Oless(U_1984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1987))
| sP155(U_1985,U_1984,U_1986,U_1987)
| ~ sP156(U_1985,U_1984,U_1986,U_1987) )
& ! [U_1985,U_1984,U_1986,U_1987] :
( sP154(U_1985,U_1984,U_1986,U_1987)
| sP153(U_1985,U_1984,U_1986,U_1987)
| ~ c_Orderings_Oord__class_Oless(U_1984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1987))
| ~ sP156(U_1985,U_1984,U_1986,U_1987) )
& ! [U_1985,U_1984,U_1986,U_1987] :
( sP156(U_1985,U_1984,U_1986,U_1987)
| ~ class_Rings_Olinordered__ring__strict(U_1984) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153,sP154,sP155,sP156])],[f_697_2]) ).
cnf(f_697_4,plain,
( sP156(U_1985,U_1984,U_1986,U_1987)
| ~ class_Rings_Olinordered__ring__strict(U_1984) ),
inference(clausify,[status(thm)],[f_697_3]) ).
cnf(f_697_5,plain,
( sP154(U_1985,U_1984,U_1986,U_1987)
| sP153(U_1985,U_1984,U_1986,U_1987)
| ~ c_Orderings_Oord__class_Oless(U_1984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1987))
| ~ sP156(U_1985,U_1984,U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_697_3]) ).
cnf(f_697_6,plain,
( c_Orderings_Oord__class_Oless(U_1984,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1986),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1984),U_1985),U_1987))
| sP155(U_1985,U_1984,U_1986,U_1987)
| ~ sP156(U_1985,U_1984,U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_697_3]) ).
cnf(f_697_7,plain,
( c_Orderings_Oord__class_Oless(U_1984,c_Groups_Ozero__class_Ozero(U_1984),U_1985)
| ~ sP153(U_1985,U_1984,U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_697_3]) ).
cnf(f_697_8,plain,
( c_Orderings_Oord__class_Oless(U_1984,U_1986,U_1987)
| ~ sP153(U_1985,U_1984,U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_697_3]) ).
cnf(f_697_9,plain,
( c_Orderings_Oord__class_Oless(U_1984,U_1985,c_Groups_Ozero__class_Ozero(U_1984))
| ~ sP154(U_1985,U_1984,U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_697_3]) ).
cnf(f_697_10,plain,
( c_Orderings_Oord__class_Oless(U_1984,U_1987,U_1986)
| ~ sP154(U_1985,U_1984,U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_697_3]) ).
cnf(f_697_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1984,U_1986,U_1987)
| ~ c_Orderings_Oord__class_Oless(U_1984,c_Groups_Ozero__class_Ozero(U_1984),U_1985)
| ~ sP155(U_1985,U_1984,U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_697_3]) ).
cnf(f_697_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1984,U_1987,U_1986)
| ~ c_Orderings_Oord__class_Oless(U_1984,U_1985,c_Groups_Ozero__class_Ozero(U_1984))
| ~ sP155(U_1985,U_1984,U_1986,U_1987) ),
inference(clausify,[status(thm)],[f_697_3]) ).
fof(f_698_1,plain,
! [V_b_2,V_c_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),hAPP(hAPP(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_698_2,plain,
! [U_1991,U_1990,U_1989,U_1988] :
( ( ( c_Orderings_Oord__class_Oless(U_1988,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1989),U_1990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1991),U_1990))
| ( ( ~ c_Orderings_Oord__class_Oless(U_1988,U_1991,U_1989)
| ~ c_Orderings_Oord__class_Oless(U_1988,U_1990,c_Groups_Ozero__class_Ozero(U_1988)) )
& ( ~ c_Orderings_Oord__class_Oless(U_1988,U_1989,U_1991)
| ~ c_Orderings_Oord__class_Oless(U_1988,c_Groups_Ozero__class_Ozero(U_1988),U_1990) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_1988,U_1991,U_1989)
& c_Orderings_Oord__class_Oless(U_1988,U_1990,c_Groups_Ozero__class_Ozero(U_1988)) )
| ( c_Orderings_Oord__class_Oless(U_1988,U_1989,U_1991)
& c_Orderings_Oord__class_Oless(U_1988,c_Groups_Ozero__class_Ozero(U_1988),U_1990) )
| ~ c_Orderings_Oord__class_Oless(U_1988,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1989),U_1990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1991),U_1990)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_1988) ),
inference(variable_rename,[status(thm)],[f_698_1]) ).
fof(f_698_3,plain,
( ! [U_1989,U_1991,U_1990,U_1988] :
( ~ c_Orderings_Oord__class_Oless(U_1988,U_1991,U_1989)
| ~ c_Orderings_Oord__class_Oless(U_1988,U_1990,c_Groups_Ozero__class_Ozero(U_1988))
| ~ sP159(U_1989,U_1991,U_1990,U_1988) )
& ! [U_1989,U_1991,U_1990,U_1988] :
( ~ c_Orderings_Oord__class_Oless(U_1988,U_1989,U_1991)
| ~ c_Orderings_Oord__class_Oless(U_1988,c_Groups_Ozero__class_Ozero(U_1988),U_1990)
| ~ sP159(U_1989,U_1991,U_1990,U_1988) )
& ! [U_1989,U_1991,U_1990,U_1988] :
( c_Orderings_Oord__class_Oless(U_1988,U_1991,U_1989)
| ~ sP158(U_1989,U_1991,U_1990,U_1988) )
& ! [U_1989,U_1991,U_1990,U_1988] :
( c_Orderings_Oord__class_Oless(U_1988,U_1990,c_Groups_Ozero__class_Ozero(U_1988))
| ~ sP158(U_1989,U_1991,U_1990,U_1988) )
& ! [U_1989,U_1991,U_1990,U_1988] :
( c_Orderings_Oord__class_Oless(U_1988,U_1989,U_1991)
| ~ sP157(U_1989,U_1991,U_1990,U_1988) )
& ! [U_1989,U_1991,U_1990,U_1988] :
( c_Orderings_Oord__class_Oless(U_1988,c_Groups_Ozero__class_Ozero(U_1988),U_1990)
| ~ sP157(U_1989,U_1991,U_1990,U_1988) )
& ! [U_1989,U_1991,U_1990,U_1988] :
( c_Orderings_Oord__class_Oless(U_1988,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1989),U_1990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1991),U_1990))
| sP159(U_1989,U_1991,U_1990,U_1988)
| ~ sP160(U_1989,U_1991,U_1990,U_1988) )
& ! [U_1989,U_1991,U_1990,U_1988] :
( sP158(U_1989,U_1991,U_1990,U_1988)
| sP157(U_1989,U_1991,U_1990,U_1988)
| ~ c_Orderings_Oord__class_Oless(U_1988,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1989),U_1990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1991),U_1990))
| ~ sP160(U_1989,U_1991,U_1990,U_1988) )
& ! [U_1989,U_1991,U_1990,U_1988] :
( sP160(U_1989,U_1991,U_1990,U_1988)
| ~ class_Rings_Olinordered__ring__strict(U_1988) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157,sP158,sP159,sP160])],[f_698_2]) ).
cnf(f_698_4,plain,
( sP160(U_1989,U_1991,U_1990,U_1988)
| ~ class_Rings_Olinordered__ring__strict(U_1988) ),
inference(clausify,[status(thm)],[f_698_3]) ).
cnf(f_698_5,plain,
( sP158(U_1989,U_1991,U_1990,U_1988)
| sP157(U_1989,U_1991,U_1990,U_1988)
| ~ c_Orderings_Oord__class_Oless(U_1988,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1989),U_1990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1991),U_1990))
| ~ sP160(U_1989,U_1991,U_1990,U_1988) ),
inference(clausify,[status(thm)],[f_698_3]) ).
cnf(f_698_6,plain,
( c_Orderings_Oord__class_Oless(U_1988,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1989),U_1990),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1988),U_1991),U_1990))
| sP159(U_1989,U_1991,U_1990,U_1988)
| ~ sP160(U_1989,U_1991,U_1990,U_1988) ),
inference(clausify,[status(thm)],[f_698_3]) ).
cnf(f_698_7,plain,
( c_Orderings_Oord__class_Oless(U_1988,c_Groups_Ozero__class_Ozero(U_1988),U_1990)
| ~ sP157(U_1989,U_1991,U_1990,U_1988) ),
inference(clausify,[status(thm)],[f_698_3]) ).
cnf(f_698_8,plain,
( c_Orderings_Oord__class_Oless(U_1988,U_1989,U_1991)
| ~ sP157(U_1989,U_1991,U_1990,U_1988) ),
inference(clausify,[status(thm)],[f_698_3]) ).
cnf(f_698_9,plain,
( c_Orderings_Oord__class_Oless(U_1988,U_1990,c_Groups_Ozero__class_Ozero(U_1988))
| ~ sP158(U_1989,U_1991,U_1990,U_1988) ),
inference(clausify,[status(thm)],[f_698_3]) ).
cnf(f_698_10,plain,
( c_Orderings_Oord__class_Oless(U_1988,U_1991,U_1989)
| ~ sP158(U_1989,U_1991,U_1990,U_1988) ),
inference(clausify,[status(thm)],[f_698_3]) ).
cnf(f_698_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_1988,U_1989,U_1991)
| ~ c_Orderings_Oord__class_Oless(U_1988,c_Groups_Ozero__class_Ozero(U_1988),U_1990)
| ~ sP159(U_1989,U_1991,U_1990,U_1988) ),
inference(clausify,[status(thm)],[f_698_3]) ).
cnf(f_698_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_1988,U_1991,U_1989)
| ~ c_Orderings_Oord__class_Oless(U_1988,U_1990,c_Groups_Ozero__class_Ozero(U_1988))
| ~ sP159(U_1989,U_1991,U_1990,U_1988) ),
inference(clausify,[status(thm)],[f_698_3]) ).
fof(f_699_1,plain,
! [V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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_699_2,plain,
! [U_1993,U_1992] :
( ~ c_Orderings_Oord__class_Oless(U_1992,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1992),U_1993),U_1993),c_Groups_Ozero__class_Ozero(U_1992))
| ~ class_Rings_Olinordered__ring(U_1992) ),
inference(variable_rename,[status(thm)],[f_699_1]) ).
fof(f_699_3,plain,
! [U_1992,U_1993] :
( ~ c_Orderings_Oord__class_Oless(U_1992,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1992),U_1993),U_1993),c_Groups_Ozero__class_Ozero(U_1992))
| ~ class_Rings_Olinordered__ring(U_1992) ),
inference(definitional_conversion,[status(esa)],[f_699_2]) ).
cnf(f_699_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_1992,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1992),U_1993),U_1993),c_Groups_Ozero__class_Ozero(U_1992))
| ~ class_Rings_Olinordered__ring(U_1992) ),
inference(clausify,[status(thm)],[f_699_3]) ).
fof(f_700_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_700_2,plain,
! [U_1996,U_1995,U_1994] :
( c_Orderings_Oord__class_Oless(U_1994,c_Groups_Oplus__class_Oplus(U_1994,U_1995,U_1996),c_Groups_Ozero__class_Ozero(U_1994))
| ~ c_Orderings_Oord__class_Oless(U_1994,U_1996,c_Groups_Ozero__class_Ozero(U_1994))
| ~ c_Orderings_Oord__class_Oless(U_1994,U_1995,c_Groups_Ozero__class_Ozero(U_1994))
| ~ class_Groups_Oordered__comm__monoid__add(U_1994) ),
inference(variable_rename,[status(thm)],[f_700_1]) ).
fof(f_700_3,plain,
! [U_1996,U_1995,U_1994] :
( c_Orderings_Oord__class_Oless(U_1994,c_Groups_Oplus__class_Oplus(U_1994,U_1995,U_1996),c_Groups_Ozero__class_Ozero(U_1994))
| ~ c_Orderings_Oord__class_Oless(U_1994,U_1996,c_Groups_Ozero__class_Ozero(U_1994))
| ~ c_Orderings_Oord__class_Oless(U_1994,U_1995,c_Groups_Ozero__class_Ozero(U_1994))
| ~ class_Groups_Oordered__comm__monoid__add(U_1994) ),
inference(definitional_conversion,[status(esa)],[f_700_2]) ).
cnf(f_700_4,plain,
( c_Orderings_Oord__class_Oless(U_1994,c_Groups_Oplus__class_Oplus(U_1994,U_1995,U_1996),c_Groups_Ozero__class_Ozero(U_1994))
| ~ c_Orderings_Oord__class_Oless(U_1994,U_1996,c_Groups_Ozero__class_Ozero(U_1994))
| ~ c_Orderings_Oord__class_Oless(U_1994,U_1995,c_Groups_Ozero__class_Ozero(U_1994))
| ~ class_Groups_Oordered__comm__monoid__add(U_1994) ),
inference(clausify,[status(thm)],[f_700_3]) ).
fof(f_701_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_701_2,plain,
! [U_1999,U_1998,U_1997] :
( c_Orderings_Oord__class_Oless(U_1997,c_Groups_Ozero__class_Ozero(U_1997),c_Groups_Oplus__class_Oplus(U_1997,U_1998,U_1999))
| ~ c_Orderings_Oord__class_Oless(U_1997,c_Groups_Ozero__class_Ozero(U_1997),U_1999)
| ~ c_Orderings_Oord__class_Oless(U_1997,c_Groups_Ozero__class_Ozero(U_1997),U_1998)
| ~ class_Groups_Oordered__comm__monoid__add(U_1997) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
fof(f_701_3,plain,
! [U_1997,U_1999,U_1998] :
( c_Orderings_Oord__class_Oless(U_1997,c_Groups_Ozero__class_Ozero(U_1997),c_Groups_Oplus__class_Oplus(U_1997,U_1998,U_1999))
| ~ c_Orderings_Oord__class_Oless(U_1997,c_Groups_Ozero__class_Ozero(U_1997),U_1999)
| ~ c_Orderings_Oord__class_Oless(U_1997,c_Groups_Ozero__class_Ozero(U_1997),U_1998)
| ~ class_Groups_Oordered__comm__monoid__add(U_1997) ),
inference(definitional_conversion,[status(esa)],[f_701_2]) ).
cnf(f_701_4,plain,
( c_Orderings_Oord__class_Oless(U_1997,c_Groups_Ozero__class_Ozero(U_1997),c_Groups_Oplus__class_Oplus(U_1997,U_1998,U_1999))
| ~ c_Orderings_Oord__class_Oless(U_1997,c_Groups_Ozero__class_Ozero(U_1997),U_1999)
| ~ c_Orderings_Oord__class_Oless(U_1997,c_Groups_Ozero__class_Ozero(U_1997),U_1998)
| ~ class_Groups_Oordered__comm__monoid__add(U_1997) ),
inference(clausify,[status(thm)],[f_701_3]) ).
fof(f_702_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_702_2,plain,
! [U_2001,U_2000] :
( ( ( c_Orderings_Oord__class_Oless(U_2000,c_Groups_Oplus__class_Oplus(U_2000,U_2001,U_2001),c_Groups_Ozero__class_Ozero(U_2000))
| ~ c_Orderings_Oord__class_Oless(U_2000,U_2001,c_Groups_Ozero__class_Ozero(U_2000)) )
& ( c_Orderings_Oord__class_Oless(U_2000,U_2001,c_Groups_Ozero__class_Ozero(U_2000))
| ~ c_Orderings_Oord__class_Oless(U_2000,c_Groups_Oplus__class_Oplus(U_2000,U_2001,U_2001),c_Groups_Ozero__class_Ozero(U_2000)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2000) ),
inference(variable_rename,[status(thm)],[f_702_1]) ).
fof(f_702_3,plain,
( ! [U_2001,U_2000] :
( c_Orderings_Oord__class_Oless(U_2000,c_Groups_Oplus__class_Oplus(U_2000,U_2001,U_2001),c_Groups_Ozero__class_Ozero(U_2000))
| ~ c_Orderings_Oord__class_Oless(U_2000,U_2001,c_Groups_Ozero__class_Ozero(U_2000))
| ~ sP161(U_2001,U_2000) )
& ! [U_2001,U_2000] :
( c_Orderings_Oord__class_Oless(U_2000,U_2001,c_Groups_Ozero__class_Ozero(U_2000))
| ~ c_Orderings_Oord__class_Oless(U_2000,c_Groups_Oplus__class_Oplus(U_2000,U_2001,U_2001),c_Groups_Ozero__class_Ozero(U_2000))
| ~ sP161(U_2001,U_2000) )
& ! [U_2001,U_2000] :
( sP161(U_2001,U_2000)
| ~ class_Groups_Olinordered__ab__group__add(U_2000) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_702_2]) ).
cnf(f_702_4,plain,
( sP161(U_2001,U_2000)
| ~ class_Groups_Olinordered__ab__group__add(U_2000) ),
inference(clausify,[status(thm)],[f_702_3]) ).
cnf(f_702_5,plain,
( c_Orderings_Oord__class_Oless(U_2000,U_2001,c_Groups_Ozero__class_Ozero(U_2000))
| ~ c_Orderings_Oord__class_Oless(U_2000,c_Groups_Oplus__class_Oplus(U_2000,U_2001,U_2001),c_Groups_Ozero__class_Ozero(U_2000))
| ~ sP161(U_2001,U_2000) ),
inference(clausify,[status(thm)],[f_702_3]) ).
cnf(f_702_6,plain,
( c_Orderings_Oord__class_Oless(U_2000,c_Groups_Oplus__class_Oplus(U_2000,U_2001,U_2001),c_Groups_Ozero__class_Ozero(U_2000))
| ~ c_Orderings_Oord__class_Oless(U_2000,U_2001,c_Groups_Ozero__class_Ozero(U_2000))
| ~ sP161(U_2001,U_2000) ),
inference(clausify,[status(thm)],[f_702_3]) ).
fof(f_703_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_703_2,plain,
! [U_2003,U_2002] :
( ( ( c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),c_Groups_Oplus__class_Oplus(U_2002,U_2003,U_2003))
| ~ c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),U_2003) )
& ( c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),U_2003)
| ~ c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),c_Groups_Oplus__class_Oplus(U_2002,U_2003,U_2003)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_2002) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
fof(f_703_3,plain,
( ! [U_2003,U_2002] :
( c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),c_Groups_Oplus__class_Oplus(U_2002,U_2003,U_2003))
| ~ c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),U_2003)
| ~ sP162(U_2003,U_2002) )
& ! [U_2003,U_2002] :
( c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),U_2003)
| ~ c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),c_Groups_Oplus__class_Oplus(U_2002,U_2003,U_2003))
| ~ sP162(U_2003,U_2002) )
& ! [U_2003,U_2002] :
( sP162(U_2003,U_2002)
| ~ class_Groups_Olinordered__ab__group__add(U_2002) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162])],[f_703_2]) ).
cnf(f_703_4,plain,
( sP162(U_2003,U_2002)
| ~ class_Groups_Olinordered__ab__group__add(U_2002) ),
inference(clausify,[status(thm)],[f_703_3]) ).
cnf(f_703_5,plain,
( c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),U_2003)
| ~ c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),c_Groups_Oplus__class_Oplus(U_2002,U_2003,U_2003))
| ~ sP162(U_2003,U_2002) ),
inference(clausify,[status(thm)],[f_703_3]) ).
cnf(f_703_6,plain,
( c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),c_Groups_Oplus__class_Oplus(U_2002,U_2003,U_2003))
| ~ c_Orderings_Oord__class_Oless(U_2002,c_Groups_Ozero__class_Ozero(U_2002),U_2003)
| ~ sP162(U_2003,U_2002) ),
inference(clausify,[status(thm)],[f_703_3]) ).
fof(f_704_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_704_2,plain,
! [U_2005,U_2004] :
( ( ( c_Orderings_Oord__class_Oless(U_2004,c_Groups_Oplus__class_Oplus(U_2004,U_2005,U_2005),c_Groups_Ozero__class_Ozero(U_2004))
| ~ c_Orderings_Oord__class_Oless(U_2004,U_2005,c_Groups_Ozero__class_Ozero(U_2004)) )
& ( c_Orderings_Oord__class_Oless(U_2004,U_2005,c_Groups_Ozero__class_Ozero(U_2004))
| ~ c_Orderings_Oord__class_Oless(U_2004,c_Groups_Oplus__class_Oplus(U_2004,U_2005,U_2005),c_Groups_Ozero__class_Ozero(U_2004)) ) )
| ~ class_Rings_Olinordered__idom(U_2004) ),
inference(variable_rename,[status(thm)],[f_704_1]) ).
fof(f_704_3,plain,
( ! [U_2005,U_2004] :
( c_Orderings_Oord__class_Oless(U_2004,c_Groups_Oplus__class_Oplus(U_2004,U_2005,U_2005),c_Groups_Ozero__class_Ozero(U_2004))
| ~ c_Orderings_Oord__class_Oless(U_2004,U_2005,c_Groups_Ozero__class_Ozero(U_2004))
| ~ sP163(U_2005,U_2004) )
& ! [U_2005,U_2004] :
( c_Orderings_Oord__class_Oless(U_2004,U_2005,c_Groups_Ozero__class_Ozero(U_2004))
| ~ c_Orderings_Oord__class_Oless(U_2004,c_Groups_Oplus__class_Oplus(U_2004,U_2005,U_2005),c_Groups_Ozero__class_Ozero(U_2004))
| ~ sP163(U_2005,U_2004) )
& ! [U_2005,U_2004] :
( sP163(U_2005,U_2004)
| ~ class_Rings_Olinordered__idom(U_2004) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_704_2]) ).
cnf(f_704_4,plain,
( sP163(U_2005,U_2004)
| ~ class_Rings_Olinordered__idom(U_2004) ),
inference(clausify,[status(thm)],[f_704_3]) ).
cnf(f_704_5,plain,
( c_Orderings_Oord__class_Oless(U_2004,U_2005,c_Groups_Ozero__class_Ozero(U_2004))
| ~ c_Orderings_Oord__class_Oless(U_2004,c_Groups_Oplus__class_Oplus(U_2004,U_2005,U_2005),c_Groups_Ozero__class_Ozero(U_2004))
| ~ sP163(U_2005,U_2004) ),
inference(clausify,[status(thm)],[f_704_3]) ).
cnf(f_704_6,plain,
( c_Orderings_Oord__class_Oless(U_2004,c_Groups_Oplus__class_Oplus(U_2004,U_2005,U_2005),c_Groups_Ozero__class_Ozero(U_2004))
| ~ c_Orderings_Oord__class_Oless(U_2004,U_2005,c_Groups_Ozero__class_Ozero(U_2004))
| ~ sP163(U_2005,U_2004) ),
inference(clausify,[status(thm)],[f_704_3]) ).
fof(f_705_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_705_2,plain,
! [U_2009,U_2008,U_2007,U_2006] :
( c_Orderings_Oord__class_Oless(U_2006,U_2008,c_Groups_Oplus__class_Oplus(U_2006,U_2007,U_2009))
| ~ c_Orderings_Oord__class_Oless(U_2006,U_2008,U_2009)
| ~ c_Orderings_Oord__class_Oless(U_2006,c_Groups_Ozero__class_Ozero(U_2006),U_2007)
| ~ class_Rings_Olinordered__semidom(U_2006) ),
inference(variable_rename,[status(thm)],[f_705_1]) ).
fof(f_705_3,plain,
! [U_2009,U_2007,U_2008,U_2006] :
( c_Orderings_Oord__class_Oless(U_2006,U_2008,c_Groups_Oplus__class_Oplus(U_2006,U_2007,U_2009))
| ~ c_Orderings_Oord__class_Oless(U_2006,U_2008,U_2009)
| ~ c_Orderings_Oord__class_Oless(U_2006,c_Groups_Ozero__class_Ozero(U_2006),U_2007)
| ~ class_Rings_Olinordered__semidom(U_2006) ),
inference(definitional_conversion,[status(esa)],[f_705_2]) ).
cnf(f_705_4,plain,
( c_Orderings_Oord__class_Oless(U_2006,U_2008,c_Groups_Oplus__class_Oplus(U_2006,U_2007,U_2009))
| ~ c_Orderings_Oord__class_Oless(U_2006,U_2008,U_2009)
| ~ c_Orderings_Oord__class_Oless(U_2006,c_Groups_Ozero__class_Ozero(U_2006),U_2007)
| ~ class_Rings_Olinordered__semidom(U_2006) ),
inference(clausify,[status(thm)],[f_705_3]) ).
fof(f_706_1,plain,
c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_arctan__zero__zero]) ).
fof(f_706_2,plain,
c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_706_1]) ).
cnf(f_706_3,plain,
c_Transcendental_Oarctan(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_706_2]) ).
fof(f_707_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_arctan__monotone_H]) ).
fof(f_707_2,plain,
! [U_2011,U_2010] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(U_2010),c_Transcendental_Oarctan(U_2011))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2010,U_2011) ),
inference(variable_rename,[status(thm)],[f_707_1]) ).
fof(f_707_3,plain,
! [U_2011,U_2010] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(U_2010),c_Transcendental_Oarctan(U_2011))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2010,U_2011) ),
inference(definitional_conversion,[status(esa)],[f_707_2]) ).
cnf(f_707_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Transcendental_Oarctan(U_2010),c_Transcendental_Oarctan(U_2011))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2010,U_2011) ),
inference(clausify,[status(thm)],[f_707_3]) ).
fof(f_708_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_arctan__monotone]) ).
fof(f_708_2,plain,
! [U_2013,U_2012] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(U_2012),c_Transcendental_Oarctan(U_2013))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2012,U_2013) ),
inference(variable_rename,[status(thm)],[f_708_1]) ).
fof(f_708_3,plain,
! [U_2012,U_2013] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(U_2012),c_Transcendental_Oarctan(U_2013))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2012,U_2013) ),
inference(definitional_conversion,[status(esa)],[f_708_2]) ).
cnf(f_708_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Oarctan(U_2012),c_Transcendental_Oarctan(U_2013))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2012,U_2013) ),
inference(clausify,[status(thm)],[f_708_3]) ).
fof(f_709_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_709_2,plain,
! [U_2015,U_2014] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2014),c_NthRoot_Osqrt(U_2015))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2014,U_2015) ),
inference(variable_rename,[status(thm)],[f_709_1]) ).
fof(f_709_3,plain,
! [U_2015,U_2014] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2014),c_NthRoot_Osqrt(U_2015))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2014,U_2015) ),
inference(definitional_conversion,[status(esa)],[f_709_2]) ).
cnf(f_709_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2014),c_NthRoot_Osqrt(U_2015))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2014,U_2015) ),
inference(clausify,[status(thm)],[f_709_3]) ).
fof(f_710_1,plain,
! [V_ya_2,V_xa_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_NthRoot_Osqrt(V_ya_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__less__iff]) ).
fof(f_710_2,plain,
! [U_2017,U_2016] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2016),c_NthRoot_Osqrt(U_2017))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2016,U_2017) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2016,U_2017)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2016),c_NthRoot_Osqrt(U_2017)) ) ),
inference(variable_rename,[status(thm)],[f_710_1]) ).
fof(f_710_3,plain,
( ! [U_2021,U_2019] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2019),c_NthRoot_Osqrt(U_2021))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2019,U_2021) )
& ! [U_2020,U_2018] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2018,U_2020)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2018),c_NthRoot_Osqrt(U_2020)) ) ),
inference(miniscope,[status(thm)],[f_710_2]) ).
fof(f_710_4,plain,
( ! [U_2021,U_2019] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2019),c_NthRoot_Osqrt(U_2021))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2019,U_2021) )
& ! [U_2020,U_2018] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2018,U_2020)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2018),c_NthRoot_Osqrt(U_2020)) ) ),
inference(definitional_conversion,[status(esa)],[f_710_3]) ).
cnf(f_710_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2018,U_2020)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2018),c_NthRoot_Osqrt(U_2020)) ),
inference(clausify,[status(thm)],[f_710_4]) ).
cnf(f_710_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2019),c_NthRoot_Osqrt(U_2021))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2019,U_2021) ),
inference(clausify,[status(thm)],[f_710_4]) ).
fof(f_711_1,plain,
! [V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_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_711_2,plain,
! [U_2023,U_2022] :
( ( ( c_Orderings_Oord__class_Oless(U_2022,c_Int_Onumber__class_Onumber__of(U_2022,U_2023),c_Groups_Ozero__class_Ozero(U_2022))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2023,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2023,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(U_2022,c_Int_Onumber__class_Onumber__of(U_2022,U_2023),c_Groups_Ozero__class_Ozero(U_2022)) ) )
| ~ class_Rings_Olinordered__idom(U_2022)
| ~ class_Int_Onumber__ring(U_2022) ),
inference(variable_rename,[status(thm)],[f_711_1]) ).
fof(f_711_3,plain,
( ! [U_2023,U_2022] :
( c_Orderings_Oord__class_Oless(U_2022,c_Int_Onumber__class_Onumber__of(U_2022,U_2023),c_Groups_Ozero__class_Ozero(U_2022))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2023,c_Int_OPls)
| ~ sP164(U_2023,U_2022) )
& ! [U_2023,U_2022] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2023,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(U_2022,c_Int_Onumber__class_Onumber__of(U_2022,U_2023),c_Groups_Ozero__class_Ozero(U_2022))
| ~ sP164(U_2023,U_2022) )
& ! [U_2023,U_2022] :
( sP164(U_2023,U_2022)
| ~ class_Rings_Olinordered__idom(U_2022)
| ~ class_Int_Onumber__ring(U_2022) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164])],[f_711_2]) ).
cnf(f_711_4,plain,
( sP164(U_2023,U_2022)
| ~ class_Rings_Olinordered__idom(U_2022)
| ~ class_Int_Onumber__ring(U_2022) ),
inference(clausify,[status(thm)],[f_711_3]) ).
cnf(f_711_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2023,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(U_2022,c_Int_Onumber__class_Onumber__of(U_2022,U_2023),c_Groups_Ozero__class_Ozero(U_2022))
| ~ sP164(U_2023,U_2022) ),
inference(clausify,[status(thm)],[f_711_3]) ).
cnf(f_711_6,plain,
( c_Orderings_Oord__class_Oless(U_2022,c_Int_Onumber__class_Onumber__of(U_2022,U_2023),c_Groups_Ozero__class_Ozero(U_2022))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2023,c_Int_OPls)
| ~ sP164(U_2023,U_2022) ),
inference(clausify,[status(thm)],[f_711_3]) ).
fof(f_712_1,plain,
! [V_ya_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_ya_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_ya_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,V_ya_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_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_712_2,plain,
! [U_2025,U_2024] :
( ( ( c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),c_Int_Onumber__class_Onumber__of(U_2024,U_2025))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2025) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2025)
| ~ c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),c_Int_Onumber__class_Onumber__of(U_2024,U_2025)) ) )
| ~ class_Rings_Olinordered__idom(U_2024)
| ~ class_Int_Onumber__ring(U_2024) ),
inference(variable_rename,[status(thm)],[f_712_1]) ).
fof(f_712_3,plain,
( ! [U_2025,U_2024] :
( c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),c_Int_Onumber__class_Onumber__of(U_2024,U_2025))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2025)
| ~ sP165(U_2025,U_2024) )
& ! [U_2025,U_2024] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2025)
| ~ c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),c_Int_Onumber__class_Onumber__of(U_2024,U_2025))
| ~ sP165(U_2025,U_2024) )
& ! [U_2025,U_2024] :
( sP165(U_2025,U_2024)
| ~ class_Rings_Olinordered__idom(U_2024)
| ~ class_Int_Onumber__ring(U_2024) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_712_2]) ).
cnf(f_712_4,plain,
( sP165(U_2025,U_2024)
| ~ class_Rings_Olinordered__idom(U_2024)
| ~ class_Int_Onumber__ring(U_2024) ),
inference(clausify,[status(thm)],[f_712_3]) ).
cnf(f_712_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2025)
| ~ c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),c_Int_Onumber__class_Onumber__of(U_2024,U_2025))
| ~ sP165(U_2025,U_2024) ),
inference(clausify,[status(thm)],[f_712_3]) ).
cnf(f_712_6,plain,
( c_Orderings_Oord__class_Oless(U_2024,c_Groups_Ozero__class_Ozero(U_2024),c_Int_Onumber__class_Onumber__of(U_2024,U_2025))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2025)
| ~ sP165(U_2025,U_2024) ),
inference(clausify,[status(thm)],[f_712_3]) ).
fof(f_713_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N),hAPP(hAPP(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_713_2,plain,
! [U_2029,U_2028,U_2027,U_2026] :
( c_Orderings_Oord__class_Oless(U_2026,hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2029),U_2028),hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2029),U_2027))
| ~ c_Orderings_Oord__class_Oless(U_2026,U_2029,c_Groups_Oone__class_Oone(U_2026))
| ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ozero__class_Ozero(U_2026),U_2029)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2027,U_2028)
| ~ class_Rings_Olinordered__semidom(U_2026) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
! [U_2026,U_2027,U_2028,U_2029] :
( c_Orderings_Oord__class_Oless(U_2026,hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2029),U_2028),hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2029),U_2027))
| ~ c_Orderings_Oord__class_Oless(U_2026,U_2029,c_Groups_Oone__class_Oone(U_2026))
| ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ozero__class_Ozero(U_2026),U_2029)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2027,U_2028)
| ~ class_Rings_Olinordered__semidom(U_2026) ),
inference(definitional_conversion,[status(esa)],[f_713_2]) ).
cnf(f_713_4,plain,
( c_Orderings_Oord__class_Oless(U_2026,hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2029),U_2028),hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2029),U_2027))
| ~ c_Orderings_Oord__class_Oless(U_2026,U_2029,c_Groups_Oone__class_Oone(U_2026))
| ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Ozero__class_Ozero(U_2026),U_2029)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2027,U_2028)
| ~ class_Rings_Olinordered__semidom(U_2026) ),
inference(clausify,[status(thm)],[f_713_3]) ).
fof(f_714_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(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_714_2,plain,
! [U_2032,U_2031,U_2030] :
( c_Orderings_Oord__class_Oless(U_2030,c_Groups_Oone__class_Oone(U_2030),hAPP(hAPP(c_Power_Opower__class_Opower(U_2030),U_2031),U_2032))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2032)
| ~ c_Orderings_Oord__class_Oless(U_2030,c_Groups_Oone__class_Oone(U_2030),U_2031)
| ~ class_Rings_Olinordered__semidom(U_2030) ),
inference(variable_rename,[status(thm)],[f_714_1]) ).
fof(f_714_3,plain,
! [U_2030,U_2031,U_2032] :
( c_Orderings_Oord__class_Oless(U_2030,c_Groups_Oone__class_Oone(U_2030),hAPP(hAPP(c_Power_Opower__class_Opower(U_2030),U_2031),U_2032))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2032)
| ~ c_Orderings_Oord__class_Oless(U_2030,c_Groups_Oone__class_Oone(U_2030),U_2031)
| ~ class_Rings_Olinordered__semidom(U_2030) ),
inference(definitional_conversion,[status(esa)],[f_714_2]) ).
cnf(f_714_4,plain,
( c_Orderings_Oord__class_Oless(U_2030,c_Groups_Oone__class_Oone(U_2030),hAPP(hAPP(c_Power_Opower__class_Opower(U_2030),U_2031),U_2032))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2032)
| ~ c_Orderings_Oord__class_Oless(U_2030,c_Groups_Oone__class_Oone(U_2030),U_2031)
| ~ class_Rings_Olinordered__semidom(U_2030) ),
inference(clausify,[status(thm)],[f_714_3]) ).
fof(f_715_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_715_2,plain,
! [U_2034,U_2033] :
( ~ c_Orderings_Oord__class_Oless(U_2033,U_2034,U_2034)
| ~ class_Orderings_Opreorder(U_2033) ),
inference(variable_rename,[status(thm)],[f_715_1]) ).
fof(f_715_3,plain,
! [U_2033,U_2034] :
( ~ c_Orderings_Oord__class_Oless(U_2033,U_2034,U_2034)
| ~ class_Orderings_Opreorder(U_2033) ),
inference(definitional_conversion,[status(esa)],[f_715_2]) ).
cnf(f_715_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2033,U_2034,U_2034)
| ~ class_Orderings_Opreorder(U_2033) ),
inference(clausify,[status(thm)],[f_715_3]) ).
fof(f_716_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( V_xa_2 != V_ya_2
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)
& ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)
| c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
| V_xa_2 = V_ya_2 ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).
fof(f_716_2,plain,
! [U_2037,U_2036,U_2035] :
( ( ( U_2036 != U_2037
| ( ~ c_Orderings_Oord__class_Oless(U_2035,U_2037,U_2036)
& ~ c_Orderings_Oord__class_Oless(U_2035,U_2036,U_2037) ) )
& ( c_Orderings_Oord__class_Oless(U_2035,U_2037,U_2036)
| c_Orderings_Oord__class_Oless(U_2035,U_2036,U_2037)
| U_2036 = U_2037 ) )
| ~ class_Orderings_Olinorder(U_2035) ),
inference(variable_rename,[status(thm)],[f_716_1]) ).
fof(f_716_3,plain,
( ! [U_2035,U_2036,U_2037] :
( ~ c_Orderings_Oord__class_Oless(U_2035,U_2037,U_2036)
| ~ sP166(U_2035,U_2036,U_2037) )
& ! [U_2035,U_2036,U_2037] :
( ~ c_Orderings_Oord__class_Oless(U_2035,U_2036,U_2037)
| ~ sP166(U_2035,U_2036,U_2037) )
& ! [U_2035,U_2036,U_2037] :
( U_2036 != U_2037
| sP166(U_2035,U_2036,U_2037)
| ~ sP167(U_2035,U_2036,U_2037) )
& ! [U_2035,U_2036,U_2037] :
( c_Orderings_Oord__class_Oless(U_2035,U_2037,U_2036)
| c_Orderings_Oord__class_Oless(U_2035,U_2036,U_2037)
| U_2036 = U_2037
| ~ sP167(U_2035,U_2036,U_2037) )
& ! [U_2035,U_2036,U_2037] :
( sP167(U_2035,U_2036,U_2037)
| ~ class_Orderings_Olinorder(U_2035) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166,sP167])],[f_716_2]) ).
cnf(f_716_4,plain,
( sP167(U_2035,U_2036,U_2037)
| ~ class_Orderings_Olinorder(U_2035) ),
inference(clausify,[status(thm)],[f_716_3]) ).
cnf(f_716_5,plain,
( c_Orderings_Oord__class_Oless(U_2035,U_2037,U_2036)
| c_Orderings_Oord__class_Oless(U_2035,U_2036,U_2037)
| U_2036 = U_2037
| ~ sP167(U_2035,U_2036,U_2037) ),
inference(clausify,[status(thm)],[f_716_3]) ).
cnf(f_716_6,plain,
( U_2036 != U_2037
| sP166(U_2035,U_2036,U_2037)
| ~ sP167(U_2035,U_2036,U_2037) ),
inference(clausify,[status(thm)],[f_716_3]) ).
cnf(f_716_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_2035,U_2036,U_2037)
| ~ sP166(U_2035,U_2036,U_2037) ),
inference(clausify,[status(thm)],[f_716_3]) ).
cnf(f_716_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_2035,U_2037,U_2036)
| ~ sP166(U_2035,U_2036,U_2037) ),
inference(clausify,[status(thm)],[f_716_3]) ).
fof(f_717_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
| ( V_xa_2 != V_ya_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2) ) )
& ( V_xa_2 = V_ya_2
| c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)
| c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(f_717_2,plain,
! [U_2040,U_2039,U_2038] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2038,U_2039,U_2040)
| ( U_2039 != U_2040
& ~ c_Orderings_Oord__class_Oless(U_2038,U_2040,U_2039) ) )
& ( U_2039 = U_2040
| c_Orderings_Oord__class_Oless(U_2038,U_2040,U_2039)
| c_Orderings_Oord__class_Oless(U_2038,U_2039,U_2040) ) )
| ~ class_Orderings_Olinorder(U_2038) ),
inference(variable_rename,[status(thm)],[f_717_1]) ).
fof(f_717_3,plain,
( ! [U_2039,U_2038,U_2040] :
( U_2039 != U_2040
| ~ sP168(U_2039,U_2038,U_2040) )
& ! [U_2039,U_2038,U_2040] :
( ~ c_Orderings_Oord__class_Oless(U_2038,U_2040,U_2039)
| ~ sP168(U_2039,U_2038,U_2040) )
& ! [U_2039,U_2038,U_2040] :
( ~ c_Orderings_Oord__class_Oless(U_2038,U_2039,U_2040)
| sP168(U_2039,U_2038,U_2040)
| ~ sP169(U_2039,U_2038,U_2040) )
& ! [U_2039,U_2038,U_2040] :
( U_2039 = U_2040
| c_Orderings_Oord__class_Oless(U_2038,U_2040,U_2039)
| c_Orderings_Oord__class_Oless(U_2038,U_2039,U_2040)
| ~ sP169(U_2039,U_2038,U_2040) )
& ! [U_2039,U_2038,U_2040] :
( sP169(U_2039,U_2038,U_2040)
| ~ class_Orderings_Olinorder(U_2038) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168,sP169])],[f_717_2]) ).
cnf(f_717_4,plain,
( sP169(U_2039,U_2038,U_2040)
| ~ class_Orderings_Olinorder(U_2038) ),
inference(clausify,[status(thm)],[f_717_3]) ).
cnf(f_717_5,plain,
( U_2039 = U_2040
| c_Orderings_Oord__class_Oless(U_2038,U_2040,U_2039)
| c_Orderings_Oord__class_Oless(U_2038,U_2039,U_2040)
| ~ sP169(U_2039,U_2038,U_2040) ),
inference(clausify,[status(thm)],[f_717_3]) ).
cnf(f_717_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_2038,U_2039,U_2040)
| sP168(U_2039,U_2038,U_2040)
| ~ sP169(U_2039,U_2038,U_2040) ),
inference(clausify,[status(thm)],[f_717_3]) ).
cnf(f_717_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_2038,U_2040,U_2039)
| ~ sP168(U_2039,U_2038,U_2040) ),
inference(clausify,[status(thm)],[f_717_3]) ).
cnf(f_717_8,plain,
( U_2039 != U_2040
| ~ sP168(U_2039,U_2038,U_2040) ),
inference(clausify,[status(thm)],[f_717_3]) ).
fof(f_718_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_718_2,plain,
! [U_2043,U_2042,U_2041] :
( c_Orderings_Oord__class_Oless(U_2041,U_2043,U_2042)
| U_2042 = U_2043
| c_Orderings_Oord__class_Oless(U_2041,U_2042,U_2043)
| ~ class_Orderings_Olinorder(U_2041) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
fof(f_718_3,plain,
! [U_2043,U_2041,U_2042] :
( c_Orderings_Oord__class_Oless(U_2041,U_2043,U_2042)
| U_2042 = U_2043
| c_Orderings_Oord__class_Oless(U_2041,U_2042,U_2043)
| ~ class_Orderings_Olinorder(U_2041) ),
inference(definitional_conversion,[status(esa)],[f_718_2]) ).
cnf(f_718_4,plain,
( c_Orderings_Oord__class_Oless(U_2041,U_2043,U_2042)
| U_2042 = U_2043
| c_Orderings_Oord__class_Oless(U_2041,U_2042,U_2043)
| ~ class_Orderings_Olinorder(U_2041) ),
inference(clausify,[status(thm)],[f_718_3]) ).
fof(f_719_1,plain,
! [V_xa_2,V_ya_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
| V_xa_2 != V_ya_2 )
& ( V_xa_2 = V_ya_2
| c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(f_719_2,plain,
! [U_2046,U_2045,U_2044] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2044,U_2046,U_2045)
| U_2046 != U_2045 )
& ( U_2046 = U_2045
| c_Orderings_Oord__class_Oless(U_2044,U_2046,U_2045) ) )
| c_Orderings_Oord__class_Oless(U_2044,U_2045,U_2046)
| ~ class_Orderings_Olinorder(U_2044) ),
inference(variable_rename,[status(thm)],[f_719_1]) ).
fof(f_719_3,plain,
( ! [U_2044,U_2045,U_2046] :
( ~ c_Orderings_Oord__class_Oless(U_2044,U_2046,U_2045)
| U_2046 != U_2045
| ~ sP170(U_2044,U_2045,U_2046) )
& ! [U_2044,U_2045,U_2046] :
( U_2046 = U_2045
| c_Orderings_Oord__class_Oless(U_2044,U_2046,U_2045)
| ~ sP170(U_2044,U_2045,U_2046) )
& ! [U_2044,U_2045,U_2046] :
( sP170(U_2044,U_2045,U_2046)
| c_Orderings_Oord__class_Oless(U_2044,U_2045,U_2046)
| ~ class_Orderings_Olinorder(U_2044) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_719_2]) ).
cnf(f_719_4,plain,
( sP170(U_2044,U_2045,U_2046)
| c_Orderings_Oord__class_Oless(U_2044,U_2045,U_2046)
| ~ class_Orderings_Olinorder(U_2044) ),
inference(clausify,[status(thm)],[f_719_3]) ).
cnf(f_719_5,plain,
( U_2046 = U_2045
| c_Orderings_Oord__class_Oless(U_2044,U_2046,U_2045)
| ~ sP170(U_2044,U_2045,U_2046) ),
inference(clausify,[status(thm)],[f_719_3]) ).
cnf(f_719_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_2044,U_2046,U_2045)
| U_2046 != U_2045
| ~ sP170(U_2044,U_2045,U_2046) ),
inference(clausify,[status(thm)],[f_719_3]) ).
fof(f_720_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_720_2,plain,
! [U_2049,U_2048,U_2047] :
( c_Orderings_Oord__class_Oless(U_2047,U_2049,U_2048)
| c_Orderings_Oord__class_Oless(U_2047,U_2048,U_2049)
| U_2048 = U_2049
| ~ class_Orderings_Olinorder(U_2047) ),
inference(variable_rename,[status(thm)],[f_720_1]) ).
fof(f_720_3,plain,
! [U_2049,U_2048,U_2047] :
( c_Orderings_Oord__class_Oless(U_2047,U_2049,U_2048)
| c_Orderings_Oord__class_Oless(U_2047,U_2048,U_2049)
| U_2048 = U_2049
| ~ class_Orderings_Olinorder(U_2047) ),
inference(definitional_conversion,[status(esa)],[f_720_2]) ).
cnf(f_720_4,plain,
( c_Orderings_Oord__class_Oless(U_2047,U_2049,U_2048)
| c_Orderings_Oord__class_Oless(U_2047,U_2048,U_2049)
| U_2048 = U_2049
| ~ class_Orderings_Olinorder(U_2047) ),
inference(clausify,[status(thm)],[f_720_3]) ).
fof(f_721_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_721_2,plain,
! [U_2052,U_2051,U_2050] :
( U_2051 != U_2052
| ~ c_Orderings_Oord__class_Oless(U_2050,U_2051,U_2052)
| ~ class_Orderings_Oorder(U_2050) ),
inference(variable_rename,[status(thm)],[f_721_1]) ).
fof(f_721_3,plain,
! [U_2050,U_2051,U_2052] :
( U_2051 != U_2052
| ~ c_Orderings_Oord__class_Oless(U_2050,U_2051,U_2052)
| ~ class_Orderings_Oorder(U_2050) ),
inference(definitional_conversion,[status(esa)],[f_721_2]) ).
cnf(f_721_4,plain,
( U_2051 != U_2052
| ~ c_Orderings_Oord__class_Oless(U_2050,U_2051,U_2052)
| ~ class_Orderings_Oorder(U_2050) ),
inference(clausify,[status(thm)],[f_721_3]) ).
fof(f_722_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_722_2,plain,
! [U_2055,U_2054,U_2053] :
( ~ c_Orderings_Oord__class_Oless(U_2053,U_2055,U_2054)
| ~ c_Orderings_Oord__class_Oless(U_2053,U_2054,U_2055)
| ~ class_Orderings_Opreorder(U_2053) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
fof(f_722_3,plain,
! [U_2053,U_2054,U_2055] :
( ~ c_Orderings_Oord__class_Oless(U_2053,U_2055,U_2054)
| ~ c_Orderings_Oord__class_Oless(U_2053,U_2054,U_2055)
| ~ class_Orderings_Opreorder(U_2053) ),
inference(definitional_conversion,[status(esa)],[f_722_2]) ).
cnf(f_722_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2053,U_2055,U_2054)
| ~ c_Orderings_Oord__class_Oless(U_2053,U_2054,U_2055)
| ~ class_Orderings_Opreorder(U_2053) ),
inference(clausify,[status(thm)],[f_722_3]) ).
fof(f_723_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_723_2,plain,
! [U_2058,U_2057,U_2056] :
( ~ c_Orderings_Oord__class_Oless(U_2056,U_2058,U_2057)
| ~ c_Orderings_Oord__class_Oless(U_2056,U_2057,U_2058)
| ~ class_Orderings_Opreorder(U_2056) ),
inference(variable_rename,[status(thm)],[f_723_1]) ).
fof(f_723_3,plain,
! [U_2058,U_2056,U_2057] :
( ~ c_Orderings_Oord__class_Oless(U_2056,U_2058,U_2057)
| ~ c_Orderings_Oord__class_Oless(U_2056,U_2057,U_2058)
| ~ class_Orderings_Opreorder(U_2056) ),
inference(definitional_conversion,[status(esa)],[f_723_2]) ).
cnf(f_723_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2056,U_2058,U_2057)
| ~ c_Orderings_Oord__class_Oless(U_2056,U_2057,U_2058)
| ~ class_Orderings_Opreorder(U_2056) ),
inference(clausify,[status(thm)],[f_723_3]) ).
fof(f_724_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_724_2,plain,
! [U_2061,U_2060,U_2059] :
( U_2060 != U_2061
| ~ c_Orderings_Oord__class_Oless(U_2059,U_2060,U_2061)
| ~ class_Orderings_Oorder(U_2059) ),
inference(variable_rename,[status(thm)],[f_724_1]) ).
fof(f_724_3,plain,
! [U_2060,U_2059,U_2061] :
( U_2060 != U_2061
| ~ c_Orderings_Oord__class_Oless(U_2059,U_2060,U_2061)
| ~ class_Orderings_Oorder(U_2059) ),
inference(definitional_conversion,[status(esa)],[f_724_2]) ).
cnf(f_724_4,plain,
( U_2060 != U_2061
| ~ c_Orderings_Oord__class_Oless(U_2059,U_2060,U_2061)
| ~ class_Orderings_Oorder(U_2059) ),
inference(clausify,[status(thm)],[f_724_3]) ).
fof(f_725_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_725_2,plain,
! [U_2064,U_2063,U_2062] :
( U_2064 != U_2063
| ~ c_Orderings_Oord__class_Oless(U_2062,U_2063,U_2064)
| ~ class_Orderings_Oorder(U_2062) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
fof(f_725_3,plain,
! [U_2062,U_2063,U_2064] :
( U_2064 != U_2063
| ~ c_Orderings_Oord__class_Oless(U_2062,U_2063,U_2064)
| ~ class_Orderings_Oorder(U_2062) ),
inference(definitional_conversion,[status(esa)],[f_725_2]) ).
cnf(f_725_4,plain,
( U_2064 != U_2063
| ~ c_Orderings_Oord__class_Oless(U_2062,U_2063,U_2064)
| ~ class_Orderings_Oorder(U_2062) ),
inference(clausify,[status(thm)],[f_725_3]) ).
fof(f_726_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_726_2,plain,
! [U_2067,U_2066,U_2065] :
( ~ c_Orderings_Oord__class_Oless(U_2065,U_2067,U_2066)
| ~ c_Orderings_Oord__class_Oless(U_2065,U_2066,U_2067)
| ~ class_Orderings_Opreorder(U_2065) ),
inference(variable_rename,[status(thm)],[f_726_1]) ).
fof(f_726_3,plain,
! [U_2067,U_2066,U_2065] :
( ~ c_Orderings_Oord__class_Oless(U_2065,U_2067,U_2066)
| ~ c_Orderings_Oord__class_Oless(U_2065,U_2066,U_2067)
| ~ class_Orderings_Opreorder(U_2065) ),
inference(definitional_conversion,[status(esa)],[f_726_2]) ).
cnf(f_726_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2065,U_2067,U_2066)
| ~ c_Orderings_Oord__class_Oless(U_2065,U_2066,U_2067)
| ~ class_Orderings_Opreorder(U_2065) ),
inference(clausify,[status(thm)],[f_726_3]) ).
fof(f_727_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_727_2,plain,
! [U_2070,U_2069,U_2068] :
( ~ c_Orderings_Oord__class_Oless(U_2068,U_2070,U_2069)
| ~ c_Orderings_Oord__class_Oless(U_2068,U_2069,U_2070)
| ~ class_Orderings_Oorder(U_2068) ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
fof(f_727_3,plain,
! [U_2070,U_2068,U_2069] :
( ~ c_Orderings_Oord__class_Oless(U_2068,U_2070,U_2069)
| ~ c_Orderings_Oord__class_Oless(U_2068,U_2069,U_2070)
| ~ class_Orderings_Oorder(U_2068) ),
inference(definitional_conversion,[status(esa)],[f_727_2]) ).
cnf(f_727_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2068,U_2070,U_2069)
| ~ c_Orderings_Oord__class_Oless(U_2068,U_2069,U_2070)
| ~ class_Orderings_Oorder(U_2068) ),
inference(clausify,[status(thm)],[f_727_3]) ).
fof(f_728_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_728_2,plain,
! [U_2074,U_2073,U_2072,U_2071] :
( c_Orderings_Oord__class_Oless(U_2071,U_2072,U_2074)
| ~ c_Orderings_Oord__class_Oless(U_2071,U_2073,U_2074)
| U_2072 != U_2073
| ~ class_Orderings_Oord(U_2071) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
fof(f_728_3,plain,
! [U_2073,U_2071,U_2072,U_2074] :
( c_Orderings_Oord__class_Oless(U_2071,U_2072,U_2074)
| ~ c_Orderings_Oord__class_Oless(U_2071,U_2073,U_2074)
| U_2072 != U_2073
| ~ class_Orderings_Oord(U_2071) ),
inference(definitional_conversion,[status(esa)],[f_728_2]) ).
cnf(f_728_4,plain,
( c_Orderings_Oord__class_Oless(U_2071,U_2072,U_2074)
| ~ c_Orderings_Oord__class_Oless(U_2071,U_2073,U_2074)
| U_2072 != U_2073
| ~ class_Orderings_Oord(U_2071) ),
inference(clausify,[status(thm)],[f_728_3]) ).
fof(f_729_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_729_2,plain,
! [U_2078,U_2077,U_2076,U_2075] :
( c_Orderings_Oord__class_Oless(U_2075,U_2078,U_2076)
| ~ c_Orderings_Oord__class_Oless(U_2075,U_2078,U_2077)
| U_2076 != U_2077
| ~ class_Orderings_Oorder(U_2075) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
fof(f_729_3,plain,
! [U_2078,U_2077,U_2075,U_2076] :
( c_Orderings_Oord__class_Oless(U_2075,U_2078,U_2076)
| ~ c_Orderings_Oord__class_Oless(U_2075,U_2078,U_2077)
| U_2076 != U_2077
| ~ class_Orderings_Oorder(U_2075) ),
inference(definitional_conversion,[status(esa)],[f_729_2]) ).
cnf(f_729_4,plain,
( c_Orderings_Oord__class_Oless(U_2075,U_2078,U_2076)
| ~ c_Orderings_Oord__class_Oless(U_2075,U_2078,U_2077)
| U_2076 != U_2077
| ~ class_Orderings_Oorder(U_2075) ),
inference(clausify,[status(thm)],[f_729_3]) ).
fof(f_730_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_730_2,plain,
! [U_2082,U_2081,U_2080,U_2079] :
( c_Orderings_Oord__class_Oless(U_2079,U_2080,U_2082)
| U_2081 != U_2082
| ~ c_Orderings_Oord__class_Oless(U_2079,U_2080,U_2081)
| ~ class_Orderings_Oord(U_2079) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
fof(f_730_3,plain,
! [U_2080,U_2081,U_2082,U_2079] :
( c_Orderings_Oord__class_Oless(U_2079,U_2080,U_2082)
| U_2081 != U_2082
| ~ c_Orderings_Oord__class_Oless(U_2079,U_2080,U_2081)
| ~ class_Orderings_Oord(U_2079) ),
inference(definitional_conversion,[status(esa)],[f_730_2]) ).
cnf(f_730_4,plain,
( c_Orderings_Oord__class_Oless(U_2079,U_2080,U_2082)
| U_2081 != U_2082
| ~ c_Orderings_Oord__class_Oless(U_2079,U_2080,U_2081)
| ~ class_Orderings_Oord(U_2079) ),
inference(clausify,[status(thm)],[f_730_3]) ).
fof(f_731_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_731_2,plain,
! [U_2086,U_2085,U_2084,U_2083] :
( c_Orderings_Oord__class_Oless(U_2083,U_2086,U_2085)
| U_2084 != U_2086
| ~ c_Orderings_Oord__class_Oless(U_2083,U_2084,U_2085)
| ~ class_Orderings_Oorder(U_2083) ),
inference(variable_rename,[status(thm)],[f_731_1]) ).
fof(f_731_3,plain,
! [U_2085,U_2086,U_2083,U_2084] :
( c_Orderings_Oord__class_Oless(U_2083,U_2086,U_2085)
| U_2084 != U_2086
| ~ c_Orderings_Oord__class_Oless(U_2083,U_2084,U_2085)
| ~ class_Orderings_Oorder(U_2083) ),
inference(definitional_conversion,[status(esa)],[f_731_2]) ).
cnf(f_731_4,plain,
( c_Orderings_Oord__class_Oless(U_2083,U_2086,U_2085)
| U_2084 != U_2086
| ~ c_Orderings_Oord__class_Oless(U_2083,U_2084,U_2085)
| ~ class_Orderings_Oorder(U_2083) ),
inference(clausify,[status(thm)],[f_731_3]) ).
fof(f_732_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_732_2,plain,
! [U_2090,U_2089,U_2088,U_2087] :
( c_Orderings_Oord__class_Oless(U_2087,U_2088,U_2090)
| ~ c_Orderings_Oord__class_Oless(U_2087,U_2089,U_2090)
| ~ c_Orderings_Oord__class_Oless(U_2087,U_2088,U_2089)
| ~ class_Orderings_Opreorder(U_2087) ),
inference(variable_rename,[status(thm)],[f_732_1]) ).
fof(f_732_3,plain,
! [U_2088,U_2087,U_2089,U_2090] :
( c_Orderings_Oord__class_Oless(U_2087,U_2088,U_2090)
| ~ c_Orderings_Oord__class_Oless(U_2087,U_2089,U_2090)
| ~ c_Orderings_Oord__class_Oless(U_2087,U_2088,U_2089)
| ~ class_Orderings_Opreorder(U_2087) ),
inference(definitional_conversion,[status(esa)],[f_732_2]) ).
cnf(f_732_4,plain,
( c_Orderings_Oord__class_Oless(U_2087,U_2088,U_2090)
| ~ c_Orderings_Oord__class_Oless(U_2087,U_2089,U_2090)
| ~ c_Orderings_Oord__class_Oless(U_2087,U_2088,U_2089)
| ~ class_Orderings_Opreorder(U_2087) ),
inference(clausify,[status(thm)],[f_732_3]) ).
fof(f_733_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_733_2,plain,
! [U_2094,U_2093,U_2092,U_2091] :
( c_Orderings_Oord__class_Oless(U_2091,U_2094,U_2093)
| ~ c_Orderings_Oord__class_Oless(U_2091,U_2094,U_2092)
| ~ c_Orderings_Oord__class_Oless(U_2091,U_2092,U_2093)
| ~ class_Orderings_Oorder(U_2091) ),
inference(variable_rename,[status(thm)],[f_733_1]) ).
fof(f_733_3,plain,
! [U_2092,U_2091,U_2093,U_2094] :
( c_Orderings_Oord__class_Oless(U_2091,U_2094,U_2093)
| ~ c_Orderings_Oord__class_Oless(U_2091,U_2094,U_2092)
| ~ c_Orderings_Oord__class_Oless(U_2091,U_2092,U_2093)
| ~ class_Orderings_Oorder(U_2091) ),
inference(definitional_conversion,[status(esa)],[f_733_2]) ).
cnf(f_733_4,plain,
( c_Orderings_Oord__class_Oless(U_2091,U_2094,U_2093)
| ~ c_Orderings_Oord__class_Oless(U_2091,U_2094,U_2092)
| ~ c_Orderings_Oord__class_Oless(U_2091,U_2092,U_2093)
| ~ class_Orderings_Oorder(U_2091) ),
inference(clausify,[status(thm)],[f_733_3]) ).
fof(f_734_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_734_2,plain,
! [U_2097,U_2096,U_2095] :
( ~ c_Orderings_Oord__class_Oless(U_2095,U_2097,U_2096)
| ~ c_Orderings_Oord__class_Oless(U_2095,U_2096,U_2097)
| ~ class_Orderings_Opreorder(U_2095) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
fof(f_734_3,plain,
! [U_2095,U_2097,U_2096] :
( ~ c_Orderings_Oord__class_Oless(U_2095,U_2097,U_2096)
| ~ c_Orderings_Oord__class_Oless(U_2095,U_2096,U_2097)
| ~ class_Orderings_Opreorder(U_2095) ),
inference(definitional_conversion,[status(esa)],[f_734_2]) ).
cnf(f_734_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2095,U_2097,U_2096)
| ~ c_Orderings_Oord__class_Oless(U_2095,U_2096,U_2097)
| ~ class_Orderings_Opreorder(U_2095) ),
inference(clausify,[status(thm)],[f_734_3]) ).
fof(f_735_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_735_2,plain,
! [U_2100,U_2099,U_2098] :
( c_Orderings_Oord__class_Oless(U_2098,U_2100,U_2099)
| U_2099 = U_2100
| c_Orderings_Oord__class_Oless(U_2098,U_2099,U_2100)
| ~ class_Orderings_Olinorder(U_2098) ),
inference(variable_rename,[status(thm)],[f_735_1]) ).
fof(f_735_3,plain,
! [U_2099,U_2098,U_2100] :
( c_Orderings_Oord__class_Oless(U_2098,U_2100,U_2099)
| U_2099 = U_2100
| c_Orderings_Oord__class_Oless(U_2098,U_2099,U_2100)
| ~ class_Orderings_Olinorder(U_2098) ),
inference(definitional_conversion,[status(esa)],[f_735_2]) ).
cnf(f_735_4,plain,
( c_Orderings_Oord__class_Oless(U_2098,U_2100,U_2099)
| U_2099 = U_2100
| c_Orderings_Oord__class_Oless(U_2098,U_2099,U_2100)
| ~ class_Orderings_Olinorder(U_2098) ),
inference(clausify,[status(thm)],[f_735_3]) ).
fof(f_736_1,plain,
! [V_ya_2,V_xa_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
| ( V_xa_2 != V_ya_2
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) )
& ( V_xa_2 = V_ya_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__real__def]) ).
fof(f_736_2,plain,
! [U_2102,U_2101] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2101,U_2102)
| ( U_2101 != U_2102
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2101,U_2102) ) )
& ( U_2101 = U_2102
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2101,U_2102)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2101,U_2102) ) ),
inference(variable_rename,[status(thm)],[f_736_1]) ).
fof(f_736_3,plain,
( ! [U_2106,U_2104] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2104,U_2106)
| ( U_2104 != U_2106
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2104,U_2106) ) )
& ! [U_2105,U_2103] :
( U_2103 = U_2105
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2103,U_2105)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2103,U_2105) ) ),
inference(miniscope,[status(thm)],[f_736_2]) ).
fof(f_736_4,plain,
( ! [U_2106,U_2104] :
( U_2104 != U_2106
| ~ sP171(U_2106,U_2104) )
& ! [U_2106,U_2104] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2104,U_2106)
| ~ sP171(U_2106,U_2104) )
& ! [U_2106,U_2104] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2104,U_2106)
| sP171(U_2106,U_2104) )
& ! [U_2103,U_2105] :
( U_2103 = U_2105
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2103,U_2105)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2103,U_2105) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171])],[f_736_3]) ).
cnf(f_736_5,plain,
( U_2103 = U_2105
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2103,U_2105)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2103,U_2105) ),
inference(clausify,[status(thm)],[f_736_4]) ).
cnf(f_736_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2104,U_2106)
| sP171(U_2106,U_2104) ),
inference(clausify,[status(thm)],[f_736_4]) ).
cnf(f_736_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2104,U_2106)
| ~ sP171(U_2106,U_2104) ),
inference(clausify,[status(thm)],[f_736_4]) ).
cnf(f_736_8,plain,
( U_2104 != U_2106
| ~ sP171(U_2106,U_2104) ),
inference(clausify,[status(thm)],[f_736_4]) ).
fof(f_737_1,plain,
! [V_ya_2,V_xa_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)
| V_xa_2 = V_ya_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) )
& ( ( V_xa_2 != V_ya_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__less__def]) ).
fof(f_737_2,plain,
! [U_2108,U_2107] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2107,U_2108)
| U_2107 = U_2108
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2107,U_2108) )
& ( ( U_2107 != U_2108
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2107,U_2108) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2107,U_2108) ) ),
inference(variable_rename,[status(thm)],[f_737_1]) ).
fof(f_737_3,plain,
( ! [U_2112,U_2110] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110,U_2112)
| U_2110 = U_2112
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2110,U_2112) )
& ! [U_2111,U_2109] :
( ( U_2109 != U_2111
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2109,U_2111) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2109,U_2111) ) ),
inference(miniscope,[status(thm)],[f_737_2]) ).
fof(f_737_4,plain,
( ! [U_2111,U_2109] :
( U_2109 != U_2111
| ~ sP172(U_2111,U_2109) )
& ! [U_2111,U_2109] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2109,U_2111)
| ~ sP172(U_2111,U_2109) )
& ! [U_2110,U_2112] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110,U_2112)
| U_2110 = U_2112
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2110,U_2112) )
& ! [U_2111,U_2109] :
( sP172(U_2111,U_2109)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2109,U_2111) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_737_3]) ).
cnf(f_737_5,plain,
( sP172(U_2111,U_2109)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2109,U_2111) ),
inference(clausify,[status(thm)],[f_737_4]) ).
cnf(f_737_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2110,U_2112)
| U_2110 = U_2112
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2110,U_2112) ),
inference(clausify,[status(thm)],[f_737_4]) ).
cnf(f_737_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2109,U_2111)
| ~ sP172(U_2111,U_2109) ),
inference(clausify,[status(thm)],[f_737_4]) ).
cnf(f_737_8,plain,
( U_2109 != U_2111
| ~ sP172(U_2111,U_2109) ),
inference(clausify,[status(thm)],[f_737_4]) ).
fof(f_738_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_738_2,plain,
! [U_2117,U_2116,U_2115,U_2114,U_2113] :
( ( ( c_Orderings_Oord__class_Oless(U_2113,U_2114,U_2115)
| ~ c_Orderings_Oord__class_Oless(U_2113,U_2116,U_2117) )
& ( c_Orderings_Oord__class_Oless(U_2113,U_2116,U_2117)
| ~ c_Orderings_Oord__class_Oless(U_2113,U_2114,U_2115) ) )
| c_Groups_Ominus__class_Ominus(U_2113,U_2114,U_2115) != c_Groups_Ominus__class_Ominus(U_2113,U_2116,U_2117)
| ~ class_Groups_Oordered__ab__group__add(U_2113) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
fof(f_738_3,plain,
( ! [U_2116,U_2114,U_2113,U_2117,U_2115] :
( c_Orderings_Oord__class_Oless(U_2113,U_2114,U_2115)
| ~ c_Orderings_Oord__class_Oless(U_2113,U_2116,U_2117)
| ~ sP173(U_2116,U_2114,U_2113,U_2117,U_2115) )
& ! [U_2116,U_2114,U_2113,U_2117,U_2115] :
( c_Orderings_Oord__class_Oless(U_2113,U_2116,U_2117)
| ~ c_Orderings_Oord__class_Oless(U_2113,U_2114,U_2115)
| ~ sP173(U_2116,U_2114,U_2113,U_2117,U_2115) )
& ! [U_2116,U_2114,U_2113,U_2117,U_2115] :
( sP173(U_2116,U_2114,U_2113,U_2117,U_2115)
| c_Groups_Ominus__class_Ominus(U_2113,U_2114,U_2115) != c_Groups_Ominus__class_Ominus(U_2113,U_2116,U_2117)
| ~ class_Groups_Oordered__ab__group__add(U_2113) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_738_2]) ).
cnf(f_738_4,plain,
( sP173(U_2116,U_2114,U_2113,U_2117,U_2115)
| c_Groups_Ominus__class_Ominus(U_2113,U_2114,U_2115) != c_Groups_Ominus__class_Ominus(U_2113,U_2116,U_2117)
| ~ class_Groups_Oordered__ab__group__add(U_2113) ),
inference(clausify,[status(thm)],[f_738_3]) ).
cnf(f_738_5,plain,
( c_Orderings_Oord__class_Oless(U_2113,U_2116,U_2117)
| ~ c_Orderings_Oord__class_Oless(U_2113,U_2114,U_2115)
| ~ sP173(U_2116,U_2114,U_2113,U_2117,U_2115) ),
inference(clausify,[status(thm)],[f_738_3]) ).
cnf(f_738_6,plain,
( c_Orderings_Oord__class_Oless(U_2113,U_2114,U_2115)
| ~ c_Orderings_Oord__class_Oless(U_2113,U_2116,U_2117)
| ~ sP173(U_2116,U_2114,U_2113,U_2117,U_2115) ),
inference(clausify,[status(thm)],[f_738_3]) ).
fof(f_739_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_739_2,plain,
! [U_2121,U_2120,U_2119,U_2118] :
( ( ( c_Orderings_Oord__class_Oless(U_2118,c_Groups_Oplus__class_Oplus(U_2118,U_2119,U_2120),c_Groups_Oplus__class_Oplus(U_2118,U_2121,U_2120))
| ~ c_Orderings_Oord__class_Oless(U_2118,U_2119,U_2121) )
& ( c_Orderings_Oord__class_Oless(U_2118,U_2119,U_2121)
| ~ c_Orderings_Oord__class_Oless(U_2118,c_Groups_Oplus__class_Oplus(U_2118,U_2119,U_2120),c_Groups_Oplus__class_Oplus(U_2118,U_2121,U_2120)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2118) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
fof(f_739_3,plain,
( ! [U_2120,U_2119,U_2121,U_2118] :
( c_Orderings_Oord__class_Oless(U_2118,c_Groups_Oplus__class_Oplus(U_2118,U_2119,U_2120),c_Groups_Oplus__class_Oplus(U_2118,U_2121,U_2120))
| ~ c_Orderings_Oord__class_Oless(U_2118,U_2119,U_2121)
| ~ sP174(U_2120,U_2119,U_2121,U_2118) )
& ! [U_2120,U_2119,U_2121,U_2118] :
( c_Orderings_Oord__class_Oless(U_2118,U_2119,U_2121)
| ~ c_Orderings_Oord__class_Oless(U_2118,c_Groups_Oplus__class_Oplus(U_2118,U_2119,U_2120),c_Groups_Oplus__class_Oplus(U_2118,U_2121,U_2120))
| ~ sP174(U_2120,U_2119,U_2121,U_2118) )
& ! [U_2120,U_2119,U_2121,U_2118] :
( sP174(U_2120,U_2119,U_2121,U_2118)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2118) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_739_2]) ).
cnf(f_739_4,plain,
( sP174(U_2120,U_2119,U_2121,U_2118)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2118) ),
inference(clausify,[status(thm)],[f_739_3]) ).
cnf(f_739_5,plain,
( c_Orderings_Oord__class_Oless(U_2118,U_2119,U_2121)
| ~ c_Orderings_Oord__class_Oless(U_2118,c_Groups_Oplus__class_Oplus(U_2118,U_2119,U_2120),c_Groups_Oplus__class_Oplus(U_2118,U_2121,U_2120))
| ~ sP174(U_2120,U_2119,U_2121,U_2118) ),
inference(clausify,[status(thm)],[f_739_3]) ).
cnf(f_739_6,plain,
( c_Orderings_Oord__class_Oless(U_2118,c_Groups_Oplus__class_Oplus(U_2118,U_2119,U_2120),c_Groups_Oplus__class_Oplus(U_2118,U_2121,U_2120))
| ~ c_Orderings_Oord__class_Oless(U_2118,U_2119,U_2121)
| ~ sP174(U_2120,U_2119,U_2121,U_2118) ),
inference(clausify,[status(thm)],[f_739_3]) ).
fof(f_740_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_740_2,plain,
! [U_2125,U_2124,U_2123,U_2122] :
( ( ( c_Orderings_Oord__class_Oless(U_2122,c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2124),c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2125))
| ~ c_Orderings_Oord__class_Oless(U_2122,U_2124,U_2125) )
& ( c_Orderings_Oord__class_Oless(U_2122,U_2124,U_2125)
| ~ c_Orderings_Oord__class_Oless(U_2122,c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2124),c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2125)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2122) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
fof(f_740_3,plain,
( ! [U_2123,U_2122,U_2124,U_2125] :
( c_Orderings_Oord__class_Oless(U_2122,c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2124),c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2125))
| ~ c_Orderings_Oord__class_Oless(U_2122,U_2124,U_2125)
| ~ sP175(U_2123,U_2122,U_2124,U_2125) )
& ! [U_2123,U_2122,U_2124,U_2125] :
( c_Orderings_Oord__class_Oless(U_2122,U_2124,U_2125)
| ~ c_Orderings_Oord__class_Oless(U_2122,c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2124),c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2125))
| ~ sP175(U_2123,U_2122,U_2124,U_2125) )
& ! [U_2123,U_2122,U_2124,U_2125] :
( sP175(U_2123,U_2122,U_2124,U_2125)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2122) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_740_2]) ).
cnf(f_740_4,plain,
( sP175(U_2123,U_2122,U_2124,U_2125)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2122) ),
inference(clausify,[status(thm)],[f_740_3]) ).
cnf(f_740_5,plain,
( c_Orderings_Oord__class_Oless(U_2122,U_2124,U_2125)
| ~ c_Orderings_Oord__class_Oless(U_2122,c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2124),c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2125))
| ~ sP175(U_2123,U_2122,U_2124,U_2125) ),
inference(clausify,[status(thm)],[f_740_3]) ).
cnf(f_740_6,plain,
( c_Orderings_Oord__class_Oless(U_2122,c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2124),c_Groups_Oplus__class_Oplus(U_2122,U_2123,U_2125))
| ~ c_Orderings_Oord__class_Oless(U_2122,U_2124,U_2125)
| ~ sP175(U_2123,U_2122,U_2124,U_2125) ),
inference(clausify,[status(thm)],[f_740_3]) ).
fof(f_741_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_741_2,plain,
! [U_2129,U_2128,U_2127,U_2126] :
( c_Orderings_Oord__class_Oless(U_2126,c_Groups_Oplus__class_Oplus(U_2126,U_2127,U_2129),c_Groups_Oplus__class_Oplus(U_2126,U_2128,U_2129))
| ~ c_Orderings_Oord__class_Oless(U_2126,U_2127,U_2128)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2126) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
fof(f_741_3,plain,
! [U_2128,U_2129,U_2126,U_2127] :
( c_Orderings_Oord__class_Oless(U_2126,c_Groups_Oplus__class_Oplus(U_2126,U_2127,U_2129),c_Groups_Oplus__class_Oplus(U_2126,U_2128,U_2129))
| ~ c_Orderings_Oord__class_Oless(U_2126,U_2127,U_2128)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2126) ),
inference(definitional_conversion,[status(esa)],[f_741_2]) ).
cnf(f_741_4,plain,
( c_Orderings_Oord__class_Oless(U_2126,c_Groups_Oplus__class_Oplus(U_2126,U_2127,U_2129),c_Groups_Oplus__class_Oplus(U_2126,U_2128,U_2129))
| ~ c_Orderings_Oord__class_Oless(U_2126,U_2127,U_2128)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2126) ),
inference(clausify,[status(thm)],[f_741_3]) ).
fof(f_742_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_742_2,plain,
! [U_2133,U_2132,U_2131,U_2130] :
( c_Orderings_Oord__class_Oless(U_2130,c_Groups_Oplus__class_Oplus(U_2130,U_2133,U_2131),c_Groups_Oplus__class_Oplus(U_2130,U_2133,U_2132))
| ~ c_Orderings_Oord__class_Oless(U_2130,U_2131,U_2132)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2130) ),
inference(variable_rename,[status(thm)],[f_742_1]) ).
fof(f_742_3,plain,
! [U_2131,U_2130,U_2132,U_2133] :
( c_Orderings_Oord__class_Oless(U_2130,c_Groups_Oplus__class_Oplus(U_2130,U_2133,U_2131),c_Groups_Oplus__class_Oplus(U_2130,U_2133,U_2132))
| ~ c_Orderings_Oord__class_Oless(U_2130,U_2131,U_2132)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2130) ),
inference(definitional_conversion,[status(esa)],[f_742_2]) ).
cnf(f_742_4,plain,
( c_Orderings_Oord__class_Oless(U_2130,c_Groups_Oplus__class_Oplus(U_2130,U_2133,U_2131),c_Groups_Oplus__class_Oplus(U_2130,U_2133,U_2132))
| ~ c_Orderings_Oord__class_Oless(U_2130,U_2131,U_2132)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2130) ),
inference(clausify,[status(thm)],[f_742_3]) ).
fof(f_743_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_743_2,plain,
! [U_2138,U_2137,U_2136,U_2135,U_2134] :
( c_Orderings_Oord__class_Oless(U_2134,c_Groups_Oplus__class_Oplus(U_2134,U_2135,U_2137),c_Groups_Oplus__class_Oplus(U_2134,U_2136,U_2138))
| ~ c_Orderings_Oord__class_Oless(U_2134,U_2137,U_2138)
| ~ c_Orderings_Oord__class_Oless(U_2134,U_2135,U_2136)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2134) ),
inference(variable_rename,[status(thm)],[f_743_1]) ).
fof(f_743_3,plain,
! [U_2136,U_2135,U_2134,U_2137,U_2138] :
( c_Orderings_Oord__class_Oless(U_2134,c_Groups_Oplus__class_Oplus(U_2134,U_2135,U_2137),c_Groups_Oplus__class_Oplus(U_2134,U_2136,U_2138))
| ~ c_Orderings_Oord__class_Oless(U_2134,U_2137,U_2138)
| ~ c_Orderings_Oord__class_Oless(U_2134,U_2135,U_2136)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2134) ),
inference(definitional_conversion,[status(esa)],[f_743_2]) ).
cnf(f_743_4,plain,
( c_Orderings_Oord__class_Oless(U_2134,c_Groups_Oplus__class_Oplus(U_2134,U_2135,U_2137),c_Groups_Oplus__class_Oplus(U_2134,U_2136,U_2138))
| ~ c_Orderings_Oord__class_Oless(U_2134,U_2137,U_2138)
| ~ c_Orderings_Oord__class_Oless(U_2134,U_2135,U_2136)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2134) ),
inference(clausify,[status(thm)],[f_743_3]) ).
fof(f_744_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_744_2,plain,
! [U_2142,U_2141,U_2140,U_2139] :
( c_Orderings_Oord__class_Oless(U_2139,U_2140,U_2142)
| ~ c_Orderings_Oord__class_Oless(U_2139,c_Groups_Oplus__class_Oplus(U_2139,U_2140,U_2141),c_Groups_Oplus__class_Oplus(U_2139,U_2142,U_2141))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2139) ),
inference(variable_rename,[status(thm)],[f_744_1]) ).
fof(f_744_3,plain,
! [U_2139,U_2140,U_2141,U_2142] :
( c_Orderings_Oord__class_Oless(U_2139,U_2140,U_2142)
| ~ c_Orderings_Oord__class_Oless(U_2139,c_Groups_Oplus__class_Oplus(U_2139,U_2140,U_2141),c_Groups_Oplus__class_Oplus(U_2139,U_2142,U_2141))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2139) ),
inference(definitional_conversion,[status(esa)],[f_744_2]) ).
cnf(f_744_4,plain,
( c_Orderings_Oord__class_Oless(U_2139,U_2140,U_2142)
| ~ c_Orderings_Oord__class_Oless(U_2139,c_Groups_Oplus__class_Oplus(U_2139,U_2140,U_2141),c_Groups_Oplus__class_Oplus(U_2139,U_2142,U_2141))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2139) ),
inference(clausify,[status(thm)],[f_744_3]) ).
fof(f_745_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_745_2,plain,
! [U_2146,U_2145,U_2144,U_2143] :
( c_Orderings_Oord__class_Oless(U_2143,U_2145,U_2146)
| ~ c_Orderings_Oord__class_Oless(U_2143,c_Groups_Oplus__class_Oplus(U_2143,U_2144,U_2145),c_Groups_Oplus__class_Oplus(U_2143,U_2144,U_2146))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2143) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
fof(f_745_3,plain,
! [U_2144,U_2143,U_2145,U_2146] :
( c_Orderings_Oord__class_Oless(U_2143,U_2145,U_2146)
| ~ c_Orderings_Oord__class_Oless(U_2143,c_Groups_Oplus__class_Oplus(U_2143,U_2144,U_2145),c_Groups_Oplus__class_Oplus(U_2143,U_2144,U_2146))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2143) ),
inference(definitional_conversion,[status(esa)],[f_745_2]) ).
cnf(f_745_4,plain,
( c_Orderings_Oord__class_Oless(U_2143,U_2145,U_2146)
| ~ c_Orderings_Oord__class_Oless(U_2143,c_Groups_Oplus__class_Oplus(U_2143,U_2144,U_2145),c_Groups_Oplus__class_Oplus(U_2143,U_2144,U_2146))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_2143) ),
inference(clausify,[status(thm)],[f_745_3]) ).
fof(f_746_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_746_2,plain,
! [U_2150,U_2149,U_2148,U_2147] :
( c_Orderings_Oord__class_Oless(U_2147,U_2150,U_2149)
| ~ c_Orderings_Oord__class_Oless(U_2147,U_2150,U_2148)
| ~ c_Orderings_Oord__class_Oless__eq(U_2147,U_2148,U_2149)
| ~ class_Orderings_Oorder(U_2147) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
fof(f_746_3,plain,
! [U_2149,U_2148,U_2147,U_2150] :
( c_Orderings_Oord__class_Oless(U_2147,U_2150,U_2149)
| ~ c_Orderings_Oord__class_Oless(U_2147,U_2150,U_2148)
| ~ c_Orderings_Oord__class_Oless__eq(U_2147,U_2148,U_2149)
| ~ class_Orderings_Oorder(U_2147) ),
inference(definitional_conversion,[status(esa)],[f_746_2]) ).
cnf(f_746_4,plain,
( c_Orderings_Oord__class_Oless(U_2147,U_2150,U_2149)
| ~ c_Orderings_Oord__class_Oless(U_2147,U_2150,U_2148)
| ~ c_Orderings_Oord__class_Oless__eq(U_2147,U_2148,U_2149)
| ~ class_Orderings_Oorder(U_2147) ),
inference(clausify,[status(thm)],[f_746_3]) ).
fof(f_747_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_747_2,plain,
! [U_2154,U_2153,U_2152,U_2151] :
( c_Orderings_Oord__class_Oless(U_2151,U_2152,U_2154)
| ~ c_Orderings_Oord__class_Oless(U_2151,U_2153,U_2154)
| ~ c_Orderings_Oord__class_Oless__eq(U_2151,U_2152,U_2153)
| ~ class_Orderings_Opreorder(U_2151) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
fof(f_747_3,plain,
! [U_2153,U_2151,U_2152,U_2154] :
( c_Orderings_Oord__class_Oless(U_2151,U_2152,U_2154)
| ~ c_Orderings_Oord__class_Oless(U_2151,U_2153,U_2154)
| ~ c_Orderings_Oord__class_Oless__eq(U_2151,U_2152,U_2153)
| ~ class_Orderings_Opreorder(U_2151) ),
inference(definitional_conversion,[status(esa)],[f_747_2]) ).
cnf(f_747_4,plain,
( c_Orderings_Oord__class_Oless(U_2151,U_2152,U_2154)
| ~ c_Orderings_Oord__class_Oless(U_2151,U_2153,U_2154)
| ~ c_Orderings_Oord__class_Oless__eq(U_2151,U_2152,U_2153)
| ~ class_Orderings_Opreorder(U_2151) ),
inference(clausify,[status(thm)],[f_747_3]) ).
fof(f_748_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_748_2,plain,
! [U_2158,U_2157,U_2156,U_2155] :
( c_Orderings_Oord__class_Oless(U_2155,U_2158,U_2157)
| ~ c_Orderings_Oord__class_Oless__eq(U_2155,U_2158,U_2156)
| ~ c_Orderings_Oord__class_Oless(U_2155,U_2156,U_2157)
| ~ class_Orderings_Oorder(U_2155) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
fof(f_748_3,plain,
! [U_2156,U_2155,U_2157,U_2158] :
( c_Orderings_Oord__class_Oless(U_2155,U_2158,U_2157)
| ~ c_Orderings_Oord__class_Oless__eq(U_2155,U_2158,U_2156)
| ~ c_Orderings_Oord__class_Oless(U_2155,U_2156,U_2157)
| ~ class_Orderings_Oorder(U_2155) ),
inference(definitional_conversion,[status(esa)],[f_748_2]) ).
cnf(f_748_4,plain,
( c_Orderings_Oord__class_Oless(U_2155,U_2158,U_2157)
| ~ c_Orderings_Oord__class_Oless__eq(U_2155,U_2158,U_2156)
| ~ c_Orderings_Oord__class_Oless(U_2155,U_2156,U_2157)
| ~ class_Orderings_Oorder(U_2155) ),
inference(clausify,[status(thm)],[f_748_3]) ).
fof(f_749_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_749_2,plain,
! [U_2162,U_2161,U_2160,U_2159] :
( c_Orderings_Oord__class_Oless(U_2159,U_2160,U_2162)
| ~ c_Orderings_Oord__class_Oless__eq(U_2159,U_2161,U_2162)
| ~ c_Orderings_Oord__class_Oless(U_2159,U_2160,U_2161)
| ~ class_Orderings_Opreorder(U_2159) ),
inference(variable_rename,[status(thm)],[f_749_1]) ).
fof(f_749_3,plain,
! [U_2159,U_2160,U_2162,U_2161] :
( c_Orderings_Oord__class_Oless(U_2159,U_2160,U_2162)
| ~ c_Orderings_Oord__class_Oless__eq(U_2159,U_2161,U_2162)
| ~ c_Orderings_Oord__class_Oless(U_2159,U_2160,U_2161)
| ~ class_Orderings_Opreorder(U_2159) ),
inference(definitional_conversion,[status(esa)],[f_749_2]) ).
cnf(f_749_4,plain,
( c_Orderings_Oord__class_Oless(U_2159,U_2160,U_2162)
| ~ c_Orderings_Oord__class_Oless__eq(U_2159,U_2161,U_2162)
| ~ c_Orderings_Oord__class_Oless(U_2159,U_2160,U_2161)
| ~ class_Orderings_Opreorder(U_2159) ),
inference(clausify,[status(thm)],[f_749_3]) ).
fof(f_750_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_750_2,plain,
! [U_2165,U_2164,U_2163] :
( c_Orderings_Oord__class_Oless(U_2163,U_2164,U_2165)
| U_2165 = U_2164
| ~ c_Orderings_Oord__class_Oless__eq(U_2163,U_2164,U_2165)
| ~ class_Orderings_Oorder(U_2163) ),
inference(variable_rename,[status(thm)],[f_750_1]) ).
fof(f_750_3,plain,
! [U_2165,U_2163,U_2164] :
( c_Orderings_Oord__class_Oless(U_2163,U_2164,U_2165)
| U_2165 = U_2164
| ~ c_Orderings_Oord__class_Oless__eq(U_2163,U_2164,U_2165)
| ~ class_Orderings_Oorder(U_2163) ),
inference(definitional_conversion,[status(esa)],[f_750_2]) ).
cnf(f_750_4,plain,
( c_Orderings_Oord__class_Oless(U_2163,U_2164,U_2165)
| U_2165 = U_2164
| ~ c_Orderings_Oord__class_Oless__eq(U_2163,U_2164,U_2165)
| ~ class_Orderings_Oorder(U_2163) ),
inference(clausify,[status(thm)],[f_750_3]) ).
fof(f_751_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_751_2,plain,
! [U_2168,U_2167,U_2166] :
( c_Orderings_Oord__class_Oless(U_2166,U_2167,U_2168)
| U_2167 = U_2168
| ~ c_Orderings_Oord__class_Oless__eq(U_2166,U_2167,U_2168)
| ~ class_Orderings_Oorder(U_2166) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
fof(f_751_3,plain,
! [U_2167,U_2168,U_2166] :
( c_Orderings_Oord__class_Oless(U_2166,U_2167,U_2168)
| U_2167 = U_2168
| ~ c_Orderings_Oord__class_Oless__eq(U_2166,U_2167,U_2168)
| ~ class_Orderings_Oorder(U_2166) ),
inference(definitional_conversion,[status(esa)],[f_751_2]) ).
cnf(f_751_4,plain,
( c_Orderings_Oord__class_Oless(U_2166,U_2167,U_2168)
| U_2167 = U_2168
| ~ c_Orderings_Oord__class_Oless__eq(U_2166,U_2167,U_2168)
| ~ class_Orderings_Oorder(U_2166) ),
inference(clausify,[status(thm)],[f_751_3]) ).
fof(f_752_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_752_2,plain,
! [U_2171,U_2170,U_2169] :
( U_2170 = U_2171
| c_Orderings_Oord__class_Oless(U_2169,U_2170,U_2171)
| ~ c_Orderings_Oord__class_Oless__eq(U_2169,U_2170,U_2171)
| ~ class_Orderings_Oorder(U_2169) ),
inference(variable_rename,[status(thm)],[f_752_1]) ).
fof(f_752_3,plain,
! [U_2169,U_2171,U_2170] :
( U_2170 = U_2171
| c_Orderings_Oord__class_Oless(U_2169,U_2170,U_2171)
| ~ c_Orderings_Oord__class_Oless__eq(U_2169,U_2170,U_2171)
| ~ class_Orderings_Oorder(U_2169) ),
inference(definitional_conversion,[status(esa)],[f_752_2]) ).
cnf(f_752_4,plain,
( U_2170 = U_2171
| c_Orderings_Oord__class_Oless(U_2169,U_2170,U_2171)
| ~ c_Orderings_Oord__class_Oless__eq(U_2169,U_2170,U_2171)
| ~ class_Orderings_Oorder(U_2169) ),
inference(clausify,[status(thm)],[f_752_3]) ).
fof(f_753_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
| V_xa_2 != V_ya_2 )
& ( V_xa_2 = V_ya_2
| c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(f_753_2,plain,
! [U_2174,U_2173,U_2172] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2172,U_2173,U_2174)
| U_2173 != U_2174 )
& ( U_2173 = U_2174
| c_Orderings_Oord__class_Oless(U_2172,U_2173,U_2174) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2172,U_2173,U_2174)
| ~ class_Orderings_Olinorder(U_2172) ),
inference(variable_rename,[status(thm)],[f_753_1]) ).
fof(f_753_3,plain,
( ! [U_2174,U_2173,U_2172] :
( ~ c_Orderings_Oord__class_Oless(U_2172,U_2173,U_2174)
| U_2173 != U_2174
| ~ sP176(U_2174,U_2173,U_2172) )
& ! [U_2174,U_2173,U_2172] :
( U_2173 = U_2174
| c_Orderings_Oord__class_Oless(U_2172,U_2173,U_2174)
| ~ sP176(U_2174,U_2173,U_2172) )
& ! [U_2174,U_2173,U_2172] :
( sP176(U_2174,U_2173,U_2172)
| ~ c_Orderings_Oord__class_Oless__eq(U_2172,U_2173,U_2174)
| ~ class_Orderings_Olinorder(U_2172) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_753_2]) ).
cnf(f_753_4,plain,
( sP176(U_2174,U_2173,U_2172)
| ~ c_Orderings_Oord__class_Oless__eq(U_2172,U_2173,U_2174)
| ~ class_Orderings_Olinorder(U_2172) ),
inference(clausify,[status(thm)],[f_753_3]) ).
cnf(f_753_5,plain,
( U_2173 = U_2174
| c_Orderings_Oord__class_Oless(U_2172,U_2173,U_2174)
| ~ sP176(U_2174,U_2173,U_2172) ),
inference(clausify,[status(thm)],[f_753_3]) ).
cnf(f_753_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_2172,U_2173,U_2174)
| U_2173 != U_2174
| ~ sP176(U_2174,U_2173,U_2172) ),
inference(clausify,[status(thm)],[f_753_3]) ).
fof(f_754_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_754_2,plain,
! [U_2177,U_2176,U_2175] :
( c_Orderings_Oord__class_Oless__eq(U_2175,U_2176,U_2177)
| ~ c_Orderings_Oord__class_Oless(U_2175,U_2176,U_2177)
| ~ class_Orderings_Opreorder(U_2175) ),
inference(variable_rename,[status(thm)],[f_754_1]) ).
fof(f_754_3,plain,
! [U_2176,U_2177,U_2175] :
( c_Orderings_Oord__class_Oless__eq(U_2175,U_2176,U_2177)
| ~ c_Orderings_Oord__class_Oless(U_2175,U_2176,U_2177)
| ~ class_Orderings_Opreorder(U_2175) ),
inference(definitional_conversion,[status(esa)],[f_754_2]) ).
cnf(f_754_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2175,U_2176,U_2177)
| ~ c_Orderings_Oord__class_Oless(U_2175,U_2176,U_2177)
| ~ class_Orderings_Opreorder(U_2175) ),
inference(clausify,[status(thm)],[f_754_3]) ).
fof(f_755_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_755_2,plain,
! [U_2180,U_2179,U_2178] :
( ~ c_Orderings_Oord__class_Oless(U_2178,U_2180,U_2179)
| ~ c_Orderings_Oord__class_Oless__eq(U_2178,U_2179,U_2180)
| ~ class_Orderings_Olinorder(U_2178) ),
inference(variable_rename,[status(thm)],[f_755_1]) ).
fof(f_755_3,plain,
! [U_2179,U_2178,U_2180] :
( ~ c_Orderings_Oord__class_Oless(U_2178,U_2180,U_2179)
| ~ c_Orderings_Oord__class_Oless__eq(U_2178,U_2179,U_2180)
| ~ class_Orderings_Olinorder(U_2178) ),
inference(definitional_conversion,[status(esa)],[f_755_2]) ).
cnf(f_755_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2178,U_2180,U_2179)
| ~ c_Orderings_Oord__class_Oless__eq(U_2178,U_2179,U_2180)
| ~ class_Orderings_Olinorder(U_2178) ),
inference(clausify,[status(thm)],[f_755_3]) ).
fof(f_756_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_756_2,plain,
! [U_2183,U_2182,U_2181] :
( c_Orderings_Oord__class_Oless(U_2181,U_2183,U_2182)
| ~ c_Orderings_Oord__class_Oless__eq(U_2181,U_2183,U_2182)
| U_2182 = U_2183
| ~ class_Orderings_Oorder(U_2181) ),
inference(variable_rename,[status(thm)],[f_756_1]) ).
fof(f_756_3,plain,
! [U_2182,U_2183,U_2181] :
( c_Orderings_Oord__class_Oless(U_2181,U_2183,U_2182)
| ~ c_Orderings_Oord__class_Oless__eq(U_2181,U_2183,U_2182)
| U_2182 = U_2183
| ~ class_Orderings_Oorder(U_2181) ),
inference(definitional_conversion,[status(esa)],[f_756_2]) ).
cnf(f_756_4,plain,
( c_Orderings_Oord__class_Oless(U_2181,U_2183,U_2182)
| ~ c_Orderings_Oord__class_Oless__eq(U_2181,U_2183,U_2182)
| U_2182 = U_2183
| ~ class_Orderings_Oorder(U_2181) ),
inference(clausify,[status(thm)],[f_756_3]) ).
fof(f_757_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_757_2,plain,
! [U_2186,U_2185,U_2184] :
( c_Orderings_Oord__class_Oless(U_2184,U_2185,U_2186)
| ~ c_Orderings_Oord__class_Oless__eq(U_2184,U_2185,U_2186)
| U_2185 = U_2186
| ~ class_Orderings_Oorder(U_2184) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
fof(f_757_3,plain,
! [U_2184,U_2185,U_2186] :
( c_Orderings_Oord__class_Oless(U_2184,U_2185,U_2186)
| ~ c_Orderings_Oord__class_Oless__eq(U_2184,U_2185,U_2186)
| U_2185 = U_2186
| ~ class_Orderings_Oorder(U_2184) ),
inference(definitional_conversion,[status(esa)],[f_757_2]) ).
cnf(f_757_4,plain,
( c_Orderings_Oord__class_Oless(U_2184,U_2185,U_2186)
| ~ c_Orderings_Oord__class_Oless__eq(U_2184,U_2185,U_2186)
| U_2185 = U_2186
| ~ class_Orderings_Oorder(U_2184) ),
inference(clausify,[status(thm)],[f_757_3]) ).
fof(f_758_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
| V_xa_2 != V_ya_2 )
& ( V_xa_2 = V_ya_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(f_758_2,plain,
! [U_2189,U_2188,U_2187] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2187,U_2188,U_2189)
| U_2188 != U_2189 )
& ( U_2188 = U_2189
| ~ c_Orderings_Oord__class_Oless__eq(U_2187,U_2188,U_2189) ) )
| c_Orderings_Oord__class_Oless(U_2187,U_2188,U_2189)
| ~ class_Orderings_Olinorder(U_2187) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
fof(f_758_3,plain,
( ! [U_2187,U_2188,U_2189] :
( c_Orderings_Oord__class_Oless__eq(U_2187,U_2188,U_2189)
| U_2188 != U_2189
| ~ sP177(U_2187,U_2188,U_2189) )
& ! [U_2187,U_2188,U_2189] :
( U_2188 = U_2189
| ~ c_Orderings_Oord__class_Oless__eq(U_2187,U_2188,U_2189)
| ~ sP177(U_2187,U_2188,U_2189) )
& ! [U_2187,U_2188,U_2189] :
( sP177(U_2187,U_2188,U_2189)
| c_Orderings_Oord__class_Oless(U_2187,U_2188,U_2189)
| ~ class_Orderings_Olinorder(U_2187) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_758_2]) ).
cnf(f_758_4,plain,
( sP177(U_2187,U_2188,U_2189)
| c_Orderings_Oord__class_Oless(U_2187,U_2188,U_2189)
| ~ class_Orderings_Olinorder(U_2187) ),
inference(clausify,[status(thm)],[f_758_3]) ).
cnf(f_758_5,plain,
( U_2188 = U_2189
| ~ c_Orderings_Oord__class_Oless__eq(U_2187,U_2188,U_2189)
| ~ sP177(U_2187,U_2188,U_2189) ),
inference(clausify,[status(thm)],[f_758_3]) ).
cnf(f_758_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2187,U_2188,U_2189)
| U_2188 != U_2189
| ~ sP177(U_2187,U_2188,U_2189) ),
inference(clausify,[status(thm)],[f_758_3]) ).
fof(f_759_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_759_2,plain,
! [U_2192,U_2191,U_2190] :
( c_Orderings_Oord__class_Oless(U_2190,U_2192,U_2191)
| c_Orderings_Oord__class_Oless__eq(U_2190,U_2191,U_2192)
| ~ class_Orderings_Olinorder(U_2190) ),
inference(variable_rename,[status(thm)],[f_759_1]) ).
fof(f_759_3,plain,
! [U_2191,U_2192,U_2190] :
( c_Orderings_Oord__class_Oless(U_2190,U_2192,U_2191)
| c_Orderings_Oord__class_Oless__eq(U_2190,U_2191,U_2192)
| ~ class_Orderings_Olinorder(U_2190) ),
inference(definitional_conversion,[status(esa)],[f_759_2]) ).
cnf(f_759_4,plain,
( c_Orderings_Oord__class_Oless(U_2190,U_2192,U_2191)
| c_Orderings_Oord__class_Oless__eq(U_2190,U_2191,U_2192)
| ~ class_Orderings_Olinorder(U_2190) ),
inference(clausify,[status(thm)],[f_759_3]) ).
fof(f_760_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_760_2,plain,
! [U_2195,U_2194,U_2193] :
( c_Orderings_Oord__class_Oless__eq(U_2193,U_2195,U_2194)
| c_Orderings_Oord__class_Oless(U_2193,U_2194,U_2195)
| ~ class_Orderings_Olinorder(U_2193) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
fof(f_760_3,plain,
! [U_2195,U_2194,U_2193] :
( c_Orderings_Oord__class_Oless__eq(U_2193,U_2195,U_2194)
| c_Orderings_Oord__class_Oless(U_2193,U_2194,U_2195)
| ~ class_Orderings_Olinorder(U_2193) ),
inference(definitional_conversion,[status(esa)],[f_760_2]) ).
cnf(f_760_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2193,U_2195,U_2194)
| c_Orderings_Oord__class_Oless(U_2193,U_2194,U_2195)
| ~ class_Orderings_Olinorder(U_2193) ),
inference(clausify,[status(thm)],[f_760_3]) ).
fof(f_761_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
| ( V_xa_2 != V_ya_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) )
& ( V_xa_2 = V_ya_2
| c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).
fof(f_761_2,plain,
! [U_2198,U_2197,U_2196] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2196,U_2197,U_2198)
| ( U_2197 != U_2198
& ~ c_Orderings_Oord__class_Oless(U_2196,U_2197,U_2198) ) )
& ( U_2197 = U_2198
| c_Orderings_Oord__class_Oless(U_2196,U_2197,U_2198)
| ~ c_Orderings_Oord__class_Oless__eq(U_2196,U_2197,U_2198) ) )
| ~ class_Orderings_Oorder(U_2196) ),
inference(variable_rename,[status(thm)],[f_761_1]) ).
fof(f_761_3,plain,
( ! [U_2196,U_2197,U_2198] :
( U_2197 != U_2198
| ~ sP178(U_2196,U_2197,U_2198) )
& ! [U_2196,U_2197,U_2198] :
( ~ c_Orderings_Oord__class_Oless(U_2196,U_2197,U_2198)
| ~ sP178(U_2196,U_2197,U_2198) )
& ! [U_2196,U_2197,U_2198] :
( c_Orderings_Oord__class_Oless__eq(U_2196,U_2197,U_2198)
| sP178(U_2196,U_2197,U_2198)
| ~ sP179(U_2196,U_2197,U_2198) )
& ! [U_2196,U_2197,U_2198] :
( U_2197 = U_2198
| c_Orderings_Oord__class_Oless(U_2196,U_2197,U_2198)
| ~ c_Orderings_Oord__class_Oless__eq(U_2196,U_2197,U_2198)
| ~ sP179(U_2196,U_2197,U_2198) )
& ! [U_2196,U_2197,U_2198] :
( sP179(U_2196,U_2197,U_2198)
| ~ class_Orderings_Oorder(U_2196) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178,sP179])],[f_761_2]) ).
cnf(f_761_4,plain,
( sP179(U_2196,U_2197,U_2198)
| ~ class_Orderings_Oorder(U_2196) ),
inference(clausify,[status(thm)],[f_761_3]) ).
cnf(f_761_5,plain,
( U_2197 = U_2198
| c_Orderings_Oord__class_Oless(U_2196,U_2197,U_2198)
| ~ c_Orderings_Oord__class_Oless__eq(U_2196,U_2197,U_2198)
| ~ sP179(U_2196,U_2197,U_2198) ),
inference(clausify,[status(thm)],[f_761_3]) ).
cnf(f_761_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2196,U_2197,U_2198)
| sP178(U_2196,U_2197,U_2198)
| ~ sP179(U_2196,U_2197,U_2198) ),
inference(clausify,[status(thm)],[f_761_3]) ).
cnf(f_761_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_2196,U_2197,U_2198)
| ~ sP178(U_2196,U_2197,U_2198) ),
inference(clausify,[status(thm)],[f_761_3]) ).
cnf(f_761_8,plain,
( U_2197 != U_2198
| ~ sP178(U_2196,U_2197,U_2198) ),
inference(clausify,[status(thm)],[f_761_3]) ).
fof(f_762_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) )
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).
fof(f_762_2,plain,
! [U_2201,U_2200,U_2199] :
( ( ( c_Orderings_Oord__class_Oless(U_2199,U_2200,U_2201)
| c_Orderings_Oord__class_Oless__eq(U_2199,U_2201,U_2200)
| ~ c_Orderings_Oord__class_Oless__eq(U_2199,U_2200,U_2201) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2199,U_2201,U_2200)
& c_Orderings_Oord__class_Oless__eq(U_2199,U_2200,U_2201) )
| ~ c_Orderings_Oord__class_Oless(U_2199,U_2200,U_2201) ) )
| ~ class_Orderings_Opreorder(U_2199) ),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
( ! [U_2200,U_2199,U_2201] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2199,U_2201,U_2200)
| ~ sP180(U_2200,U_2199,U_2201) )
& ! [U_2200,U_2199,U_2201] :
( c_Orderings_Oord__class_Oless__eq(U_2199,U_2200,U_2201)
| ~ sP180(U_2200,U_2199,U_2201) )
& ! [U_2200,U_2199,U_2201] :
( c_Orderings_Oord__class_Oless(U_2199,U_2200,U_2201)
| c_Orderings_Oord__class_Oless__eq(U_2199,U_2201,U_2200)
| ~ c_Orderings_Oord__class_Oless__eq(U_2199,U_2200,U_2201)
| ~ sP181(U_2200,U_2199,U_2201) )
& ! [U_2200,U_2199,U_2201] :
( sP180(U_2200,U_2199,U_2201)
| ~ c_Orderings_Oord__class_Oless(U_2199,U_2200,U_2201)
| ~ sP181(U_2200,U_2199,U_2201) )
& ! [U_2200,U_2199,U_2201] :
( sP181(U_2200,U_2199,U_2201)
| ~ class_Orderings_Opreorder(U_2199) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180,sP181])],[f_762_2]) ).
cnf(f_762_4,plain,
( sP181(U_2200,U_2199,U_2201)
| ~ class_Orderings_Opreorder(U_2199) ),
inference(clausify,[status(thm)],[f_762_3]) ).
cnf(f_762_5,plain,
( sP180(U_2200,U_2199,U_2201)
| ~ c_Orderings_Oord__class_Oless(U_2199,U_2200,U_2201)
| ~ sP181(U_2200,U_2199,U_2201) ),
inference(clausify,[status(thm)],[f_762_3]) ).
cnf(f_762_6,plain,
( c_Orderings_Oord__class_Oless(U_2199,U_2200,U_2201)
| c_Orderings_Oord__class_Oless__eq(U_2199,U_2201,U_2200)
| ~ c_Orderings_Oord__class_Oless__eq(U_2199,U_2200,U_2201)
| ~ sP181(U_2200,U_2199,U_2201) ),
inference(clausify,[status(thm)],[f_762_3]) ).
cnf(f_762_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2199,U_2200,U_2201)
| ~ sP180(U_2200,U_2199,U_2201) ),
inference(clausify,[status(thm)],[f_762_3]) ).
cnf(f_762_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2199,U_2201,U_2200)
| ~ sP180(U_2200,U_2199,U_2201) ),
inference(clausify,[status(thm)],[f_762_3]) ).
fof(f_763_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
| V_xa_2 = V_ya_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) )
& ( ( V_xa_2 != V_ya_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).
fof(f_763_2,plain,
! [U_2204,U_2203,U_2202] :
( ( ( c_Orderings_Oord__class_Oless(U_2202,U_2203,U_2204)
| U_2203 = U_2204
| ~ c_Orderings_Oord__class_Oless__eq(U_2202,U_2203,U_2204) )
& ( ( U_2203 != U_2204
& c_Orderings_Oord__class_Oless__eq(U_2202,U_2203,U_2204) )
| ~ c_Orderings_Oord__class_Oless(U_2202,U_2203,U_2204) ) )
| ~ class_Orderings_Oorder(U_2202) ),
inference(variable_rename,[status(thm)],[f_763_1]) ).
fof(f_763_3,plain,
( ! [U_2204,U_2202,U_2203] :
( U_2203 != U_2204
| ~ sP182(U_2204,U_2202,U_2203) )
& ! [U_2204,U_2202,U_2203] :
( c_Orderings_Oord__class_Oless__eq(U_2202,U_2203,U_2204)
| ~ sP182(U_2204,U_2202,U_2203) )
& ! [U_2204,U_2202,U_2203] :
( c_Orderings_Oord__class_Oless(U_2202,U_2203,U_2204)
| U_2203 = U_2204
| ~ c_Orderings_Oord__class_Oless__eq(U_2202,U_2203,U_2204)
| ~ sP183(U_2204,U_2202,U_2203) )
& ! [U_2204,U_2202,U_2203] :
( sP182(U_2204,U_2202,U_2203)
| ~ c_Orderings_Oord__class_Oless(U_2202,U_2203,U_2204)
| ~ sP183(U_2204,U_2202,U_2203) )
& ! [U_2204,U_2202,U_2203] :
( sP183(U_2204,U_2202,U_2203)
| ~ class_Orderings_Oorder(U_2202) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182,sP183])],[f_763_2]) ).
cnf(f_763_4,plain,
( sP183(U_2204,U_2202,U_2203)
| ~ class_Orderings_Oorder(U_2202) ),
inference(clausify,[status(thm)],[f_763_3]) ).
cnf(f_763_5,plain,
( sP182(U_2204,U_2202,U_2203)
| ~ c_Orderings_Oord__class_Oless(U_2202,U_2203,U_2204)
| ~ sP183(U_2204,U_2202,U_2203) ),
inference(clausify,[status(thm)],[f_763_3]) ).
cnf(f_763_6,plain,
( c_Orderings_Oord__class_Oless(U_2202,U_2203,U_2204)
| U_2203 = U_2204
| ~ c_Orderings_Oord__class_Oless__eq(U_2202,U_2203,U_2204)
| ~ sP183(U_2204,U_2202,U_2203) ),
inference(clausify,[status(thm)],[f_763_3]) ).
cnf(f_763_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2202,U_2203,U_2204)
| ~ sP182(U_2204,U_2202,U_2203) ),
inference(clausify,[status(thm)],[f_763_3]) ).
cnf(f_763_8,plain,
( U_2203 != U_2204
| ~ sP182(U_2204,U_2202,U_2203) ),
inference(clausify,[status(thm)],[f_763_3]) ).
fof(f_764_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_764_2,plain,
! [U_2207,U_2206,U_2205] :
( c_Orderings_Oord__class_Oless(U_2205,U_2207,U_2206)
| c_Orderings_Oord__class_Oless__eq(U_2205,U_2206,U_2207)
| ~ class_Orderings_Olinorder(U_2205) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
fof(f_764_3,plain,
! [U_2206,U_2207,U_2205] :
( c_Orderings_Oord__class_Oless(U_2205,U_2207,U_2206)
| c_Orderings_Oord__class_Oless__eq(U_2205,U_2206,U_2207)
| ~ class_Orderings_Olinorder(U_2205) ),
inference(definitional_conversion,[status(esa)],[f_764_2]) ).
cnf(f_764_4,plain,
( c_Orderings_Oord__class_Oless(U_2205,U_2207,U_2206)
| c_Orderings_Oord__class_Oless__eq(U_2205,U_2206,U_2207)
| ~ class_Orderings_Olinorder(U_2205) ),
inference(clausify,[status(thm)],[f_764_3]) ).
fof(f_765_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ya_2,V_xa_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_xa_2,V_ya_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).
fof(f_765_2,plain,
! [U_2210,U_2209,U_2208] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2208,U_2209,U_2210)
| ~ c_Orderings_Oord__class_Oless(U_2208,U_2210,U_2209) )
& ( c_Orderings_Oord__class_Oless(U_2208,U_2210,U_2209)
| c_Orderings_Oord__class_Oless__eq(U_2208,U_2209,U_2210) ) )
| ~ class_Orderings_Olinorder(U_2208) ),
inference(variable_rename,[status(thm)],[f_765_1]) ).
fof(f_765_3,plain,
( ! [U_2208,U_2209,U_2210] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2208,U_2209,U_2210)
| ~ c_Orderings_Oord__class_Oless(U_2208,U_2210,U_2209)
| ~ sP184(U_2208,U_2209,U_2210) )
& ! [U_2208,U_2209,U_2210] :
( c_Orderings_Oord__class_Oless(U_2208,U_2210,U_2209)
| c_Orderings_Oord__class_Oless__eq(U_2208,U_2209,U_2210)
| ~ sP184(U_2208,U_2209,U_2210) )
& ! [U_2208,U_2209,U_2210] :
( sP184(U_2208,U_2209,U_2210)
| ~ class_Orderings_Olinorder(U_2208) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_765_2]) ).
cnf(f_765_4,plain,
( sP184(U_2208,U_2209,U_2210)
| ~ class_Orderings_Olinorder(U_2208) ),
inference(clausify,[status(thm)],[f_765_3]) ).
cnf(f_765_5,plain,
( c_Orderings_Oord__class_Oless(U_2208,U_2210,U_2209)
| c_Orderings_Oord__class_Oless__eq(U_2208,U_2209,U_2210)
| ~ sP184(U_2208,U_2209,U_2210) ),
inference(clausify,[status(thm)],[f_765_3]) ).
cnf(f_765_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2208,U_2209,U_2210)
| ~ c_Orderings_Oord__class_Oless(U_2208,U_2210,U_2209)
| ~ sP184(U_2208,U_2209,U_2210) ),
inference(clausify,[status(thm)],[f_765_3]) ).
fof(f_766_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_ya_2,V_xa_2)
| c_Orderings_Oord__class_Oless(T_a,V_xa_2,V_ya_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).
fof(f_766_2,plain,
! [U_2213,U_2212,U_2211] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_2211,U_2212,U_2213)
| ~ c_Orderings_Oord__class_Oless__eq(U_2211,U_2213,U_2212) )
& ( c_Orderings_Oord__class_Oless__eq(U_2211,U_2213,U_2212)
| c_Orderings_Oord__class_Oless(U_2211,U_2212,U_2213) ) )
| ~ class_Orderings_Olinorder(U_2211) ),
inference(variable_rename,[status(thm)],[f_766_1]) ).
fof(f_766_3,plain,
( ! [U_2213,U_2211,U_2212] :
( ~ c_Orderings_Oord__class_Oless(U_2211,U_2212,U_2213)
| ~ c_Orderings_Oord__class_Oless__eq(U_2211,U_2213,U_2212)
| ~ sP185(U_2213,U_2211,U_2212) )
& ! [U_2213,U_2211,U_2212] :
( c_Orderings_Oord__class_Oless__eq(U_2211,U_2213,U_2212)
| c_Orderings_Oord__class_Oless(U_2211,U_2212,U_2213)
| ~ sP185(U_2213,U_2211,U_2212) )
& ! [U_2213,U_2211,U_2212] :
( sP185(U_2213,U_2211,U_2212)
| ~ class_Orderings_Olinorder(U_2211) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_766_2]) ).
cnf(f_766_4,plain,
( sP185(U_2213,U_2211,U_2212)
| ~ class_Orderings_Olinorder(U_2211) ),
inference(clausify,[status(thm)],[f_766_3]) ).
cnf(f_766_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2211,U_2213,U_2212)
| c_Orderings_Oord__class_Oless(U_2211,U_2212,U_2213)
| ~ sP185(U_2213,U_2211,U_2212) ),
inference(clausify,[status(thm)],[f_766_3]) ).
cnf(f_766_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_2211,U_2212,U_2213)
| ~ c_Orderings_Oord__class_Oless__eq(U_2211,U_2213,U_2212)
| ~ sP185(U_2213,U_2211,U_2212) ),
inference(clausify,[status(thm)],[f_766_3]) ).
fof(f_767_1,plain,
! [V_a,V_N,V_n,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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_767_2,plain,
! [U_2217,U_2216,U_2215,U_2214] :
( c_Orderings_Oord__class_Oless(U_2214,hAPP(hAPP(c_Power_Opower__class_Opower(U_2214),U_2217),U_2215),hAPP(hAPP(c_Power_Opower__class_Opower(U_2214),U_2217),U_2216))
| ~ c_Orderings_Oord__class_Oless(U_2214,c_Groups_Oone__class_Oone(U_2214),U_2217)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2215,U_2216)
| ~ class_Rings_Olinordered__semidom(U_2214) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
fof(f_767_3,plain,
! [U_2217,U_2216,U_2215,U_2214] :
( c_Orderings_Oord__class_Oless(U_2214,hAPP(hAPP(c_Power_Opower__class_Opower(U_2214),U_2217),U_2215),hAPP(hAPP(c_Power_Opower__class_Opower(U_2214),U_2217),U_2216))
| ~ c_Orderings_Oord__class_Oless(U_2214,c_Groups_Oone__class_Oone(U_2214),U_2217)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2215,U_2216)
| ~ class_Rings_Olinordered__semidom(U_2214) ),
inference(definitional_conversion,[status(esa)],[f_767_2]) ).
cnf(f_767_4,plain,
( c_Orderings_Oord__class_Oless(U_2214,hAPP(hAPP(c_Power_Opower__class_Opower(U_2214),U_2217),U_2215),hAPP(hAPP(c_Power_Opower__class_Opower(U_2214),U_2217),U_2216))
| ~ c_Orderings_Oord__class_Oless(U_2214,c_Groups_Oone__class_Oone(U_2214),U_2217)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2215,U_2216)
| ~ class_Rings_Olinordered__semidom(U_2214) ),
inference(clausify,[status(thm)],[f_767_3]) ).
fof(f_768_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(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_768_2,plain,
! [U_2221,U_2220,U_2219,U_2218] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2220,U_2221)
| ~ c_Orderings_Oord__class_Oless(U_2218,hAPP(hAPP(c_Power_Opower__class_Opower(U_2218),U_2219),U_2220),hAPP(hAPP(c_Power_Opower__class_Opower(U_2218),U_2219),U_2221))
| ~ c_Orderings_Oord__class_Oless(U_2218,c_Groups_Oone__class_Oone(U_2218),U_2219)
| ~ class_Rings_Olinordered__semidom(U_2218) ),
inference(variable_rename,[status(thm)],[f_768_1]) ).
fof(f_768_3,plain,
! [U_2218,U_2219,U_2220,U_2221] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2220,U_2221)
| ~ c_Orderings_Oord__class_Oless(U_2218,hAPP(hAPP(c_Power_Opower__class_Opower(U_2218),U_2219),U_2220),hAPP(hAPP(c_Power_Opower__class_Opower(U_2218),U_2219),U_2221))
| ~ c_Orderings_Oord__class_Oless(U_2218,c_Groups_Oone__class_Oone(U_2218),U_2219)
| ~ class_Rings_Olinordered__semidom(U_2218) ),
inference(definitional_conversion,[status(esa)],[f_768_2]) ).
cnf(f_768_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2220,U_2221)
| ~ c_Orderings_Oord__class_Oless(U_2218,hAPP(hAPP(c_Power_Opower__class_Opower(U_2218),U_2219),U_2220),hAPP(hAPP(c_Power_Opower__class_Opower(U_2218),U_2219),U_2221))
| ~ c_Orderings_Oord__class_Oless(U_2218,c_Groups_Oone__class_Oone(U_2218),U_2219)
| ~ class_Rings_Olinordered__semidom(U_2218) ),
inference(clausify,[status(thm)],[f_768_3]) ).
fof(f_769_1,plain,
! [V_ya_2,V_xa_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_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_769_2,plain,
! [U_2225,U_2224,U_2223,U_2222] :
( ( ( c_Orderings_Oord__class_Oless(U_2222,hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2224),hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2225))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2224,U_2225) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2224,U_2225)
| ~ c_Orderings_Oord__class_Oless(U_2222,hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2224),hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2225)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2222,c_Groups_Oone__class_Oone(U_2222),U_2223)
| ~ class_Rings_Olinordered__semidom(U_2222) ),
inference(variable_rename,[status(thm)],[f_769_1]) ).
fof(f_769_3,plain,
( ! [U_2222,U_2223,U_2224,U_2225] :
( c_Orderings_Oord__class_Oless(U_2222,hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2224),hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2225))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2224,U_2225)
| ~ sP186(U_2222,U_2223,U_2224,U_2225) )
& ! [U_2222,U_2223,U_2224,U_2225] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2224,U_2225)
| ~ c_Orderings_Oord__class_Oless(U_2222,hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2224),hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2225))
| ~ sP186(U_2222,U_2223,U_2224,U_2225) )
& ! [U_2222,U_2223,U_2224,U_2225] :
( sP186(U_2222,U_2223,U_2224,U_2225)
| ~ c_Orderings_Oord__class_Oless(U_2222,c_Groups_Oone__class_Oone(U_2222),U_2223)
| ~ class_Rings_Olinordered__semidom(U_2222) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_769_2]) ).
cnf(f_769_4,plain,
( sP186(U_2222,U_2223,U_2224,U_2225)
| ~ c_Orderings_Oord__class_Oless(U_2222,c_Groups_Oone__class_Oone(U_2222),U_2223)
| ~ class_Rings_Olinordered__semidom(U_2222) ),
inference(clausify,[status(thm)],[f_769_3]) ).
cnf(f_769_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2224,U_2225)
| ~ c_Orderings_Oord__class_Oless(U_2222,hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2224),hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2225))
| ~ sP186(U_2222,U_2223,U_2224,U_2225) ),
inference(clausify,[status(thm)],[f_769_3]) ).
cnf(f_769_6,plain,
( c_Orderings_Oord__class_Oless(U_2222,hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2224),hAPP(hAPP(c_Power_Opower__class_Opower(U_2222),U_2223),U_2225))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2224,U_2225)
| ~ sP186(U_2222,U_2223,U_2224,U_2225) ),
inference(clausify,[status(thm)],[f_769_3]) ).
fof(f_770_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_770_2,plain,
! [U_2228,U_2227,U_2226] :
( c_Orderings_Oord__class_Oless(U_2226,U_2228,U_2227)
| c_Orderings_Oord__class_Oless(U_2226,U_2227,U_2228)
| U_2227 = U_2228
| ~ class_Rings_Olinordered__idom(U_2226) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
fof(f_770_3,plain,
! [U_2226,U_2227,U_2228] :
( c_Orderings_Oord__class_Oless(U_2226,U_2228,U_2227)
| c_Orderings_Oord__class_Oless(U_2226,U_2227,U_2228)
| U_2227 = U_2228
| ~ class_Rings_Olinordered__idom(U_2226) ),
inference(definitional_conversion,[status(esa)],[f_770_2]) ).
cnf(f_770_4,plain,
( c_Orderings_Oord__class_Oless(U_2226,U_2228,U_2227)
| c_Orderings_Oord__class_Oless(U_2226,U_2227,U_2228)
| U_2227 = U_2228
| ~ class_Rings_Olinordered__idom(U_2226) ),
inference(clausify,[status(thm)],[f_770_3]) ).
fof(f_771_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Int_Onumber__class_Onumber__of(T_a,V_ya_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a)
| ~ class_Int_Onumber__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__number__of]) ).
fof(f_771_2,plain,
! [U_2231,U_2230,U_2229] :
( ( ( c_Orderings_Oord__class_Oless(U_2229,c_Int_Onumber__class_Onumber__of(U_2229,U_2230),c_Int_Onumber__class_Onumber__of(U_2229,U_2231))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2230,U_2231) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2230,U_2231)
| ~ c_Orderings_Oord__class_Oless(U_2229,c_Int_Onumber__class_Onumber__of(U_2229,U_2230),c_Int_Onumber__class_Onumber__of(U_2229,U_2231)) ) )
| ~ class_Rings_Olinordered__idom(U_2229)
| ~ class_Int_Onumber__ring(U_2229) ),
inference(variable_rename,[status(thm)],[f_771_1]) ).
fof(f_771_3,plain,
( ! [U_2230,U_2231,U_2229] :
( c_Orderings_Oord__class_Oless(U_2229,c_Int_Onumber__class_Onumber__of(U_2229,U_2230),c_Int_Onumber__class_Onumber__of(U_2229,U_2231))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2230,U_2231)
| ~ sP187(U_2230,U_2231,U_2229) )
& ! [U_2230,U_2231,U_2229] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2230,U_2231)
| ~ c_Orderings_Oord__class_Oless(U_2229,c_Int_Onumber__class_Onumber__of(U_2229,U_2230),c_Int_Onumber__class_Onumber__of(U_2229,U_2231))
| ~ sP187(U_2230,U_2231,U_2229) )
& ! [U_2230,U_2231,U_2229] :
( sP187(U_2230,U_2231,U_2229)
| ~ class_Rings_Olinordered__idom(U_2229)
| ~ class_Int_Onumber__ring(U_2229) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_771_2]) ).
cnf(f_771_4,plain,
( sP187(U_2230,U_2231,U_2229)
| ~ class_Rings_Olinordered__idom(U_2229)
| ~ class_Int_Onumber__ring(U_2229) ),
inference(clausify,[status(thm)],[f_771_3]) ).
cnf(f_771_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2230,U_2231)
| ~ c_Orderings_Oord__class_Oless(U_2229,c_Int_Onumber__class_Onumber__of(U_2229,U_2230),c_Int_Onumber__class_Onumber__of(U_2229,U_2231))
| ~ sP187(U_2230,U_2231,U_2229) ),
inference(clausify,[status(thm)],[f_771_3]) ).
cnf(f_771_6,plain,
( c_Orderings_Oord__class_Oless(U_2229,c_Int_Onumber__class_Onumber__of(U_2229,U_2230),c_Int_Onumber__class_Onumber__of(U_2229,U_2231))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2230,U_2231)
| ~ sP187(U_2230,U_2231,U_2229) ),
inference(clausify,[status(thm)],[f_771_3]) ).
fof(f_772_1,plain,
! [V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_2),c_Groups_Oone__class_Oone(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_xa_2,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_xa_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_772_2,plain,
! [U_2233,U_2232] :
( ( ( c_Orderings_Oord__class_Oless(U_2232,c_Int_Onumber__class_Onumber__of(U_2232,U_2233),c_Groups_Oone__class_Oone(U_2232))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2233,c_Int_OBit1(c_Int_OPls)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2233,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(U_2232,c_Int_Onumber__class_Onumber__of(U_2232,U_2233),c_Groups_Oone__class_Oone(U_2232)) ) )
| ~ class_Rings_Olinordered__idom(U_2232)
| ~ class_Int_Onumber__ring(U_2232) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
fof(f_772_3,plain,
( ! [U_2233,U_2232] :
( c_Orderings_Oord__class_Oless(U_2232,c_Int_Onumber__class_Onumber__of(U_2232,U_2233),c_Groups_Oone__class_Oone(U_2232))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2233,c_Int_OBit1(c_Int_OPls))
| ~ sP188(U_2233,U_2232) )
& ! [U_2233,U_2232] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2233,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(U_2232,c_Int_Onumber__class_Onumber__of(U_2232,U_2233),c_Groups_Oone__class_Oone(U_2232))
| ~ sP188(U_2233,U_2232) )
& ! [U_2233,U_2232] :
( sP188(U_2233,U_2232)
| ~ class_Rings_Olinordered__idom(U_2232)
| ~ class_Int_Onumber__ring(U_2232) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_772_2]) ).
cnf(f_772_4,plain,
( sP188(U_2233,U_2232)
| ~ class_Rings_Olinordered__idom(U_2232)
| ~ class_Int_Onumber__ring(U_2232) ),
inference(clausify,[status(thm)],[f_772_3]) ).
cnf(f_772_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2233,c_Int_OBit1(c_Int_OPls))
| ~ c_Orderings_Oord__class_Oless(U_2232,c_Int_Onumber__class_Onumber__of(U_2232,U_2233),c_Groups_Oone__class_Oone(U_2232))
| ~ sP188(U_2233,U_2232) ),
inference(clausify,[status(thm)],[f_772_3]) ).
cnf(f_772_6,plain,
( c_Orderings_Oord__class_Oless(U_2232,c_Int_Onumber__class_Onumber__of(U_2232,U_2233),c_Groups_Oone__class_Oone(U_2232))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2233,c_Int_OBit1(c_Int_OPls))
| ~ sP188(U_2233,U_2232) ),
inference(clausify,[status(thm)],[f_772_3]) ).
fof(f_773_1,plain,
! [V_ya_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_ya_2))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),V_ya_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_ya_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_773_2,plain,
! [U_2235,U_2234] :
( ( ( c_Orderings_Oord__class_Oless(U_2234,c_Groups_Oone__class_Oone(U_2234),c_Int_Onumber__class_Onumber__of(U_2234,U_2235))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_2235) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_2235)
| ~ c_Orderings_Oord__class_Oless(U_2234,c_Groups_Oone__class_Oone(U_2234),c_Int_Onumber__class_Onumber__of(U_2234,U_2235)) ) )
| ~ class_Rings_Olinordered__idom(U_2234)
| ~ class_Int_Onumber__ring(U_2234) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
fof(f_773_3,plain,
( ! [U_2235,U_2234] :
( c_Orderings_Oord__class_Oless(U_2234,c_Groups_Oone__class_Oone(U_2234),c_Int_Onumber__class_Onumber__of(U_2234,U_2235))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_2235)
| ~ sP189(U_2235,U_2234) )
& ! [U_2235,U_2234] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_2235)
| ~ c_Orderings_Oord__class_Oless(U_2234,c_Groups_Oone__class_Oone(U_2234),c_Int_Onumber__class_Onumber__of(U_2234,U_2235))
| ~ sP189(U_2235,U_2234) )
& ! [U_2235,U_2234] :
( sP189(U_2235,U_2234)
| ~ class_Rings_Olinordered__idom(U_2234)
| ~ class_Int_Onumber__ring(U_2234) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_773_2]) ).
cnf(f_773_4,plain,
( sP189(U_2235,U_2234)
| ~ class_Rings_Olinordered__idom(U_2234)
| ~ class_Int_Onumber__ring(U_2234) ),
inference(clausify,[status(thm)],[f_773_3]) ).
cnf(f_773_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_2235)
| ~ c_Orderings_Oord__class_Oless(U_2234,c_Groups_Oone__class_Oone(U_2234),c_Int_Onumber__class_Onumber__of(U_2234,U_2235))
| ~ sP189(U_2235,U_2234) ),
inference(clausify,[status(thm)],[f_773_3]) ).
cnf(f_773_6,plain,
( c_Orderings_Oord__class_Oless(U_2234,c_Groups_Oone__class_Oone(U_2234),c_Int_Onumber__class_Onumber__of(U_2234,U_2235))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(c_Int_OPls),U_2235)
| ~ sP189(U_2235,U_2234) ),
inference(clausify,[status(thm)],[f_773_3]) ).
fof(f_774_1,plain,
! [V_n,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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_774_2,plain,
! [U_2239,U_2238,U_2237,U_2236] :
( c_Orderings_Oord__class_Oless(U_2236,hAPP(hAPP(c_Power_Opower__class_Opower(U_2236),U_2237),U_2239),hAPP(hAPP(c_Power_Opower__class_Opower(U_2236),U_2238),U_2239))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2239)
| ~ c_Orderings_Oord__class_Oless__eq(U_2236,c_Groups_Ozero__class_Ozero(U_2236),U_2237)
| ~ c_Orderings_Oord__class_Oless(U_2236,U_2237,U_2238)
| ~ class_Rings_Olinordered__semidom(U_2236) ),
inference(variable_rename,[status(thm)],[f_774_1]) ).
fof(f_774_3,plain,
! [U_2236,U_2237,U_2238,U_2239] :
( c_Orderings_Oord__class_Oless(U_2236,hAPP(hAPP(c_Power_Opower__class_Opower(U_2236),U_2237),U_2239),hAPP(hAPP(c_Power_Opower__class_Opower(U_2236),U_2238),U_2239))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2239)
| ~ c_Orderings_Oord__class_Oless__eq(U_2236,c_Groups_Ozero__class_Ozero(U_2236),U_2237)
| ~ c_Orderings_Oord__class_Oless(U_2236,U_2237,U_2238)
| ~ class_Rings_Olinordered__semidom(U_2236) ),
inference(definitional_conversion,[status(esa)],[f_774_2]) ).
cnf(f_774_4,plain,
( c_Orderings_Oord__class_Oless(U_2236,hAPP(hAPP(c_Power_Opower__class_Opower(U_2236),U_2237),U_2239),hAPP(hAPP(c_Power_Opower__class_Opower(U_2236),U_2238),U_2239))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2239)
| ~ c_Orderings_Oord__class_Oless__eq(U_2236,c_Groups_Ozero__class_Ozero(U_2236),U_2237)
| ~ c_Orderings_Oord__class_Oless(U_2236,U_2237,U_2238)
| ~ class_Rings_Olinordered__semidom(U_2236) ),
inference(clausify,[status(thm)],[f_774_3]) ).
fof(f_775_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_775_2,plain,
! [U_2244,U_2243,U_2242,U_2241,U_2240] :
( c_Orderings_Oord__class_Oless(U_2240,c_Groups_Oplus__class_Oplus(U_2240,U_2241,U_2243),c_Groups_Oplus__class_Oplus(U_2240,U_2242,U_2244))
| ~ c_Orderings_Oord__class_Oless(U_2240,U_2243,U_2244)
| ~ c_Orderings_Oord__class_Oless__eq(U_2240,U_2241,U_2242)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2240) ),
inference(variable_rename,[status(thm)],[f_775_1]) ).
fof(f_775_3,plain,
! [U_2243,U_2240,U_2244,U_2241,U_2242] :
( c_Orderings_Oord__class_Oless(U_2240,c_Groups_Oplus__class_Oplus(U_2240,U_2241,U_2243),c_Groups_Oplus__class_Oplus(U_2240,U_2242,U_2244))
| ~ c_Orderings_Oord__class_Oless(U_2240,U_2243,U_2244)
| ~ c_Orderings_Oord__class_Oless__eq(U_2240,U_2241,U_2242)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2240) ),
inference(definitional_conversion,[status(esa)],[f_775_2]) ).
cnf(f_775_4,plain,
( c_Orderings_Oord__class_Oless(U_2240,c_Groups_Oplus__class_Oplus(U_2240,U_2241,U_2243),c_Groups_Oplus__class_Oplus(U_2240,U_2242,U_2244))
| ~ c_Orderings_Oord__class_Oless(U_2240,U_2243,U_2244)
| ~ c_Orderings_Oord__class_Oless__eq(U_2240,U_2241,U_2242)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2240) ),
inference(clausify,[status(thm)],[f_775_3]) ).
fof(f_776_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_776_2,plain,
! [U_2249,U_2248,U_2247,U_2246,U_2245] :
( c_Orderings_Oord__class_Oless(U_2245,c_Groups_Oplus__class_Oplus(U_2245,U_2246,U_2248),c_Groups_Oplus__class_Oplus(U_2245,U_2247,U_2249))
| ~ c_Orderings_Oord__class_Oless__eq(U_2245,U_2248,U_2249)
| ~ c_Orderings_Oord__class_Oless(U_2245,U_2246,U_2247)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2245) ),
inference(variable_rename,[status(thm)],[f_776_1]) ).
fof(f_776_3,plain,
! [U_2245,U_2246,U_2247,U_2248,U_2249] :
( c_Orderings_Oord__class_Oless(U_2245,c_Groups_Oplus__class_Oplus(U_2245,U_2246,U_2248),c_Groups_Oplus__class_Oplus(U_2245,U_2247,U_2249))
| ~ c_Orderings_Oord__class_Oless__eq(U_2245,U_2248,U_2249)
| ~ c_Orderings_Oord__class_Oless(U_2245,U_2246,U_2247)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2245) ),
inference(definitional_conversion,[status(esa)],[f_776_2]) ).
cnf(f_776_4,plain,
( c_Orderings_Oord__class_Oless(U_2245,c_Groups_Oplus__class_Oplus(U_2245,U_2246,U_2248),c_Groups_Oplus__class_Oplus(U_2245,U_2247,U_2249))
| ~ c_Orderings_Oord__class_Oless__eq(U_2245,U_2248,U_2249)
| ~ c_Orderings_Oord__class_Oless(U_2245,U_2246,U_2247)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_2245) ),
inference(clausify,[status(thm)],[f_776_3]) ).
fof(f_777_1,plain,
! [V_w_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_w_2))
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_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_w_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_777_2,plain,
! [U_2252,U_2251,U_2250] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2251),c_Int_Onumber__class_Onumber__of(U_2250,U_2252))
| c_Orderings_Oord__class_Oless(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2252),c_Int_Onumber__class_Onumber__of(U_2250,U_2251)) )
& ( ~ c_Orderings_Oord__class_Oless(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2252),c_Int_Onumber__class_Onumber__of(U_2250,U_2251))
| ~ c_Orderings_Oord__class_Oless__eq(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2251),c_Int_Onumber__class_Onumber__of(U_2250,U_2252)) ) )
| ~ class_Orderings_Olinorder(U_2250)
| ~ class_Int_Onumber(U_2250) ),
inference(variable_rename,[status(thm)],[f_777_1]) ).
fof(f_777_3,plain,
( ! [U_2250,U_2251,U_2252] :
( c_Orderings_Oord__class_Oless__eq(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2251),c_Int_Onumber__class_Onumber__of(U_2250,U_2252))
| c_Orderings_Oord__class_Oless(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2252),c_Int_Onumber__class_Onumber__of(U_2250,U_2251))
| ~ sP190(U_2250,U_2251,U_2252) )
& ! [U_2250,U_2251,U_2252] :
( ~ c_Orderings_Oord__class_Oless(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2252),c_Int_Onumber__class_Onumber__of(U_2250,U_2251))
| ~ c_Orderings_Oord__class_Oless__eq(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2251),c_Int_Onumber__class_Onumber__of(U_2250,U_2252))
| ~ sP190(U_2250,U_2251,U_2252) )
& ! [U_2250,U_2251,U_2252] :
( sP190(U_2250,U_2251,U_2252)
| ~ class_Orderings_Olinorder(U_2250)
| ~ class_Int_Onumber(U_2250) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190])],[f_777_2]) ).
cnf(f_777_4,plain,
( sP190(U_2250,U_2251,U_2252)
| ~ class_Orderings_Olinorder(U_2250)
| ~ class_Int_Onumber(U_2250) ),
inference(clausify,[status(thm)],[f_777_3]) ).
cnf(f_777_5,plain,
( ~ c_Orderings_Oord__class_Oless(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2252),c_Int_Onumber__class_Onumber__of(U_2250,U_2251))
| ~ c_Orderings_Oord__class_Oless__eq(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2251),c_Int_Onumber__class_Onumber__of(U_2250,U_2252))
| ~ sP190(U_2250,U_2251,U_2252) ),
inference(clausify,[status(thm)],[f_777_3]) ).
cnf(f_777_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2251),c_Int_Onumber__class_Onumber__of(U_2250,U_2252))
| c_Orderings_Oord__class_Oless(U_2250,c_Int_Onumber__class_Onumber__of(U_2250,U_2252),c_Int_Onumber__class_Onumber__of(U_2250,U_2251))
| ~ sP190(U_2250,U_2251,U_2252) ),
inference(clausify,[status(thm)],[f_777_3]) ).
fof(f_778_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_778_2,plain,
! [U_2253] :
( c_Orderings_Oord__class_Oless(U_2253,c_Groups_Ozero__class_Ozero(U_2253),c_Groups_Oone__class_Oone(U_2253))
| ~ class_Rings_Olinordered__semidom(U_2253) ),
inference(variable_rename,[status(thm)],[f_778_1]) ).
fof(f_778_3,plain,
! [U_2253] :
( c_Orderings_Oord__class_Oless(U_2253,c_Groups_Ozero__class_Ozero(U_2253),c_Groups_Oone__class_Oone(U_2253))
| ~ class_Rings_Olinordered__semidom(U_2253) ),
inference(definitional_conversion,[status(esa)],[f_778_2]) ).
cnf(f_778_4,plain,
( c_Orderings_Oord__class_Oless(U_2253,c_Groups_Ozero__class_Ozero(U_2253),c_Groups_Oone__class_Oone(U_2253))
| ~ class_Rings_Olinordered__semidom(U_2253) ),
inference(clausify,[status(thm)],[f_778_3]) ).
fof(f_779_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_779_2,plain,
! [U_2254] :
( ~ c_Orderings_Oord__class_Oless(U_2254,c_Groups_Oone__class_Oone(U_2254),c_Groups_Ozero__class_Ozero(U_2254))
| ~ class_Rings_Olinordered__semidom(U_2254) ),
inference(variable_rename,[status(thm)],[f_779_1]) ).
fof(f_779_3,plain,
! [U_2254] :
( ~ c_Orderings_Oord__class_Oless(U_2254,c_Groups_Oone__class_Oone(U_2254),c_Groups_Ozero__class_Ozero(U_2254))
| ~ class_Rings_Olinordered__semidom(U_2254) ),
inference(definitional_conversion,[status(esa)],[f_779_2]) ).
cnf(f_779_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2254,c_Groups_Oone__class_Oone(U_2254),c_Groups_Ozero__class_Ozero(U_2254))
| ~ class_Rings_Olinordered__semidom(U_2254) ),
inference(clausify,[status(thm)],[f_779_3]) ).
fof(f_780_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_780_2,plain,
! [U_2257,U_2256,U_2255] :
( ( ( c_Orderings_Oord__class_Oless(U_2255,U_2256,U_2257)
| ~ c_Orderings_Oord__class_Oless(U_2255,c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2257),c_Groups_Ozero__class_Ozero(U_2255)) )
& ( c_Orderings_Oord__class_Oless(U_2255,c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2257),c_Groups_Ozero__class_Ozero(U_2255))
| ~ c_Orderings_Oord__class_Oless(U_2255,U_2256,U_2257) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2255) ),
inference(variable_rename,[status(thm)],[f_780_1]) ).
fof(f_780_3,plain,
( ! [U_2255,U_2256,U_2257] :
( c_Orderings_Oord__class_Oless(U_2255,U_2256,U_2257)
| ~ c_Orderings_Oord__class_Oless(U_2255,c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2257),c_Groups_Ozero__class_Ozero(U_2255))
| ~ sP191(U_2255,U_2256,U_2257) )
& ! [U_2255,U_2256,U_2257] :
( c_Orderings_Oord__class_Oless(U_2255,c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2257),c_Groups_Ozero__class_Ozero(U_2255))
| ~ c_Orderings_Oord__class_Oless(U_2255,U_2256,U_2257)
| ~ sP191(U_2255,U_2256,U_2257) )
& ! [U_2255,U_2256,U_2257] :
( sP191(U_2255,U_2256,U_2257)
| ~ class_Groups_Oordered__ab__group__add(U_2255) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191])],[f_780_2]) ).
cnf(f_780_4,plain,
( sP191(U_2255,U_2256,U_2257)
| ~ class_Groups_Oordered__ab__group__add(U_2255) ),
inference(clausify,[status(thm)],[f_780_3]) ).
cnf(f_780_5,plain,
( c_Orderings_Oord__class_Oless(U_2255,c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2257),c_Groups_Ozero__class_Ozero(U_2255))
| ~ c_Orderings_Oord__class_Oless(U_2255,U_2256,U_2257)
| ~ sP191(U_2255,U_2256,U_2257) ),
inference(clausify,[status(thm)],[f_780_3]) ).
cnf(f_780_6,plain,
( c_Orderings_Oord__class_Oless(U_2255,U_2256,U_2257)
| ~ c_Orderings_Oord__class_Oless(U_2255,c_Groups_Ominus__class_Ominus(U_2255,U_2256,U_2257),c_Groups_Ozero__class_Ozero(U_2255))
| ~ sP191(U_2255,U_2256,U_2257) ),
inference(clausify,[status(thm)],[f_780_3]) ).
fof(f_781_1,plain,
! [V_n,V_m,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(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_781_2,plain,
! [U_2260,U_2259,U_2258] :
( c_Orderings_Oord__class_Oless(U_2258,c_Groups_Oone__class_Oone(U_2258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2258),U_2259),U_2260))
| ~ c_Orderings_Oord__class_Oless(U_2258,c_Groups_Oone__class_Oone(U_2258),U_2260)
| ~ c_Orderings_Oord__class_Oless(U_2258,c_Groups_Oone__class_Oone(U_2258),U_2259)
| ~ class_Rings_Olinordered__semidom(U_2258) ),
inference(variable_rename,[status(thm)],[f_781_1]) ).
fof(f_781_3,plain,
! [U_2258,U_2259,U_2260] :
( c_Orderings_Oord__class_Oless(U_2258,c_Groups_Oone__class_Oone(U_2258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2258),U_2259),U_2260))
| ~ c_Orderings_Oord__class_Oless(U_2258,c_Groups_Oone__class_Oone(U_2258),U_2260)
| ~ c_Orderings_Oord__class_Oless(U_2258,c_Groups_Oone__class_Oone(U_2258),U_2259)
| ~ class_Rings_Olinordered__semidom(U_2258) ),
inference(definitional_conversion,[status(esa)],[f_781_2]) ).
cnf(f_781_4,plain,
( c_Orderings_Oord__class_Oless(U_2258,c_Groups_Oone__class_Oone(U_2258),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2258),U_2259),U_2260))
| ~ c_Orderings_Oord__class_Oless(U_2258,c_Groups_Oone__class_Oone(U_2258),U_2260)
| ~ c_Orderings_Oord__class_Oless(U_2258,c_Groups_Oone__class_Oone(U_2258),U_2259)
| ~ class_Rings_Olinordered__semidom(U_2258) ),
inference(clausify,[status(thm)],[f_781_3]) ).
fof(f_782_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_782_2,plain,
! [U_2263,U_2262,U_2261] :
( c_Orderings_Oord__class_Oless(U_2261,c_Groups_Ozero__class_Ozero(U_2261),hAPP(hAPP(c_Power_Opower__class_Opower(U_2261),U_2262),U_2263))
| ~ c_Orderings_Oord__class_Oless(U_2261,c_Groups_Ozero__class_Ozero(U_2261),U_2262)
| ~ class_Rings_Olinordered__semidom(U_2261) ),
inference(variable_rename,[status(thm)],[f_782_1]) ).
fof(f_782_3,plain,
! [U_2261,U_2262,U_2263] :
( c_Orderings_Oord__class_Oless(U_2261,c_Groups_Ozero__class_Ozero(U_2261),hAPP(hAPP(c_Power_Opower__class_Opower(U_2261),U_2262),U_2263))
| ~ c_Orderings_Oord__class_Oless(U_2261,c_Groups_Ozero__class_Ozero(U_2261),U_2262)
| ~ class_Rings_Olinordered__semidom(U_2261) ),
inference(definitional_conversion,[status(esa)],[f_782_2]) ).
cnf(f_782_4,plain,
( c_Orderings_Oord__class_Oless(U_2261,c_Groups_Ozero__class_Ozero(U_2261),hAPP(hAPP(c_Power_Opower__class_Opower(U_2261),U_2262),U_2263))
| ~ c_Orderings_Oord__class_Oless(U_2261,c_Groups_Ozero__class_Ozero(U_2261),U_2262)
| ~ class_Rings_Olinordered__semidom(U_2261) ),
inference(clausify,[status(thm)],[f_782_3]) ).
fof(f_783_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_783_2,plain,
! [U_2265,U_2264] :
( c_Orderings_Oord__class_Oless(U_2264,U_2265,c_Groups_Oplus__class_Oplus(U_2264,U_2265,c_Groups_Oone__class_Oone(U_2264)))
| ~ class_Rings_Olinordered__semidom(U_2264) ),
inference(variable_rename,[status(thm)],[f_783_1]) ).
fof(f_783_3,plain,
! [U_2264,U_2265] :
( c_Orderings_Oord__class_Oless(U_2264,U_2265,c_Groups_Oplus__class_Oplus(U_2264,U_2265,c_Groups_Oone__class_Oone(U_2264)))
| ~ class_Rings_Olinordered__semidom(U_2264) ),
inference(definitional_conversion,[status(esa)],[f_783_2]) ).
cnf(f_783_4,plain,
( c_Orderings_Oord__class_Oless(U_2264,U_2265,c_Groups_Oplus__class_Oplus(U_2264,U_2265,c_Groups_Oone__class_Oone(U_2264)))
| ~ class_Rings_Olinordered__semidom(U_2264) ),
inference(clausify,[status(thm)],[f_783_3]) ).
fof(f_784_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_784_2,plain,
! [U_2269,U_2268,U_2267,U_2266] :
( c_Orderings_Oord__class_Oless(U_2266,c_Rings_Oinverse__class_Odivide(U_2266,U_2268,U_2269),c_Rings_Oinverse__class_Odivide(U_2266,U_2267,U_2269))
| ~ c_Orderings_Oord__class_Oless(U_2266,U_2269,c_Groups_Ozero__class_Ozero(U_2266))
| ~ c_Orderings_Oord__class_Oless(U_2266,U_2267,U_2268)
| ~ class_Fields_Olinordered__field(U_2266) ),
inference(variable_rename,[status(thm)],[f_784_1]) ).
fof(f_784_3,plain,
! [U_2267,U_2266,U_2268,U_2269] :
( c_Orderings_Oord__class_Oless(U_2266,c_Rings_Oinverse__class_Odivide(U_2266,U_2268,U_2269),c_Rings_Oinverse__class_Odivide(U_2266,U_2267,U_2269))
| ~ c_Orderings_Oord__class_Oless(U_2266,U_2269,c_Groups_Ozero__class_Ozero(U_2266))
| ~ c_Orderings_Oord__class_Oless(U_2266,U_2267,U_2268)
| ~ class_Fields_Olinordered__field(U_2266) ),
inference(definitional_conversion,[status(esa)],[f_784_2]) ).
cnf(f_784_4,plain,
( c_Orderings_Oord__class_Oless(U_2266,c_Rings_Oinverse__class_Odivide(U_2266,U_2268,U_2269),c_Rings_Oinverse__class_Odivide(U_2266,U_2267,U_2269))
| ~ c_Orderings_Oord__class_Oless(U_2266,U_2269,c_Groups_Ozero__class_Ozero(U_2266))
| ~ c_Orderings_Oord__class_Oless(U_2266,U_2267,U_2268)
| ~ class_Fields_Olinordered__field(U_2266) ),
inference(clausify,[status(thm)],[f_784_3]) ).
fof(f_785_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_785_2,plain,
! [U_2273,U_2272,U_2271,U_2270] :
( c_Orderings_Oord__class_Oless(U_2270,c_Rings_Oinverse__class_Odivide(U_2270,U_2271,U_2273),c_Rings_Oinverse__class_Odivide(U_2270,U_2272,U_2273))
| ~ c_Orderings_Oord__class_Oless(U_2270,c_Groups_Ozero__class_Ozero(U_2270),U_2273)
| ~ c_Orderings_Oord__class_Oless(U_2270,U_2271,U_2272)
| ~ class_Fields_Olinordered__field(U_2270) ),
inference(variable_rename,[status(thm)],[f_785_1]) ).
fof(f_785_3,plain,
! [U_2270,U_2271,U_2272,U_2273] :
( c_Orderings_Oord__class_Oless(U_2270,c_Rings_Oinverse__class_Odivide(U_2270,U_2271,U_2273),c_Rings_Oinverse__class_Odivide(U_2270,U_2272,U_2273))
| ~ c_Orderings_Oord__class_Oless(U_2270,c_Groups_Ozero__class_Ozero(U_2270),U_2273)
| ~ c_Orderings_Oord__class_Oless(U_2270,U_2271,U_2272)
| ~ class_Fields_Olinordered__field(U_2270) ),
inference(definitional_conversion,[status(esa)],[f_785_2]) ).
cnf(f_785_4,plain,
( c_Orderings_Oord__class_Oless(U_2270,c_Rings_Oinverse__class_Odivide(U_2270,U_2271,U_2273),c_Rings_Oinverse__class_Odivide(U_2270,U_2272,U_2273))
| ~ c_Orderings_Oord__class_Oless(U_2270,c_Groups_Ozero__class_Ozero(U_2270),U_2273)
| ~ c_Orderings_Oord__class_Oless(U_2270,U_2271,U_2272)
| ~ class_Fields_Olinordered__field(U_2270) ),
inference(clausify,[status(thm)],[f_785_3]) ).
fof(f_786_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_786_2,plain,
! [U_2276,U_2275,U_2274] :
( c_Orderings_Oord__class_Oless(U_2274,c_Groups_Ozero__class_Ozero(U_2274),c_Rings_Oinverse__class_Odivide(U_2274,U_2275,U_2276))
| ~ c_Orderings_Oord__class_Oless(U_2274,U_2276,c_Groups_Ozero__class_Ozero(U_2274))
| ~ c_Orderings_Oord__class_Oless(U_2274,U_2275,c_Groups_Ozero__class_Ozero(U_2274))
| ~ class_Fields_Olinordered__field(U_2274) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
fof(f_786_3,plain,
! [U_2276,U_2274,U_2275] :
( c_Orderings_Oord__class_Oless(U_2274,c_Groups_Ozero__class_Ozero(U_2274),c_Rings_Oinverse__class_Odivide(U_2274,U_2275,U_2276))
| ~ c_Orderings_Oord__class_Oless(U_2274,U_2276,c_Groups_Ozero__class_Ozero(U_2274))
| ~ c_Orderings_Oord__class_Oless(U_2274,U_2275,c_Groups_Ozero__class_Ozero(U_2274))
| ~ class_Fields_Olinordered__field(U_2274) ),
inference(definitional_conversion,[status(esa)],[f_786_2]) ).
cnf(f_786_4,plain,
( c_Orderings_Oord__class_Oless(U_2274,c_Groups_Ozero__class_Ozero(U_2274),c_Rings_Oinverse__class_Odivide(U_2274,U_2275,U_2276))
| ~ c_Orderings_Oord__class_Oless(U_2274,U_2276,c_Groups_Ozero__class_Ozero(U_2274))
| ~ c_Orderings_Oord__class_Oless(U_2274,U_2275,c_Groups_Ozero__class_Ozero(U_2274))
| ~ class_Fields_Olinordered__field(U_2274) ),
inference(clausify,[status(thm)],[f_786_3]) ).
fof(f_787_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_787_2,plain,
! [U_2279,U_2278,U_2277] :
( c_Orderings_Oord__class_Oless(U_2277,c_Rings_Oinverse__class_Odivide(U_2277,U_2278,U_2279),c_Groups_Ozero__class_Ozero(U_2277))
| ~ c_Orderings_Oord__class_Oless(U_2277,c_Groups_Ozero__class_Ozero(U_2277),U_2279)
| ~ c_Orderings_Oord__class_Oless(U_2277,U_2278,c_Groups_Ozero__class_Ozero(U_2277))
| ~ class_Fields_Olinordered__field(U_2277) ),
inference(variable_rename,[status(thm)],[f_787_1]) ).
fof(f_787_3,plain,
! [U_2277,U_2278,U_2279] :
( c_Orderings_Oord__class_Oless(U_2277,c_Rings_Oinverse__class_Odivide(U_2277,U_2278,U_2279),c_Groups_Ozero__class_Ozero(U_2277))
| ~ c_Orderings_Oord__class_Oless(U_2277,c_Groups_Ozero__class_Ozero(U_2277),U_2279)
| ~ c_Orderings_Oord__class_Oless(U_2277,U_2278,c_Groups_Ozero__class_Ozero(U_2277))
| ~ class_Fields_Olinordered__field(U_2277) ),
inference(definitional_conversion,[status(esa)],[f_787_2]) ).
cnf(f_787_4,plain,
( c_Orderings_Oord__class_Oless(U_2277,c_Rings_Oinverse__class_Odivide(U_2277,U_2278,U_2279),c_Groups_Ozero__class_Ozero(U_2277))
| ~ c_Orderings_Oord__class_Oless(U_2277,c_Groups_Ozero__class_Ozero(U_2277),U_2279)
| ~ c_Orderings_Oord__class_Oless(U_2277,U_2278,c_Groups_Ozero__class_Ozero(U_2277))
| ~ class_Fields_Olinordered__field(U_2277) ),
inference(clausify,[status(thm)],[f_787_3]) ).
fof(f_788_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_788_2,plain,
! [U_2282,U_2281,U_2280] :
( c_Orderings_Oord__class_Oless(U_2280,c_Rings_Oinverse__class_Odivide(U_2280,U_2281,U_2282),c_Groups_Ozero__class_Ozero(U_2280))
| ~ c_Orderings_Oord__class_Oless(U_2280,U_2282,c_Groups_Ozero__class_Ozero(U_2280))
| ~ c_Orderings_Oord__class_Oless(U_2280,c_Groups_Ozero__class_Ozero(U_2280),U_2281)
| ~ class_Fields_Olinordered__field(U_2280) ),
inference(variable_rename,[status(thm)],[f_788_1]) ).
fof(f_788_3,plain,
! [U_2280,U_2281,U_2282] :
( c_Orderings_Oord__class_Oless(U_2280,c_Rings_Oinverse__class_Odivide(U_2280,U_2281,U_2282),c_Groups_Ozero__class_Ozero(U_2280))
| ~ c_Orderings_Oord__class_Oless(U_2280,U_2282,c_Groups_Ozero__class_Ozero(U_2280))
| ~ c_Orderings_Oord__class_Oless(U_2280,c_Groups_Ozero__class_Ozero(U_2280),U_2281)
| ~ class_Fields_Olinordered__field(U_2280) ),
inference(definitional_conversion,[status(esa)],[f_788_2]) ).
cnf(f_788_4,plain,
( c_Orderings_Oord__class_Oless(U_2280,c_Rings_Oinverse__class_Odivide(U_2280,U_2281,U_2282),c_Groups_Ozero__class_Ozero(U_2280))
| ~ c_Orderings_Oord__class_Oless(U_2280,U_2282,c_Groups_Ozero__class_Ozero(U_2280))
| ~ c_Orderings_Oord__class_Oless(U_2280,c_Groups_Ozero__class_Ozero(U_2280),U_2281)
| ~ class_Fields_Olinordered__field(U_2280) ),
inference(clausify,[status(thm)],[f_788_3]) ).
fof(f_789_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_789_2,plain,
! [U_2285,U_2284,U_2283] :
( c_Orderings_Oord__class_Oless(U_2283,c_Groups_Ozero__class_Ozero(U_2283),c_Rings_Oinverse__class_Odivide(U_2283,U_2284,U_2285))
| ~ c_Orderings_Oord__class_Oless(U_2283,c_Groups_Ozero__class_Ozero(U_2283),U_2285)
| ~ c_Orderings_Oord__class_Oless(U_2283,c_Groups_Ozero__class_Ozero(U_2283),U_2284)
| ~ class_Fields_Olinordered__field(U_2283) ),
inference(variable_rename,[status(thm)],[f_789_1]) ).
fof(f_789_3,plain,
! [U_2283,U_2284,U_2285] :
( c_Orderings_Oord__class_Oless(U_2283,c_Groups_Ozero__class_Ozero(U_2283),c_Rings_Oinverse__class_Odivide(U_2283,U_2284,U_2285))
| ~ c_Orderings_Oord__class_Oless(U_2283,c_Groups_Ozero__class_Ozero(U_2283),U_2285)
| ~ c_Orderings_Oord__class_Oless(U_2283,c_Groups_Ozero__class_Ozero(U_2283),U_2284)
| ~ class_Fields_Olinordered__field(U_2283) ),
inference(definitional_conversion,[status(esa)],[f_789_2]) ).
cnf(f_789_4,plain,
( c_Orderings_Oord__class_Oless(U_2283,c_Groups_Ozero__class_Ozero(U_2283),c_Rings_Oinverse__class_Odivide(U_2283,U_2284,U_2285))
| ~ c_Orderings_Oord__class_Oless(U_2283,c_Groups_Ozero__class_Ozero(U_2283),U_2285)
| ~ c_Orderings_Oord__class_Oless(U_2283,c_Groups_Ozero__class_Ozero(U_2283),U_2284)
| ~ class_Fields_Olinordered__field(U_2283) ),
inference(clausify,[status(thm)],[f_789_3]) ).
fof(f_790_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_790_2,plain,
! [U_2288,U_2287,U_2286] :
( ( ( c_Orderings_Oord__class_Oless(U_2286,c_Rings_Oinverse__class_Odivide(U_2286,U_2287,U_2288),c_Groups_Ozero__class_Ozero(U_2286))
| ( ( ~ c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2288)
| ~ c_Orderings_Oord__class_Oless(U_2286,U_2287,c_Groups_Ozero__class_Ozero(U_2286)) )
& ( ~ c_Orderings_Oord__class_Oless(U_2286,U_2288,c_Groups_Ozero__class_Ozero(U_2286))
| ~ c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2287) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2288)
& c_Orderings_Oord__class_Oless(U_2286,U_2287,c_Groups_Ozero__class_Ozero(U_2286)) )
| ( c_Orderings_Oord__class_Oless(U_2286,U_2288,c_Groups_Ozero__class_Ozero(U_2286))
& c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2287) )
| ~ c_Orderings_Oord__class_Oless(U_2286,c_Rings_Oinverse__class_Odivide(U_2286,U_2287,U_2288),c_Groups_Ozero__class_Ozero(U_2286)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_2286) ),
inference(variable_rename,[status(thm)],[f_790_1]) ).
fof(f_790_3,plain,
( ! [U_2287,U_2288,U_2286] :
( ~ c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2288)
| ~ c_Orderings_Oord__class_Oless(U_2286,U_2287,c_Groups_Ozero__class_Ozero(U_2286))
| ~ sP194(U_2287,U_2288,U_2286) )
& ! [U_2287,U_2288,U_2286] :
( ~ c_Orderings_Oord__class_Oless(U_2286,U_2288,c_Groups_Ozero__class_Ozero(U_2286))
| ~ c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2287)
| ~ sP194(U_2287,U_2288,U_2286) )
& ! [U_2287,U_2288,U_2286] :
( c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2288)
| ~ sP193(U_2287,U_2288,U_2286) )
& ! [U_2287,U_2288,U_2286] :
( c_Orderings_Oord__class_Oless(U_2286,U_2287,c_Groups_Ozero__class_Ozero(U_2286))
| ~ sP193(U_2287,U_2288,U_2286) )
& ! [U_2287,U_2288,U_2286] :
( c_Orderings_Oord__class_Oless(U_2286,U_2288,c_Groups_Ozero__class_Ozero(U_2286))
| ~ sP192(U_2287,U_2288,U_2286) )
& ! [U_2287,U_2288,U_2286] :
( c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2287)
| ~ sP192(U_2287,U_2288,U_2286) )
& ! [U_2287,U_2288,U_2286] :
( c_Orderings_Oord__class_Oless(U_2286,c_Rings_Oinverse__class_Odivide(U_2286,U_2287,U_2288),c_Groups_Ozero__class_Ozero(U_2286))
| sP194(U_2287,U_2288,U_2286)
| ~ sP195(U_2287,U_2288,U_2286) )
& ! [U_2287,U_2288,U_2286] :
( sP193(U_2287,U_2288,U_2286)
| sP192(U_2287,U_2288,U_2286)
| ~ c_Orderings_Oord__class_Oless(U_2286,c_Rings_Oinverse__class_Odivide(U_2286,U_2287,U_2288),c_Groups_Ozero__class_Ozero(U_2286))
| ~ sP195(U_2287,U_2288,U_2286) )
& ! [U_2287,U_2288,U_2286] :
( sP195(U_2287,U_2288,U_2286)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2286) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192,sP193,sP194,sP195])],[f_790_2]) ).
cnf(f_790_4,plain,
( sP195(U_2287,U_2288,U_2286)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2286) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_5,plain,
( sP193(U_2287,U_2288,U_2286)
| sP192(U_2287,U_2288,U_2286)
| ~ c_Orderings_Oord__class_Oless(U_2286,c_Rings_Oinverse__class_Odivide(U_2286,U_2287,U_2288),c_Groups_Ozero__class_Ozero(U_2286))
| ~ sP195(U_2287,U_2288,U_2286) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_6,plain,
( c_Orderings_Oord__class_Oless(U_2286,c_Rings_Oinverse__class_Odivide(U_2286,U_2287,U_2288),c_Groups_Ozero__class_Ozero(U_2286))
| sP194(U_2287,U_2288,U_2286)
| ~ sP195(U_2287,U_2288,U_2286) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_7,plain,
( c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2287)
| ~ sP192(U_2287,U_2288,U_2286) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_8,plain,
( c_Orderings_Oord__class_Oless(U_2286,U_2288,c_Groups_Ozero__class_Ozero(U_2286))
| ~ sP192(U_2287,U_2288,U_2286) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_9,plain,
( c_Orderings_Oord__class_Oless(U_2286,U_2287,c_Groups_Ozero__class_Ozero(U_2286))
| ~ sP193(U_2287,U_2288,U_2286) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_10,plain,
( c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2288)
| ~ sP193(U_2287,U_2288,U_2286) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_2286,U_2288,c_Groups_Ozero__class_Ozero(U_2286))
| ~ c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2287)
| ~ sP194(U_2287,U_2288,U_2286) ),
inference(clausify,[status(thm)],[f_790_3]) ).
cnf(f_790_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_2286,c_Groups_Ozero__class_Ozero(U_2286),U_2288)
| ~ c_Orderings_Oord__class_Oless(U_2286,U_2287,c_Groups_Ozero__class_Ozero(U_2286))
| ~ sP194(U_2287,U_2288,U_2286) ),
inference(clausify,[status(thm)],[f_790_3]) ).
fof(f_791_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_791_2,plain,
! [U_2291,U_2290,U_2289] :
( ( ( c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),c_Rings_Oinverse__class_Odivide(U_2289,U_2290,U_2291))
| ( ( ~ c_Orderings_Oord__class_Oless(U_2289,U_2291,c_Groups_Ozero__class_Ozero(U_2289))
| ~ c_Orderings_Oord__class_Oless(U_2289,U_2290,c_Groups_Ozero__class_Ozero(U_2289)) )
& ( ~ c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2291)
| ~ c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2290) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_2289,U_2291,c_Groups_Ozero__class_Ozero(U_2289))
& c_Orderings_Oord__class_Oless(U_2289,U_2290,c_Groups_Ozero__class_Ozero(U_2289)) )
| ( c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2291)
& c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2290) )
| ~ c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),c_Rings_Oinverse__class_Odivide(U_2289,U_2290,U_2291)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_2289) ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
fof(f_791_3,plain,
( ! [U_2290,U_2291,U_2289] :
( ~ c_Orderings_Oord__class_Oless(U_2289,U_2291,c_Groups_Ozero__class_Ozero(U_2289))
| ~ c_Orderings_Oord__class_Oless(U_2289,U_2290,c_Groups_Ozero__class_Ozero(U_2289))
| ~ sP198(U_2290,U_2291,U_2289) )
& ! [U_2290,U_2291,U_2289] :
( ~ c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2291)
| ~ c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2290)
| ~ sP198(U_2290,U_2291,U_2289) )
& ! [U_2290,U_2291,U_2289] :
( c_Orderings_Oord__class_Oless(U_2289,U_2291,c_Groups_Ozero__class_Ozero(U_2289))
| ~ sP197(U_2290,U_2291,U_2289) )
& ! [U_2290,U_2291,U_2289] :
( c_Orderings_Oord__class_Oless(U_2289,U_2290,c_Groups_Ozero__class_Ozero(U_2289))
| ~ sP197(U_2290,U_2291,U_2289) )
& ! [U_2290,U_2291,U_2289] :
( c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2291)
| ~ sP196(U_2290,U_2291,U_2289) )
& ! [U_2290,U_2291,U_2289] :
( c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2290)
| ~ sP196(U_2290,U_2291,U_2289) )
& ! [U_2290,U_2291,U_2289] :
( c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),c_Rings_Oinverse__class_Odivide(U_2289,U_2290,U_2291))
| sP198(U_2290,U_2291,U_2289)
| ~ sP199(U_2290,U_2291,U_2289) )
& ! [U_2290,U_2291,U_2289] :
( sP197(U_2290,U_2291,U_2289)
| sP196(U_2290,U_2291,U_2289)
| ~ c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),c_Rings_Oinverse__class_Odivide(U_2289,U_2290,U_2291))
| ~ sP199(U_2290,U_2291,U_2289) )
& ! [U_2290,U_2291,U_2289] :
( sP199(U_2290,U_2291,U_2289)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2289) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196,sP197,sP198,sP199])],[f_791_2]) ).
cnf(f_791_4,plain,
( sP199(U_2290,U_2291,U_2289)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2289) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_5,plain,
( sP197(U_2290,U_2291,U_2289)
| sP196(U_2290,U_2291,U_2289)
| ~ c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),c_Rings_Oinverse__class_Odivide(U_2289,U_2290,U_2291))
| ~ sP199(U_2290,U_2291,U_2289) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_6,plain,
( c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),c_Rings_Oinverse__class_Odivide(U_2289,U_2290,U_2291))
| sP198(U_2290,U_2291,U_2289)
| ~ sP199(U_2290,U_2291,U_2289) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_7,plain,
( c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2290)
| ~ sP196(U_2290,U_2291,U_2289) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_8,plain,
( c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2291)
| ~ sP196(U_2290,U_2291,U_2289) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_9,plain,
( c_Orderings_Oord__class_Oless(U_2289,U_2290,c_Groups_Ozero__class_Ozero(U_2289))
| ~ sP197(U_2290,U_2291,U_2289) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_10,plain,
( c_Orderings_Oord__class_Oless(U_2289,U_2291,c_Groups_Ozero__class_Ozero(U_2289))
| ~ sP197(U_2290,U_2291,U_2289) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2291)
| ~ c_Orderings_Oord__class_Oless(U_2289,c_Groups_Ozero__class_Ozero(U_2289),U_2290)
| ~ sP198(U_2290,U_2291,U_2289) ),
inference(clausify,[status(thm)],[f_791_3]) ).
cnf(f_791_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_2289,U_2291,c_Groups_Ozero__class_Ozero(U_2289))
| ~ c_Orderings_Oord__class_Oless(U_2289,U_2290,c_Groups_Ozero__class_Ozero(U_2289))
| ~ sP198(U_2290,U_2291,U_2289) ),
inference(clausify,[status(thm)],[f_791_3]) ).
fof(f_792_1,plain,
! [V_n_2,V_m_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) = hAPP(hAPP(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
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_m_2) != hAPP(hAPP(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_792_2,plain,
! [U_2295,U_2294,U_2293,U_2292] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2294) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2295)
| U_2294 != U_2295 )
& ( U_2294 = U_2295
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2294) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2295) ) )
| ~ c_Orderings_Oord__class_Oless(U_2292,c_Groups_Oone__class_Oone(U_2292),U_2293)
| ~ class_Rings_Olinordered__semidom(U_2292) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
fof(f_792_3,plain,
( ! [U_2292,U_2293,U_2294,U_2295] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2294) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2295)
| U_2294 != U_2295
| ~ sP200(U_2292,U_2293,U_2294,U_2295) )
& ! [U_2292,U_2293,U_2294,U_2295] :
( U_2294 = U_2295
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2294) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2295)
| ~ sP200(U_2292,U_2293,U_2294,U_2295) )
& ! [U_2292,U_2293,U_2294,U_2295] :
( sP200(U_2292,U_2293,U_2294,U_2295)
| ~ c_Orderings_Oord__class_Oless(U_2292,c_Groups_Oone__class_Oone(U_2292),U_2293)
| ~ class_Rings_Olinordered__semidom(U_2292) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200])],[f_792_2]) ).
cnf(f_792_4,plain,
( sP200(U_2292,U_2293,U_2294,U_2295)
| ~ c_Orderings_Oord__class_Oless(U_2292,c_Groups_Oone__class_Oone(U_2292),U_2293)
| ~ class_Rings_Olinordered__semidom(U_2292) ),
inference(clausify,[status(thm)],[f_792_3]) ).
cnf(f_792_5,plain,
( U_2294 = U_2295
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2294) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2295)
| ~ sP200(U_2292,U_2293,U_2294,U_2295) ),
inference(clausify,[status(thm)],[f_792_3]) ).
cnf(f_792_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2294) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2292),U_2293),U_2295)
| U_2294 != U_2295
| ~ sP200(U_2292,U_2293,U_2294,U_2295) ),
inference(clausify,[status(thm)],[f_792_3]) ).
fof(f_793_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_793_2,plain,
! [U_2297,U_2296] :
( ~ c_Orderings_Oord__class_Oless(U_2296,c_Groups_Oabs__class_Oabs(U_2296,U_2297),c_Groups_Ozero__class_Ozero(U_2296))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2296) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
fof(f_793_3,plain,
! [U_2296,U_2297] :
( ~ c_Orderings_Oord__class_Oless(U_2296,c_Groups_Oabs__class_Oabs(U_2296,U_2297),c_Groups_Ozero__class_Ozero(U_2296))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2296) ),
inference(definitional_conversion,[status(esa)],[f_793_2]) ).
cnf(f_793_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2296,c_Groups_Oabs__class_Oabs(U_2296,U_2297),c_Groups_Ozero__class_Ozero(U_2296))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2296) ),
inference(clausify,[status(thm)],[f_793_3]) ).
fof(f_794_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_794_2,plain,
! [U_2299,U_2298] :
( ( ( c_Orderings_Oord__class_Oless(U_2298,c_Groups_Ozero__class_Ozero(U_2298),c_Groups_Oabs__class_Oabs(U_2298,U_2299))
| U_2299 = c_Groups_Ozero__class_Ozero(U_2298) )
& ( U_2299 != c_Groups_Ozero__class_Ozero(U_2298)
| ~ c_Orderings_Oord__class_Oless(U_2298,c_Groups_Ozero__class_Ozero(U_2298),c_Groups_Oabs__class_Oabs(U_2298,U_2299)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_2298) ),
inference(variable_rename,[status(thm)],[f_794_1]) ).
fof(f_794_3,plain,
( ! [U_2299,U_2298] :
( c_Orderings_Oord__class_Oless(U_2298,c_Groups_Ozero__class_Ozero(U_2298),c_Groups_Oabs__class_Oabs(U_2298,U_2299))
| U_2299 = c_Groups_Ozero__class_Ozero(U_2298)
| ~ sP201(U_2299,U_2298) )
& ! [U_2299,U_2298] :
( U_2299 != c_Groups_Ozero__class_Ozero(U_2298)
| ~ c_Orderings_Oord__class_Oless(U_2298,c_Groups_Ozero__class_Ozero(U_2298),c_Groups_Oabs__class_Oabs(U_2298,U_2299))
| ~ sP201(U_2299,U_2298) )
& ! [U_2299,U_2298] :
( sP201(U_2299,U_2298)
| ~ class_Groups_Oordered__ab__group__add__abs(U_2298) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201])],[f_794_2]) ).
cnf(f_794_4,plain,
( sP201(U_2299,U_2298)
| ~ class_Groups_Oordered__ab__group__add__abs(U_2298) ),
inference(clausify,[status(thm)],[f_794_3]) ).
cnf(f_794_5,plain,
( U_2299 != c_Groups_Ozero__class_Ozero(U_2298)
| ~ c_Orderings_Oord__class_Oless(U_2298,c_Groups_Ozero__class_Ozero(U_2298),c_Groups_Oabs__class_Oabs(U_2298,U_2299))
| ~ sP201(U_2299,U_2298) ),
inference(clausify,[status(thm)],[f_794_3]) ).
cnf(f_794_6,plain,
( c_Orderings_Oord__class_Oless(U_2298,c_Groups_Ozero__class_Ozero(U_2298),c_Groups_Oabs__class_Oabs(U_2298,U_2299))
| U_2299 = c_Groups_Ozero__class_Ozero(U_2298)
| ~ sP201(U_2299,U_2298) ),
inference(clausify,[status(thm)],[f_794_3]) ).
fof(f_795_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_795_2,plain,
! [U_2301,U_2300] :
( c_Groups_Oabs__class_Oabs(U_2300,U_2301) = U_2301
| ~ c_Orderings_Oord__class_Oless(U_2300,c_Groups_Ozero__class_Ozero(U_2300),U_2301)
| ~ class_Groups_Oordered__ab__group__add__abs(U_2300) ),
inference(variable_rename,[status(thm)],[f_795_1]) ).
fof(f_795_3,plain,
! [U_2301,U_2300] :
( c_Groups_Oabs__class_Oabs(U_2300,U_2301) = U_2301
| ~ c_Orderings_Oord__class_Oless(U_2300,c_Groups_Ozero__class_Ozero(U_2300),U_2301)
| ~ class_Groups_Oordered__ab__group__add__abs(U_2300) ),
inference(definitional_conversion,[status(esa)],[f_795_2]) ).
cnf(f_795_4,plain,
( c_Groups_Oabs__class_Oabs(U_2300,U_2301) = U_2301
| ~ c_Orderings_Oord__class_Oless(U_2300,c_Groups_Ozero__class_Ozero(U_2300),U_2301)
| ~ class_Groups_Oordered__ab__group__add__abs(U_2300) ),
inference(clausify,[status(thm)],[f_795_3]) ).
fof(f_796_1,plain,
! [V_d,V_b,V_c,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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)),hAPP(hAPP(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_796_2,plain,
! [U_2306,U_2305,U_2304,U_2303,U_2302] :
( c_Orderings_Oord__class_Oless(U_2302,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2302),c_Groups_Oabs__class_Oabs(U_2302,U_2303)),c_Groups_Oabs__class_Oabs(U_2302,U_2305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2302),U_2304),U_2306))
| ~ c_Orderings_Oord__class_Oless(U_2302,c_Groups_Oabs__class_Oabs(U_2302,U_2305),U_2306)
| ~ c_Orderings_Oord__class_Oless(U_2302,c_Groups_Oabs__class_Oabs(U_2302,U_2303),U_2304)
| ~ class_Rings_Olinordered__idom(U_2302) ),
inference(variable_rename,[status(thm)],[f_796_1]) ).
fof(f_796_3,plain,
! [U_2302,U_2303,U_2304,U_2305,U_2306] :
( c_Orderings_Oord__class_Oless(U_2302,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2302),c_Groups_Oabs__class_Oabs(U_2302,U_2303)),c_Groups_Oabs__class_Oabs(U_2302,U_2305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2302),U_2304),U_2306))
| ~ c_Orderings_Oord__class_Oless(U_2302,c_Groups_Oabs__class_Oabs(U_2302,U_2305),U_2306)
| ~ c_Orderings_Oord__class_Oless(U_2302,c_Groups_Oabs__class_Oabs(U_2302,U_2303),U_2304)
| ~ class_Rings_Olinordered__idom(U_2302) ),
inference(definitional_conversion,[status(esa)],[f_796_2]) ).
cnf(f_796_4,plain,
( c_Orderings_Oord__class_Oless(U_2302,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2302),c_Groups_Oabs__class_Oabs(U_2302,U_2303)),c_Groups_Oabs__class_Oabs(U_2302,U_2305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2302),U_2304),U_2306))
| ~ c_Orderings_Oord__class_Oless(U_2302,c_Groups_Oabs__class_Oabs(U_2302,U_2305),U_2306)
| ~ c_Orderings_Oord__class_Oless(U_2302,c_Groups_Oabs__class_Oabs(U_2302,U_2303),U_2304)
| ~ class_Rings_Olinordered__idom(U_2302) ),
inference(clausify,[status(thm)],[f_796_3]) ).
fof(f_797_1,plain,
! [V_y,V_x,V_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z),V_x),hAPP(hAPP(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_797_2,plain,
! [U_2309,U_2308,U_2307] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2307),U_2308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2307),U_2309))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2308,U_2309)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2307) ),
inference(variable_rename,[status(thm)],[f_797_1]) ).
fof(f_797_3,plain,
! [U_2307,U_2308,U_2309] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2307),U_2308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2307),U_2309))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2308,U_2309)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2307) ),
inference(definitional_conversion,[status(esa)],[f_797_2]) ).
cnf(f_797_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2307),U_2308),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2307),U_2309))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2308,U_2309)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2307) ),
inference(clausify,[status(thm)],[f_797_3]) ).
fof(f_798_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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_798_2,plain,
! [U_2311,U_2310] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2310),U_2311))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2311)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2310) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
fof(f_798_3,plain,
! [U_2310,U_2311] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2310),U_2311))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2311)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2310) ),
inference(definitional_conversion,[status(esa)],[f_798_2]) ).
cnf(f_798_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2310),U_2311))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2311)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2310) ),
inference(clausify,[status(thm)],[f_798_3]) ).
fof(f_799_1,plain,
! [V_ya_2,V_xa_2,V_za_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_za_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_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_799_2,plain,
! [U_2314,U_2313,U_2312] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2313),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2314),U_2312))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2313,U_2314) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2313,U_2314)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2313),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2314),U_2312)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2312) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
fof(f_799_3,plain,
( ! [U_2312,U_2313,U_2314] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2313),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2314),U_2312))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2313,U_2314)
| ~ sP202(U_2312,U_2313,U_2314) )
& ! [U_2312,U_2313,U_2314] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2313,U_2314)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2313),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2314),U_2312))
| ~ sP202(U_2312,U_2313,U_2314) )
& ! [U_2312,U_2313,U_2314] :
( sP202(U_2312,U_2313,U_2314)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2312) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202])],[f_799_2]) ).
cnf(f_799_4,plain,
( sP202(U_2312,U_2313,U_2314)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2312) ),
inference(clausify,[status(thm)],[f_799_3]) ).
cnf(f_799_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2313,U_2314)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2313),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2314),U_2312))
| ~ sP202(U_2312,U_2313,U_2314) ),
inference(clausify,[status(thm)],[f_799_3]) ).
cnf(f_799_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2313),U_2312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2314),U_2312))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2313,U_2314)
| ~ sP202(U_2312,U_2313,U_2314) ),
inference(clausify,[status(thm)],[f_799_3]) ).
fof(f_800_1,plain,
! [V_xa_2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2))
| V_xa_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( V_xa_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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_xa_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(f_800_2,plain,
! [U_2315] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2315),U_2315))
| U_2315 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_2315 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2315),U_2315)) ) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
fof(f_800_3,plain,
( ! [U_2317] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2317),U_2317))
| U_2317 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_2316] :
( U_2316 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2316),U_2316)) ) ),
inference(miniscope,[status(thm)],[f_800_2]) ).
fof(f_800_4,plain,
( ! [U_2317] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2317),U_2317))
| U_2317 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_2316] :
( U_2316 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2316),U_2316)) ) ),
inference(definitional_conversion,[status(esa)],[f_800_3]) ).
cnf(f_800_5,plain,
( U_2316 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2316),U_2316)) ),
inference(clausify,[status(thm)],[f_800_4]) ).
cnf(f_800_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2317),U_2317))
| U_2317 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_800_4]) ).
fof(f_801_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_801_2,plain,
! [U_2319,U_2318] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2318,U_2319),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_2318) ),
inference(variable_rename,[status(thm)],[f_801_1]) ).
fof(f_801_3,plain,
! [U_2319,U_2318] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2318,U_2319),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_2318) ),
inference(definitional_conversion,[status(esa)],[f_801_2]) ).
cnf(f_801_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2318,U_2319),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_2318) ),
inference(clausify,[status(thm)],[f_801_3]) ).
fof(f_802_1,plain,
! [V_ya_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_ya_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__0__iff]) ).
fof(f_802_2,plain,
! [U_2320] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2320))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2320) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2320)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2320)) ) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
fof(f_802_3,plain,
( ! [U_2322] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2322))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2322) )
& ! [U_2321] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2321)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2321)) ) ),
inference(miniscope,[status(thm)],[f_802_2]) ).
fof(f_802_4,plain,
( ! [U_2322] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2322))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2322) )
& ! [U_2321] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2321)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2321)) ) ),
inference(definitional_conversion,[status(esa)],[f_802_3]) ).
cnf(f_802_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2321)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2321)) ),
inference(clausify,[status(thm)],[f_802_4]) ).
cnf(f_802_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2322))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2322) ),
inference(clausify,[status(thm)],[f_802_4]) ).
fof(f_803_1,plain,
! [V_xa_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__lt__0__iff]) ).
fof(f_803_2,plain,
! [U_2323] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2323),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2323,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2323,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2323),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
fof(f_803_3,plain,
( ! [U_2325] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2325),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2325,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_2324] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2324,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2324),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_803_2]) ).
fof(f_803_4,plain,
( ! [U_2325] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2325),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2325,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_2324] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2324,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2324),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_803_3]) ).
cnf(f_803_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2324,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2324),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_803_4]) ).
cnf(f_803_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2325),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2325,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_803_4]) ).
fof(f_804_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_804_2,plain,
! [U_2326] :
( c_NthRoot_Osqrt(U_2326) != 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_2326) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
fof(f_804_3,plain,
! [U_2326] :
( c_NthRoot_Osqrt(U_2326) != 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_2326) ),
inference(definitional_conversion,[status(esa)],[f_804_2]) ).
cnf(f_804_4,plain,
( c_NthRoot_Osqrt(U_2326) != 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_2326) ),
inference(clausify,[status(thm)],[f_804_3]) ).
fof(f_805_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_805_2,plain,
! [U_2327] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2327))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2327) ),
inference(variable_rename,[status(thm)],[f_805_1]) ).
fof(f_805_3,plain,
! [U_2327] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2327))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2327) ),
inference(definitional_conversion,[status(esa)],[f_805_2]) ).
cnf(f_805_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2327))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2327) ),
inference(clausify,[status(thm)],[f_805_3]) ).
fof(f_806_1,plain,
! [V_xa_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_xa_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(V_xa_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__lt__1__iff]) ).
fof(f_806_2,plain,
! [U_2328] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2328),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2328,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2328,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2328),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_806_1]) ).
fof(f_806_3,plain,
( ! [U_2330] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2330),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2330,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_2329] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2329,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2329),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_806_2]) ).
fof(f_806_4,plain,
( ! [U_2330] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2330),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2330,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_2329] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2329,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2329),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_806_3]) ).
cnf(f_806_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2329,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2329),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_806_4]) ).
cnf(f_806_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_NthRoot_Osqrt(U_2330),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2330,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_806_4]) ).
fof(f_807_1,plain,
! [V_ya_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_ya_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(V_ya_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sqrt__gt__1__iff]) ).
fof(f_807_2,plain,
! [U_2331] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2331))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2331) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2331)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2331)) ) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
fof(f_807_3,plain,
( ! [U_2333] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2333))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2333) )
& ! [U_2332] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2332)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2332)) ) ),
inference(miniscope,[status(thm)],[f_807_2]) ).
fof(f_807_4,plain,
( ! [U_2333] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2333))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2333) )
& ! [U_2332] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2332)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2332)) ) ),
inference(definitional_conversion,[status(esa)],[f_807_3]) ).
cnf(f_807_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2332)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2332)) ),
inference(clausify,[status(thm)],[f_807_4]) ).
cnf(f_807_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2333))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2333) ),
inference(clausify,[status(thm)],[f_807_4]) ).
fof(f_808_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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__le__cancel__left__pos]) ).
fof(f_808_2,plain,
! [U_2337,U_2336,U_2335,U_2334] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2337))
| ~ c_Orderings_Oord__class_Oless__eq(U_2334,U_2336,U_2337) )
& ( c_Orderings_Oord__class_Oless__eq(U_2334,U_2336,U_2337)
| ~ c_Orderings_Oord__class_Oless__eq(U_2334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2337)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2334,c_Groups_Ozero__class_Ozero(U_2334),U_2335)
| ~ class_Rings_Olinordered__ring__strict(U_2334) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
fof(f_808_3,plain,
( ! [U_2334,U_2335,U_2336,U_2337] :
( c_Orderings_Oord__class_Oless__eq(U_2334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2337))
| ~ c_Orderings_Oord__class_Oless__eq(U_2334,U_2336,U_2337)
| ~ sP203(U_2334,U_2335,U_2336,U_2337) )
& ! [U_2334,U_2335,U_2336,U_2337] :
( c_Orderings_Oord__class_Oless__eq(U_2334,U_2336,U_2337)
| ~ c_Orderings_Oord__class_Oless__eq(U_2334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2337))
| ~ sP203(U_2334,U_2335,U_2336,U_2337) )
& ! [U_2334,U_2335,U_2336,U_2337] :
( sP203(U_2334,U_2335,U_2336,U_2337)
| ~ c_Orderings_Oord__class_Oless(U_2334,c_Groups_Ozero__class_Ozero(U_2334),U_2335)
| ~ class_Rings_Olinordered__ring__strict(U_2334) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_808_2]) ).
cnf(f_808_4,plain,
( sP203(U_2334,U_2335,U_2336,U_2337)
| ~ c_Orderings_Oord__class_Oless(U_2334,c_Groups_Ozero__class_Ozero(U_2334),U_2335)
| ~ class_Rings_Olinordered__ring__strict(U_2334) ),
inference(clausify,[status(thm)],[f_808_3]) ).
cnf(f_808_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2334,U_2336,U_2337)
| ~ c_Orderings_Oord__class_Oless__eq(U_2334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2337))
| ~ sP203(U_2334,U_2335,U_2336,U_2337) ),
inference(clausify,[status(thm)],[f_808_3]) ).
cnf(f_808_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2334,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2336),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2334),U_2335),U_2337))
| ~ c_Orderings_Oord__class_Oless__eq(U_2334,U_2336,U_2337)
| ~ sP203(U_2334,U_2335,U_2336,U_2337) ),
inference(clausify,[status(thm)],[f_808_3]) ).
fof(f_809_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2),hAPP(hAPP(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__le__cancel__left__neg]) ).
fof(f_809_2,plain,
! [U_2341,U_2340,U_2339,U_2338] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2338,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2341))
| ~ c_Orderings_Oord__class_Oless__eq(U_2338,U_2341,U_2340) )
& ( c_Orderings_Oord__class_Oless__eq(U_2338,U_2341,U_2340)
| ~ c_Orderings_Oord__class_Oless__eq(U_2338,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2341)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2338,U_2339,c_Groups_Ozero__class_Ozero(U_2338))
| ~ class_Rings_Olinordered__ring__strict(U_2338) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
fof(f_809_3,plain,
( ! [U_2338,U_2339,U_2340,U_2341] :
( c_Orderings_Oord__class_Oless__eq(U_2338,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2341))
| ~ c_Orderings_Oord__class_Oless__eq(U_2338,U_2341,U_2340)
| ~ sP204(U_2338,U_2339,U_2340,U_2341) )
& ! [U_2338,U_2339,U_2340,U_2341] :
( c_Orderings_Oord__class_Oless__eq(U_2338,U_2341,U_2340)
| ~ c_Orderings_Oord__class_Oless__eq(U_2338,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2341))
| ~ sP204(U_2338,U_2339,U_2340,U_2341) )
& ! [U_2338,U_2339,U_2340,U_2341] :
( sP204(U_2338,U_2339,U_2340,U_2341)
| ~ c_Orderings_Oord__class_Oless(U_2338,U_2339,c_Groups_Ozero__class_Ozero(U_2338))
| ~ class_Rings_Olinordered__ring__strict(U_2338) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_809_2]) ).
cnf(f_809_4,plain,
( sP204(U_2338,U_2339,U_2340,U_2341)
| ~ c_Orderings_Oord__class_Oless(U_2338,U_2339,c_Groups_Ozero__class_Ozero(U_2338))
| ~ class_Rings_Olinordered__ring__strict(U_2338) ),
inference(clausify,[status(thm)],[f_809_3]) ).
cnf(f_809_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2338,U_2341,U_2340)
| ~ c_Orderings_Oord__class_Oless__eq(U_2338,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2341))
| ~ sP204(U_2338,U_2339,U_2340,U_2341) ),
inference(clausify,[status(thm)],[f_809_3]) ).
cnf(f_809_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2338,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2340),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2338),U_2339),U_2341))
| ~ c_Orderings_Oord__class_Oless__eq(U_2338,U_2341,U_2340)
| ~ sP204(U_2338,U_2339,U_2340,U_2341) ),
inference(clausify,[status(thm)],[f_809_3]) ).
fof(f_810_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ 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__mono]) ).
fof(f_810_2,plain,
! [U_2346,U_2345,U_2344,U_2343,U_2342] :
( c_Orderings_Oord__class_Oless(U_2342,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2342),U_2343),U_2345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2342),U_2344),U_2346))
| ~ c_Orderings_Oord__class_Oless__eq(U_2342,c_Groups_Ozero__class_Ozero(U_2342),U_2345)
| ~ c_Orderings_Oord__class_Oless(U_2342,c_Groups_Ozero__class_Ozero(U_2342),U_2344)
| ~ c_Orderings_Oord__class_Oless(U_2342,U_2345,U_2346)
| ~ c_Orderings_Oord__class_Oless(U_2342,U_2343,U_2344)
| ~ class_Rings_Olinordered__semiring__strict(U_2342) ),
inference(variable_rename,[status(thm)],[f_810_1]) ).
fof(f_810_3,plain,
! [U_2344,U_2342,U_2343,U_2345,U_2346] :
( c_Orderings_Oord__class_Oless(U_2342,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2342),U_2343),U_2345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2342),U_2344),U_2346))
| ~ c_Orderings_Oord__class_Oless__eq(U_2342,c_Groups_Ozero__class_Ozero(U_2342),U_2345)
| ~ c_Orderings_Oord__class_Oless(U_2342,c_Groups_Ozero__class_Ozero(U_2342),U_2344)
| ~ c_Orderings_Oord__class_Oless(U_2342,U_2345,U_2346)
| ~ c_Orderings_Oord__class_Oless(U_2342,U_2343,U_2344)
| ~ class_Rings_Olinordered__semiring__strict(U_2342) ),
inference(definitional_conversion,[status(esa)],[f_810_2]) ).
cnf(f_810_4,plain,
( c_Orderings_Oord__class_Oless(U_2342,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2342),U_2343),U_2345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2342),U_2344),U_2346))
| ~ c_Orderings_Oord__class_Oless__eq(U_2342,c_Groups_Ozero__class_Ozero(U_2342),U_2345)
| ~ c_Orderings_Oord__class_Oless(U_2342,c_Groups_Ozero__class_Ozero(U_2342),U_2344)
| ~ c_Orderings_Oord__class_Oless(U_2342,U_2345,U_2346)
| ~ c_Orderings_Oord__class_Oless(U_2342,U_2343,U_2344)
| ~ class_Rings_Olinordered__semiring__strict(U_2342) ),
inference(clausify,[status(thm)],[f_810_3]) ).
fof(f_811_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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(T_a,V_c,V_d)
| ~ 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__mono_H]) ).
fof(f_811_2,plain,
! [U_2351,U_2350,U_2349,U_2348,U_2347] :
( c_Orderings_Oord__class_Oless(U_2347,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),U_2348),U_2350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),U_2349),U_2351))
| ~ c_Orderings_Oord__class_Oless__eq(U_2347,c_Groups_Ozero__class_Ozero(U_2347),U_2350)
| ~ c_Orderings_Oord__class_Oless__eq(U_2347,c_Groups_Ozero__class_Ozero(U_2347),U_2348)
| ~ c_Orderings_Oord__class_Oless(U_2347,U_2350,U_2351)
| ~ c_Orderings_Oord__class_Oless(U_2347,U_2348,U_2349)
| ~ class_Rings_Olinordered__semiring__strict(U_2347) ),
inference(variable_rename,[status(thm)],[f_811_1]) ).
fof(f_811_3,plain,
! [U_2351,U_2348,U_2350,U_2349,U_2347] :
( c_Orderings_Oord__class_Oless(U_2347,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),U_2348),U_2350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),U_2349),U_2351))
| ~ c_Orderings_Oord__class_Oless__eq(U_2347,c_Groups_Ozero__class_Ozero(U_2347),U_2350)
| ~ c_Orderings_Oord__class_Oless__eq(U_2347,c_Groups_Ozero__class_Ozero(U_2347),U_2348)
| ~ c_Orderings_Oord__class_Oless(U_2347,U_2350,U_2351)
| ~ c_Orderings_Oord__class_Oless(U_2347,U_2348,U_2349)
| ~ class_Rings_Olinordered__semiring__strict(U_2347) ),
inference(definitional_conversion,[status(esa)],[f_811_2]) ).
cnf(f_811_4,plain,
( c_Orderings_Oord__class_Oless(U_2347,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),U_2348),U_2350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2347),U_2349),U_2351))
| ~ c_Orderings_Oord__class_Oless__eq(U_2347,c_Groups_Ozero__class_Ozero(U_2347),U_2350)
| ~ c_Orderings_Oord__class_Oless__eq(U_2347,c_Groups_Ozero__class_Ozero(U_2347),U_2348)
| ~ c_Orderings_Oord__class_Oless(U_2347,U_2350,U_2351)
| ~ c_Orderings_Oord__class_Oless(U_2347,U_2348,U_2349)
| ~ class_Rings_Olinordered__semiring__strict(U_2347) ),
inference(clausify,[status(thm)],[f_811_3]) ).
fof(f_812_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_d))
| ~ c_Orderings_Oord__class_Oless(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(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__le__imp__less]) ).
fof(f_812_2,plain,
! [U_2356,U_2355,U_2354,U_2353,U_2352] :
( c_Orderings_Oord__class_Oless(U_2352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2352),U_2353),U_2355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2352),U_2354),U_2356))
| ~ c_Orderings_Oord__class_Oless(U_2352,c_Groups_Ozero__class_Ozero(U_2352),U_2355)
| ~ c_Orderings_Oord__class_Oless__eq(U_2352,c_Groups_Ozero__class_Ozero(U_2352),U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(U_2352,U_2355,U_2356)
| ~ c_Orderings_Oord__class_Oless(U_2352,U_2353,U_2354)
| ~ class_Rings_Olinordered__semiring__strict(U_2352) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
fof(f_812_3,plain,
! [U_2353,U_2355,U_2354,U_2356,U_2352] :
( c_Orderings_Oord__class_Oless(U_2352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2352),U_2353),U_2355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2352),U_2354),U_2356))
| ~ c_Orderings_Oord__class_Oless(U_2352,c_Groups_Ozero__class_Ozero(U_2352),U_2355)
| ~ c_Orderings_Oord__class_Oless__eq(U_2352,c_Groups_Ozero__class_Ozero(U_2352),U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(U_2352,U_2355,U_2356)
| ~ c_Orderings_Oord__class_Oless(U_2352,U_2353,U_2354)
| ~ class_Rings_Olinordered__semiring__strict(U_2352) ),
inference(definitional_conversion,[status(esa)],[f_812_2]) ).
cnf(f_812_4,plain,
( c_Orderings_Oord__class_Oless(U_2352,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2352),U_2353),U_2355),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2352),U_2354),U_2356))
| ~ c_Orderings_Oord__class_Oless(U_2352,c_Groups_Ozero__class_Ozero(U_2352),U_2355)
| ~ c_Orderings_Oord__class_Oless__eq(U_2352,c_Groups_Ozero__class_Ozero(U_2352),U_2353)
| ~ c_Orderings_Oord__class_Oless__eq(U_2352,U_2355,U_2356)
| ~ c_Orderings_Oord__class_Oless(U_2352,U_2353,U_2354)
| ~ class_Rings_Olinordered__semiring__strict(U_2352) ),
inference(clausify,[status(thm)],[f_812_3]) ).
fof(f_813_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(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(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_c,V_d)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__less__imp__less]) ).
fof(f_813_2,plain,
! [U_2361,U_2360,U_2359,U_2358,U_2357] :
( c_Orderings_Oord__class_Oless(U_2357,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2357),U_2358),U_2360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2357),U_2359),U_2361))
| ~ c_Orderings_Oord__class_Oless__eq(U_2357,c_Groups_Ozero__class_Ozero(U_2357),U_2360)
| ~ c_Orderings_Oord__class_Oless(U_2357,c_Groups_Ozero__class_Ozero(U_2357),U_2358)
| ~ c_Orderings_Oord__class_Oless(U_2357,U_2360,U_2361)
| ~ c_Orderings_Oord__class_Oless__eq(U_2357,U_2358,U_2359)
| ~ class_Rings_Olinordered__semiring__strict(U_2357) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
fof(f_813_3,plain,
! [U_2358,U_2359,U_2357,U_2360,U_2361] :
( c_Orderings_Oord__class_Oless(U_2357,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2357),U_2358),U_2360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2357),U_2359),U_2361))
| ~ c_Orderings_Oord__class_Oless__eq(U_2357,c_Groups_Ozero__class_Ozero(U_2357),U_2360)
| ~ c_Orderings_Oord__class_Oless(U_2357,c_Groups_Ozero__class_Ozero(U_2357),U_2358)
| ~ c_Orderings_Oord__class_Oless(U_2357,U_2360,U_2361)
| ~ c_Orderings_Oord__class_Oless__eq(U_2357,U_2358,U_2359)
| ~ class_Rings_Olinordered__semiring__strict(U_2357) ),
inference(definitional_conversion,[status(esa)],[f_813_2]) ).
cnf(f_813_4,plain,
( c_Orderings_Oord__class_Oless(U_2357,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2357),U_2358),U_2360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2357),U_2359),U_2361))
| ~ c_Orderings_Oord__class_Oless__eq(U_2357,c_Groups_Ozero__class_Ozero(U_2357),U_2360)
| ~ c_Orderings_Oord__class_Oless(U_2357,c_Groups_Ozero__class_Ozero(U_2357),U_2358)
| ~ c_Orderings_Oord__class_Oless(U_2357,U_2360,U_2361)
| ~ c_Orderings_Oord__class_Oless__eq(U_2357,U_2358,U_2359)
| ~ class_Rings_Olinordered__semiring__strict(U_2357) ),
inference(clausify,[status(thm)],[f_813_3]) ).
fof(f_814_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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Olinordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__less__imp__less]) ).
fof(f_814_2,plain,
! [U_2365,U_2364,U_2363,U_2362] :
( c_Orderings_Oord__class_Oless(U_2362,U_2363,U_2365)
| ~ c_Orderings_Oord__class_Oless__eq(U_2362,c_Groups_Ozero__class_Ozero(U_2362),U_2364)
| ~ c_Orderings_Oord__class_Oless(U_2362,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2362),U_2363),U_2364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2362),U_2365),U_2364))
| ~ class_Rings_Olinordered__semiring(U_2362) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
fof(f_814_3,plain,
! [U_2363,U_2362,U_2365,U_2364] :
( c_Orderings_Oord__class_Oless(U_2362,U_2363,U_2365)
| ~ c_Orderings_Oord__class_Oless__eq(U_2362,c_Groups_Ozero__class_Ozero(U_2362),U_2364)
| ~ c_Orderings_Oord__class_Oless(U_2362,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2362),U_2363),U_2364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2362),U_2365),U_2364))
| ~ class_Rings_Olinordered__semiring(U_2362) ),
inference(definitional_conversion,[status(esa)],[f_814_2]) ).
cnf(f_814_4,plain,
( c_Orderings_Oord__class_Oless(U_2362,U_2363,U_2365)
| ~ c_Orderings_Oord__class_Oless__eq(U_2362,c_Groups_Ozero__class_Ozero(U_2362),U_2364)
| ~ c_Orderings_Oord__class_Oless(U_2362,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2362),U_2363),U_2364),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2362),U_2365),U_2364))
| ~ class_Rings_Olinordered__semiring(U_2362) ),
inference(clausify,[status(thm)],[f_814_3]) ).
fof(f_815_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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__right]) ).
fof(f_815_2,plain,
! [U_2369,U_2368,U_2367,U_2366] :
( c_Orderings_Oord__class_Oless(U_2366,U_2367,U_2369)
| ~ c_Orderings_Oord__class_Oless__eq(U_2366,c_Groups_Ozero__class_Ozero(U_2366),U_2368)
| ~ c_Orderings_Oord__class_Oless(U_2366,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2366),U_2367),U_2368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2366),U_2369),U_2368))
| ~ class_Rings_Olinordered__semiring__strict(U_2366) ),
inference(variable_rename,[status(thm)],[f_815_1]) ).
fof(f_815_3,plain,
! [U_2366,U_2367,U_2368,U_2369] :
( c_Orderings_Oord__class_Oless(U_2366,U_2367,U_2369)
| ~ c_Orderings_Oord__class_Oless__eq(U_2366,c_Groups_Ozero__class_Ozero(U_2366),U_2368)
| ~ c_Orderings_Oord__class_Oless(U_2366,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2366),U_2367),U_2368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2366),U_2369),U_2368))
| ~ class_Rings_Olinordered__semiring__strict(U_2366) ),
inference(definitional_conversion,[status(esa)],[f_815_2]) ).
cnf(f_815_4,plain,
( c_Orderings_Oord__class_Oless(U_2366,U_2367,U_2369)
| ~ c_Orderings_Oord__class_Oless__eq(U_2366,c_Groups_Ozero__class_Ozero(U_2366),U_2368)
| ~ c_Orderings_Oord__class_Oless(U_2366,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2366),U_2367),U_2368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2366),U_2369),U_2368))
| ~ class_Rings_Olinordered__semiring__strict(U_2366) ),
inference(clausify,[status(thm)],[f_815_3]) ).
fof(f_816_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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ class_Rings_Olinordered__semiring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__less__imp__less]) ).
fof(f_816_2,plain,
! [U_2373,U_2372,U_2371,U_2370] :
( c_Orderings_Oord__class_Oless(U_2370,U_2372,U_2373)
| ~ c_Orderings_Oord__class_Oless__eq(U_2370,c_Groups_Ozero__class_Ozero(U_2370),U_2371)
| ~ c_Orderings_Oord__class_Oless(U_2370,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2370),U_2371),U_2372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2370),U_2371),U_2373))
| ~ class_Rings_Olinordered__semiring(U_2370) ),
inference(variable_rename,[status(thm)],[f_816_1]) ).
fof(f_816_3,plain,
! [U_2370,U_2371,U_2372,U_2373] :
( c_Orderings_Oord__class_Oless(U_2370,U_2372,U_2373)
| ~ c_Orderings_Oord__class_Oless__eq(U_2370,c_Groups_Ozero__class_Ozero(U_2370),U_2371)
| ~ c_Orderings_Oord__class_Oless(U_2370,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2370),U_2371),U_2372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2370),U_2371),U_2373))
| ~ class_Rings_Olinordered__semiring(U_2370) ),
inference(definitional_conversion,[status(esa)],[f_816_2]) ).
cnf(f_816_4,plain,
( c_Orderings_Oord__class_Oless(U_2370,U_2372,U_2373)
| ~ c_Orderings_Oord__class_Oless__eq(U_2370,c_Groups_Ozero__class_Ozero(U_2370),U_2371)
| ~ c_Orderings_Oord__class_Oless(U_2370,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2370),U_2371),U_2372),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2370),U_2371),U_2373))
| ~ class_Rings_Olinordered__semiring(U_2370) ),
inference(clausify,[status(thm)],[f_816_3]) ).
fof(f_817_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__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__imp__less__left]) ).
fof(f_817_2,plain,
! [U_2377,U_2376,U_2375,U_2374] :
( c_Orderings_Oord__class_Oless(U_2374,U_2376,U_2377)
| ~ c_Orderings_Oord__class_Oless__eq(U_2374,c_Groups_Ozero__class_Ozero(U_2374),U_2375)
| ~ c_Orderings_Oord__class_Oless(U_2374,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2374),U_2375),U_2376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2374),U_2375),U_2377))
| ~ class_Rings_Olinordered__semiring__strict(U_2374) ),
inference(variable_rename,[status(thm)],[f_817_1]) ).
fof(f_817_3,plain,
! [U_2374,U_2375,U_2376,U_2377] :
( c_Orderings_Oord__class_Oless(U_2374,U_2376,U_2377)
| ~ c_Orderings_Oord__class_Oless__eq(U_2374,c_Groups_Ozero__class_Ozero(U_2374),U_2375)
| ~ c_Orderings_Oord__class_Oless(U_2374,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2374),U_2375),U_2376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2374),U_2375),U_2377))
| ~ class_Rings_Olinordered__semiring__strict(U_2374) ),
inference(definitional_conversion,[status(esa)],[f_817_2]) ).
cnf(f_817_4,plain,
( c_Orderings_Oord__class_Oless(U_2374,U_2376,U_2377)
| ~ c_Orderings_Oord__class_Oless__eq(U_2374,c_Groups_Ozero__class_Ozero(U_2374),U_2375)
| ~ c_Orderings_Oord__class_Oless(U_2374,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2374),U_2375),U_2376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2374),U_2375),U_2377))
| ~ class_Rings_Olinordered__semiring__strict(U_2374) ),
inference(clausify,[status(thm)],[f_817_3]) ).
fof(f_818_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(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right__le__imp__le]) ).
fof(f_818_2,plain,
! [U_2381,U_2380,U_2379,U_2378] :
( c_Orderings_Oord__class_Oless__eq(U_2378,U_2379,U_2381)
| ~ c_Orderings_Oord__class_Oless(U_2378,c_Groups_Ozero__class_Ozero(U_2378),U_2380)
| ~ c_Orderings_Oord__class_Oless__eq(U_2378,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2378),U_2379),U_2380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2378),U_2381),U_2380))
| ~ class_Rings_Olinordered__semiring__strict(U_2378) ),
inference(variable_rename,[status(thm)],[f_818_1]) ).
fof(f_818_3,plain,
! [U_2378,U_2380,U_2379,U_2381] :
( c_Orderings_Oord__class_Oless__eq(U_2378,U_2379,U_2381)
| ~ c_Orderings_Oord__class_Oless(U_2378,c_Groups_Ozero__class_Ozero(U_2378),U_2380)
| ~ c_Orderings_Oord__class_Oless__eq(U_2378,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2378),U_2379),U_2380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2378),U_2381),U_2380))
| ~ class_Rings_Olinordered__semiring__strict(U_2378) ),
inference(definitional_conversion,[status(esa)],[f_818_2]) ).
cnf(f_818_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2378,U_2379,U_2381)
| ~ c_Orderings_Oord__class_Oless(U_2378,c_Groups_Ozero__class_Ozero(U_2378),U_2380)
| ~ c_Orderings_Oord__class_Oless__eq(U_2378,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2378),U_2379),U_2380),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2378),U_2381),U_2380))
| ~ class_Rings_Olinordered__semiring__strict(U_2378) ),
inference(clausify,[status(thm)],[f_818_3]) ).
fof(f_819_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(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b))
| ~ class_Rings_Olinordered__semiring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__le__imp__le]) ).
fof(f_819_2,plain,
! [U_2385,U_2384,U_2383,U_2382] :
( c_Orderings_Oord__class_Oless__eq(U_2382,U_2384,U_2385)
| ~ c_Orderings_Oord__class_Oless(U_2382,c_Groups_Ozero__class_Ozero(U_2382),U_2383)
| ~ c_Orderings_Oord__class_Oless__eq(U_2382,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2382),U_2383),U_2384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2382),U_2383),U_2385))
| ~ class_Rings_Olinordered__semiring__strict(U_2382) ),
inference(variable_rename,[status(thm)],[f_819_1]) ).
fof(f_819_3,plain,
! [U_2382,U_2383,U_2384,U_2385] :
( c_Orderings_Oord__class_Oless__eq(U_2382,U_2384,U_2385)
| ~ c_Orderings_Oord__class_Oless(U_2382,c_Groups_Ozero__class_Ozero(U_2382),U_2383)
| ~ c_Orderings_Oord__class_Oless__eq(U_2382,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2382),U_2383),U_2384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2382),U_2383),U_2385))
| ~ class_Rings_Olinordered__semiring__strict(U_2382) ),
inference(definitional_conversion,[status(esa)],[f_819_2]) ).
cnf(f_819_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2382,U_2384,U_2385)
| ~ c_Orderings_Oord__class_Oless(U_2382,c_Groups_Ozero__class_Ozero(U_2382),U_2383)
| ~ c_Orderings_Oord__class_Oless__eq(U_2382,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2382),U_2383),U_2384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2382),U_2383),U_2385))
| ~ class_Rings_Olinordered__semiring__strict(U_2382) ),
inference(clausify,[status(thm)],[f_819_3]) ).
fof(f_820_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_820_2,plain,
! [U_2388,U_2387,U_2386] :
( c_Orderings_Oord__class_Oless(U_2386,c_Groups_Oplus__class_Oplus(U_2386,U_2387,U_2388),c_Groups_Ozero__class_Ozero(U_2386))
| ~ c_Orderings_Oord__class_Oless(U_2386,U_2388,c_Groups_Ozero__class_Ozero(U_2386))
| ~ c_Orderings_Oord__class_Oless__eq(U_2386,U_2387,c_Groups_Ozero__class_Ozero(U_2386))
| ~ class_Groups_Oordered__comm__monoid__add(U_2386) ),
inference(variable_rename,[status(thm)],[f_820_1]) ).
fof(f_820_3,plain,
! [U_2387,U_2386,U_2388] :
( c_Orderings_Oord__class_Oless(U_2386,c_Groups_Oplus__class_Oplus(U_2386,U_2387,U_2388),c_Groups_Ozero__class_Ozero(U_2386))
| ~ c_Orderings_Oord__class_Oless(U_2386,U_2388,c_Groups_Ozero__class_Ozero(U_2386))
| ~ c_Orderings_Oord__class_Oless__eq(U_2386,U_2387,c_Groups_Ozero__class_Ozero(U_2386))
| ~ class_Groups_Oordered__comm__monoid__add(U_2386) ),
inference(definitional_conversion,[status(esa)],[f_820_2]) ).
cnf(f_820_4,plain,
( c_Orderings_Oord__class_Oless(U_2386,c_Groups_Oplus__class_Oplus(U_2386,U_2387,U_2388),c_Groups_Ozero__class_Ozero(U_2386))
| ~ c_Orderings_Oord__class_Oless(U_2386,U_2388,c_Groups_Ozero__class_Ozero(U_2386))
| ~ c_Orderings_Oord__class_Oless__eq(U_2386,U_2387,c_Groups_Ozero__class_Ozero(U_2386))
| ~ class_Groups_Oordered__comm__monoid__add(U_2386) ),
inference(clausify,[status(thm)],[f_820_3]) ).
fof(f_821_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_821_2,plain,
! [U_2391,U_2390,U_2389] :
( c_Orderings_Oord__class_Oless(U_2389,c_Groups_Oplus__class_Oplus(U_2389,U_2390,U_2391),c_Groups_Ozero__class_Ozero(U_2389))
| ~ c_Orderings_Oord__class_Oless__eq(U_2389,U_2391,c_Groups_Ozero__class_Ozero(U_2389))
| ~ c_Orderings_Oord__class_Oless(U_2389,U_2390,c_Groups_Ozero__class_Ozero(U_2389))
| ~ class_Groups_Oordered__comm__monoid__add(U_2389) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
fof(f_821_3,plain,
! [U_2389,U_2390,U_2391] :
( c_Orderings_Oord__class_Oless(U_2389,c_Groups_Oplus__class_Oplus(U_2389,U_2390,U_2391),c_Groups_Ozero__class_Ozero(U_2389))
| ~ c_Orderings_Oord__class_Oless__eq(U_2389,U_2391,c_Groups_Ozero__class_Ozero(U_2389))
| ~ c_Orderings_Oord__class_Oless(U_2389,U_2390,c_Groups_Ozero__class_Ozero(U_2389))
| ~ class_Groups_Oordered__comm__monoid__add(U_2389) ),
inference(definitional_conversion,[status(esa)],[f_821_2]) ).
cnf(f_821_4,plain,
( c_Orderings_Oord__class_Oless(U_2389,c_Groups_Oplus__class_Oplus(U_2389,U_2390,U_2391),c_Groups_Ozero__class_Ozero(U_2389))
| ~ c_Orderings_Oord__class_Oless__eq(U_2389,U_2391,c_Groups_Ozero__class_Ozero(U_2389))
| ~ c_Orderings_Oord__class_Oless(U_2389,U_2390,c_Groups_Ozero__class_Ozero(U_2389))
| ~ class_Groups_Oordered__comm__monoid__add(U_2389) ),
inference(clausify,[status(thm)],[f_821_3]) ).
fof(f_822_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_822_2,plain,
! [U_2395,U_2394,U_2393,U_2392] :
( c_Orderings_Oord__class_Oless(U_2392,U_2394,c_Groups_Oplus__class_Oplus(U_2392,U_2393,U_2395))
| ~ c_Orderings_Oord__class_Oless(U_2392,U_2394,U_2395)
| ~ c_Orderings_Oord__class_Oless__eq(U_2392,c_Groups_Ozero__class_Ozero(U_2392),U_2393)
| ~ class_Groups_Oordered__comm__monoid__add(U_2392) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
fof(f_822_3,plain,
! [U_2393,U_2392,U_2394,U_2395] :
( c_Orderings_Oord__class_Oless(U_2392,U_2394,c_Groups_Oplus__class_Oplus(U_2392,U_2393,U_2395))
| ~ c_Orderings_Oord__class_Oless(U_2392,U_2394,U_2395)
| ~ c_Orderings_Oord__class_Oless__eq(U_2392,c_Groups_Ozero__class_Ozero(U_2392),U_2393)
| ~ class_Groups_Oordered__comm__monoid__add(U_2392) ),
inference(definitional_conversion,[status(esa)],[f_822_2]) ).
cnf(f_822_4,plain,
( c_Orderings_Oord__class_Oless(U_2392,U_2394,c_Groups_Oplus__class_Oplus(U_2392,U_2393,U_2395))
| ~ c_Orderings_Oord__class_Oless(U_2392,U_2394,U_2395)
| ~ c_Orderings_Oord__class_Oless__eq(U_2392,c_Groups_Ozero__class_Ozero(U_2392),U_2393)
| ~ class_Groups_Oordered__comm__monoid__add(U_2392) ),
inference(clausify,[status(thm)],[f_822_3]) ).
fof(f_823_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_823_2,plain,
! [U_2399,U_2398,U_2397,U_2396] :
( c_Orderings_Oord__class_Oless(U_2396,U_2398,c_Groups_Oplus__class_Oplus(U_2396,U_2397,U_2399))
| ~ c_Orderings_Oord__class_Oless__eq(U_2396,U_2398,U_2399)
| ~ c_Orderings_Oord__class_Oless(U_2396,c_Groups_Ozero__class_Ozero(U_2396),U_2397)
| ~ class_Groups_Oordered__comm__monoid__add(U_2396) ),
inference(variable_rename,[status(thm)],[f_823_1]) ).
fof(f_823_3,plain,
! [U_2397,U_2396,U_2398,U_2399] :
( c_Orderings_Oord__class_Oless(U_2396,U_2398,c_Groups_Oplus__class_Oplus(U_2396,U_2397,U_2399))
| ~ c_Orderings_Oord__class_Oless__eq(U_2396,U_2398,U_2399)
| ~ c_Orderings_Oord__class_Oless(U_2396,c_Groups_Ozero__class_Ozero(U_2396),U_2397)
| ~ class_Groups_Oordered__comm__monoid__add(U_2396) ),
inference(definitional_conversion,[status(esa)],[f_823_2]) ).
cnf(f_823_4,plain,
( c_Orderings_Oord__class_Oless(U_2396,U_2398,c_Groups_Oplus__class_Oplus(U_2396,U_2397,U_2399))
| ~ c_Orderings_Oord__class_Oless__eq(U_2396,U_2398,U_2399)
| ~ c_Orderings_Oord__class_Oless(U_2396,c_Groups_Ozero__class_Ozero(U_2396),U_2397)
| ~ class_Groups_Oordered__comm__monoid__add(U_2396) ),
inference(clausify,[status(thm)],[f_823_3]) ).
fof(f_824_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_824_2,plain,
! [U_2402,U_2401,U_2400] :
( c_Orderings_Oord__class_Oless(U_2400,c_Groups_Ozero__class_Ozero(U_2400),c_Groups_Oplus__class_Oplus(U_2400,U_2401,U_2402))
| ~ c_Orderings_Oord__class_Oless(U_2400,c_Groups_Ozero__class_Ozero(U_2400),U_2402)
| ~ c_Orderings_Oord__class_Oless__eq(U_2400,c_Groups_Ozero__class_Ozero(U_2400),U_2401)
| ~ class_Groups_Oordered__comm__monoid__add(U_2400) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
fof(f_824_3,plain,
! [U_2400,U_2401,U_2402] :
( c_Orderings_Oord__class_Oless(U_2400,c_Groups_Ozero__class_Ozero(U_2400),c_Groups_Oplus__class_Oplus(U_2400,U_2401,U_2402))
| ~ c_Orderings_Oord__class_Oless(U_2400,c_Groups_Ozero__class_Ozero(U_2400),U_2402)
| ~ c_Orderings_Oord__class_Oless__eq(U_2400,c_Groups_Ozero__class_Ozero(U_2400),U_2401)
| ~ class_Groups_Oordered__comm__monoid__add(U_2400) ),
inference(definitional_conversion,[status(esa)],[f_824_2]) ).
cnf(f_824_4,plain,
( c_Orderings_Oord__class_Oless(U_2400,c_Groups_Ozero__class_Ozero(U_2400),c_Groups_Oplus__class_Oplus(U_2400,U_2401,U_2402))
| ~ c_Orderings_Oord__class_Oless(U_2400,c_Groups_Ozero__class_Ozero(U_2400),U_2402)
| ~ c_Orderings_Oord__class_Oless__eq(U_2400,c_Groups_Ozero__class_Ozero(U_2400),U_2401)
| ~ class_Groups_Oordered__comm__monoid__add(U_2400) ),
inference(clausify,[status(thm)],[f_824_3]) ).
fof(f_825_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_825_2,plain,
! [U_2405,U_2404,U_2403] :
( c_Orderings_Oord__class_Oless(U_2403,c_Groups_Ozero__class_Ozero(U_2403),c_Groups_Oplus__class_Oplus(U_2403,U_2404,U_2405))
| ~ c_Orderings_Oord__class_Oless__eq(U_2403,c_Groups_Ozero__class_Ozero(U_2403),U_2405)
| ~ c_Orderings_Oord__class_Oless(U_2403,c_Groups_Ozero__class_Ozero(U_2403),U_2404)
| ~ class_Groups_Oordered__comm__monoid__add(U_2403) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
fof(f_825_3,plain,
! [U_2403,U_2404,U_2405] :
( c_Orderings_Oord__class_Oless(U_2403,c_Groups_Ozero__class_Ozero(U_2403),c_Groups_Oplus__class_Oplus(U_2403,U_2404,U_2405))
| ~ c_Orderings_Oord__class_Oless__eq(U_2403,c_Groups_Ozero__class_Ozero(U_2403),U_2405)
| ~ c_Orderings_Oord__class_Oless(U_2403,c_Groups_Ozero__class_Ozero(U_2403),U_2404)
| ~ class_Groups_Oordered__comm__monoid__add(U_2403) ),
inference(definitional_conversion,[status(esa)],[f_825_2]) ).
cnf(f_825_4,plain,
( c_Orderings_Oord__class_Oless(U_2403,c_Groups_Ozero__class_Ozero(U_2403),c_Groups_Oplus__class_Oplus(U_2403,U_2404,U_2405))
| ~ c_Orderings_Oord__class_Oless__eq(U_2403,c_Groups_Ozero__class_Ozero(U_2403),U_2405)
| ~ c_Orderings_Oord__class_Oless(U_2403,c_Groups_Ozero__class_Ozero(U_2403),U_2404)
| ~ class_Groups_Oordered__comm__monoid__add(U_2403) ),
inference(clausify,[status(thm)],[f_825_3]) ).
fof(f_826_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_y)),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__sum__squares__lt__zero]) ).
fof(f_826_2,plain,
! [U_2408,U_2407,U_2406] :
( ~ c_Orderings_Oord__class_Oless(U_2406,c_Groups_Oplus__class_Oplus(U_2406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),U_2407),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),U_2408),U_2408)),c_Groups_Ozero__class_Ozero(U_2406))
| ~ class_Rings_Olinordered__ring(U_2406) ),
inference(variable_rename,[status(thm)],[f_826_1]) ).
fof(f_826_3,plain,
! [U_2406,U_2407,U_2408] :
( ~ c_Orderings_Oord__class_Oless(U_2406,c_Groups_Oplus__class_Oplus(U_2406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),U_2407),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),U_2408),U_2408)),c_Groups_Ozero__class_Ozero(U_2406))
| ~ class_Rings_Olinordered__ring(U_2406) ),
inference(definitional_conversion,[status(esa)],[f_826_2]) ).
cnf(f_826_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2406,c_Groups_Oplus__class_Oplus(U_2406,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),U_2407),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2406),U_2408),U_2408)),c_Groups_Ozero__class_Ozero(U_2406))
| ~ class_Rings_Olinordered__ring(U_2406) ),
inference(clausify,[status(thm)],[f_826_3]) ).
fof(f_827_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2)))
| ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_xa_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ya_2),V_ya_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).
fof(f_827_2,plain,
! [U_2411,U_2410,U_2409] :
( ( ( c_Orderings_Oord__class_Oless(U_2409,c_Groups_Ozero__class_Ozero(U_2409),c_Groups_Oplus__class_Oplus(U_2409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2410),U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2411),U_2411)))
| ( U_2411 = c_Groups_Ozero__class_Ozero(U_2409)
& U_2410 = c_Groups_Ozero__class_Ozero(U_2409) ) )
& ( U_2411 != c_Groups_Ozero__class_Ozero(U_2409)
| U_2410 != c_Groups_Ozero__class_Ozero(U_2409)
| ~ c_Orderings_Oord__class_Oless(U_2409,c_Groups_Ozero__class_Ozero(U_2409),c_Groups_Oplus__class_Oplus(U_2409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2410),U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2411),U_2411))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_2409) ),
inference(variable_rename,[status(thm)],[f_827_1]) ).
fof(f_827_3,plain,
( ! [U_2409,U_2410,U_2411] :
( U_2411 = c_Groups_Ozero__class_Ozero(U_2409)
| ~ sP205(U_2409,U_2410,U_2411) )
& ! [U_2409,U_2410,U_2411] :
( U_2410 = c_Groups_Ozero__class_Ozero(U_2409)
| ~ sP205(U_2409,U_2410,U_2411) )
& ! [U_2409,U_2410,U_2411] :
( c_Orderings_Oord__class_Oless(U_2409,c_Groups_Ozero__class_Ozero(U_2409),c_Groups_Oplus__class_Oplus(U_2409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2410),U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2411),U_2411)))
| sP205(U_2409,U_2410,U_2411)
| ~ sP206(U_2409,U_2410,U_2411) )
& ! [U_2409,U_2410,U_2411] :
( U_2411 != c_Groups_Ozero__class_Ozero(U_2409)
| U_2410 != c_Groups_Ozero__class_Ozero(U_2409)
| ~ c_Orderings_Oord__class_Oless(U_2409,c_Groups_Ozero__class_Ozero(U_2409),c_Groups_Oplus__class_Oplus(U_2409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2410),U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2411),U_2411)))
| ~ sP206(U_2409,U_2410,U_2411) )
& ! [U_2409,U_2410,U_2411] :
( sP206(U_2409,U_2410,U_2411)
| ~ class_Rings_Olinordered__ring__strict(U_2409) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205,sP206])],[f_827_2]) ).
cnf(f_827_4,plain,
( sP206(U_2409,U_2410,U_2411)
| ~ class_Rings_Olinordered__ring__strict(U_2409) ),
inference(clausify,[status(thm)],[f_827_3]) ).
cnf(f_827_5,plain,
( U_2411 != c_Groups_Ozero__class_Ozero(U_2409)
| U_2410 != c_Groups_Ozero__class_Ozero(U_2409)
| ~ c_Orderings_Oord__class_Oless(U_2409,c_Groups_Ozero__class_Ozero(U_2409),c_Groups_Oplus__class_Oplus(U_2409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2410),U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2411),U_2411)))
| ~ sP206(U_2409,U_2410,U_2411) ),
inference(clausify,[status(thm)],[f_827_3]) ).
cnf(f_827_6,plain,
( c_Orderings_Oord__class_Oless(U_2409,c_Groups_Ozero__class_Ozero(U_2409),c_Groups_Oplus__class_Oplus(U_2409,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2410),U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2409),U_2411),U_2411)))
| sP205(U_2409,U_2410,U_2411)
| ~ sP206(U_2409,U_2410,U_2411) ),
inference(clausify,[status(thm)],[f_827_3]) ).
cnf(f_827_7,plain,
( U_2410 = c_Groups_Ozero__class_Ozero(U_2409)
| ~ sP205(U_2409,U_2410,U_2411) ),
inference(clausify,[status(thm)],[f_827_3]) ).
cnf(f_827_8,plain,
( U_2411 = c_Groups_Ozero__class_Ozero(U_2409)
| ~ sP205(U_2409,U_2410,U_2411) ),
inference(clausify,[status(thm)],[f_827_3]) ).
fof(f_828_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(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_828_2,plain,
! [U_2415,U_2414,U_2413,U_2412] :
( c_Orderings_Oord__class_Oless(U_2412,U_2413,U_2415)
| ~ c_Orderings_Oord__class_Oless__eq(U_2412,c_Groups_Ozero__class_Ozero(U_2412),U_2415)
| ~ c_Orderings_Oord__class_Oless(U_2412,hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2413),U_2414),hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2415),U_2414))
| ~ class_Rings_Olinordered__semidom(U_2412) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
fof(f_828_3,plain,
! [U_2412,U_2413,U_2415,U_2414] :
( c_Orderings_Oord__class_Oless(U_2412,U_2413,U_2415)
| ~ c_Orderings_Oord__class_Oless__eq(U_2412,c_Groups_Ozero__class_Ozero(U_2412),U_2415)
| ~ c_Orderings_Oord__class_Oless(U_2412,hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2413),U_2414),hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2415),U_2414))
| ~ class_Rings_Olinordered__semidom(U_2412) ),
inference(definitional_conversion,[status(esa)],[f_828_2]) ).
cnf(f_828_4,plain,
( c_Orderings_Oord__class_Oless(U_2412,U_2413,U_2415)
| ~ c_Orderings_Oord__class_Oless__eq(U_2412,c_Groups_Ozero__class_Ozero(U_2412),U_2415)
| ~ c_Orderings_Oord__class_Oless(U_2412,hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2413),U_2414),hAPP(hAPP(c_Power_Opower__class_Opower(U_2412),U_2415),U_2414))
| ~ class_Rings_Olinordered__semidom(U_2412) ),
inference(clausify,[status(thm)],[f_828_3]) ).
fof(f_829_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_829_2,plain,
! [U_2416] :
( c_Orderings_Oord__class_Oless(U_2416,c_Groups_Ozero__class_Ozero(U_2416),c_Groups_Oplus__class_Oplus(U_2416,c_Groups_Oone__class_Oone(U_2416),c_Groups_Oone__class_Oone(U_2416)))
| ~ class_Rings_Olinordered__semidom(U_2416) ),
inference(variable_rename,[status(thm)],[f_829_1]) ).
fof(f_829_3,plain,
! [U_2416] :
( c_Orderings_Oord__class_Oless(U_2416,c_Groups_Ozero__class_Ozero(U_2416),c_Groups_Oplus__class_Oplus(U_2416,c_Groups_Oone__class_Oone(U_2416),c_Groups_Oone__class_Oone(U_2416)))
| ~ class_Rings_Olinordered__semidom(U_2416) ),
inference(definitional_conversion,[status(esa)],[f_829_2]) ).
cnf(f_829_4,plain,
( c_Orderings_Oord__class_Oless(U_2416,c_Groups_Ozero__class_Ozero(U_2416),c_Groups_Oplus__class_Oplus(U_2416,c_Groups_Oone__class_Oone(U_2416),c_Groups_Oone__class_Oone(U_2416)))
| ~ class_Rings_Olinordered__semidom(U_2416) ),
inference(clausify,[status(thm)],[f_829_3]) ).
fof(f_830_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_830_2,plain,
! [U_2419,U_2418,U_2417] :
( c_Orderings_Oord__class_Oless__eq(U_2417,c_Groups_Ozero__class_Ozero(U_2417),c_Rings_Oinverse__class_Odivide(U_2417,U_2418,U_2419))
| ~ c_Orderings_Oord__class_Oless(U_2417,c_Groups_Ozero__class_Ozero(U_2417),U_2419)
| ~ c_Orderings_Oord__class_Oless__eq(U_2417,c_Groups_Ozero__class_Ozero(U_2417),U_2418)
| ~ class_Fields_Olinordered__field(U_2417) ),
inference(variable_rename,[status(thm)],[f_830_1]) ).
fof(f_830_3,plain,
! [U_2418,U_2417,U_2419] :
( c_Orderings_Oord__class_Oless__eq(U_2417,c_Groups_Ozero__class_Ozero(U_2417),c_Rings_Oinverse__class_Odivide(U_2417,U_2418,U_2419))
| ~ c_Orderings_Oord__class_Oless(U_2417,c_Groups_Ozero__class_Ozero(U_2417),U_2419)
| ~ c_Orderings_Oord__class_Oless__eq(U_2417,c_Groups_Ozero__class_Ozero(U_2417),U_2418)
| ~ class_Fields_Olinordered__field(U_2417) ),
inference(definitional_conversion,[status(esa)],[f_830_2]) ).
cnf(f_830_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2417,c_Groups_Ozero__class_Ozero(U_2417),c_Rings_Oinverse__class_Odivide(U_2417,U_2418,U_2419))
| ~ c_Orderings_Oord__class_Oless(U_2417,c_Groups_Ozero__class_Ozero(U_2417),U_2419)
| ~ c_Orderings_Oord__class_Oless__eq(U_2417,c_Groups_Ozero__class_Ozero(U_2417),U_2418)
| ~ class_Fields_Olinordered__field(U_2417) ),
inference(clausify,[status(thm)],[f_830_3]) ).
fof(f_831_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_831_2,plain,
! [U_2422,U_2421,U_2420] :
( c_Orderings_Oord__class_Oless__eq(U_2420,c_Rings_Oinverse__class_Odivide(U_2420,U_2421,U_2422),c_Groups_Ozero__class_Ozero(U_2420))
| ~ c_Orderings_Oord__class_Oless(U_2420,U_2422,c_Groups_Ozero__class_Ozero(U_2420))
| ~ c_Orderings_Oord__class_Oless__eq(U_2420,c_Groups_Ozero__class_Ozero(U_2420),U_2421)
| ~ class_Fields_Olinordered__field(U_2420) ),
inference(variable_rename,[status(thm)],[f_831_1]) ).
fof(f_831_3,plain,
! [U_2421,U_2420,U_2422] :
( c_Orderings_Oord__class_Oless__eq(U_2420,c_Rings_Oinverse__class_Odivide(U_2420,U_2421,U_2422),c_Groups_Ozero__class_Ozero(U_2420))
| ~ c_Orderings_Oord__class_Oless(U_2420,U_2422,c_Groups_Ozero__class_Ozero(U_2420))
| ~ c_Orderings_Oord__class_Oless__eq(U_2420,c_Groups_Ozero__class_Ozero(U_2420),U_2421)
| ~ class_Fields_Olinordered__field(U_2420) ),
inference(definitional_conversion,[status(esa)],[f_831_2]) ).
cnf(f_831_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2420,c_Rings_Oinverse__class_Odivide(U_2420,U_2421,U_2422),c_Groups_Ozero__class_Ozero(U_2420))
| ~ c_Orderings_Oord__class_Oless(U_2420,U_2422,c_Groups_Ozero__class_Ozero(U_2420))
| ~ c_Orderings_Oord__class_Oless__eq(U_2420,c_Groups_Ozero__class_Ozero(U_2420),U_2421)
| ~ class_Fields_Olinordered__field(U_2420) ),
inference(clausify,[status(thm)],[f_831_3]) ).
fof(f_832_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_832_2,plain,
! [U_2427,U_2426,U_2425,U_2424,U_2423] :
( c_Orderings_Oord__class_Oless(U_2423,c_Rings_Oinverse__class_Odivide(U_2423,U_2424,U_2427),c_Rings_Oinverse__class_Odivide(U_2423,U_2425,U_2426))
| ~ c_Orderings_Oord__class_Oless(U_2423,U_2426,U_2427)
| ~ c_Orderings_Oord__class_Oless(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2426)
| ~ c_Orderings_Oord__class_Oless__eq(U_2423,U_2424,U_2425)
| ~ c_Orderings_Oord__class_Oless(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2424)
| ~ class_Fields_Olinordered__field(U_2423) ),
inference(variable_rename,[status(thm)],[f_832_1]) ).
fof(f_832_3,plain,
! [U_2423,U_2424,U_2425,U_2426,U_2427] :
( c_Orderings_Oord__class_Oless(U_2423,c_Rings_Oinverse__class_Odivide(U_2423,U_2424,U_2427),c_Rings_Oinverse__class_Odivide(U_2423,U_2425,U_2426))
| ~ c_Orderings_Oord__class_Oless(U_2423,U_2426,U_2427)
| ~ c_Orderings_Oord__class_Oless(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2426)
| ~ c_Orderings_Oord__class_Oless__eq(U_2423,U_2424,U_2425)
| ~ c_Orderings_Oord__class_Oless(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2424)
| ~ class_Fields_Olinordered__field(U_2423) ),
inference(definitional_conversion,[status(esa)],[f_832_2]) ).
cnf(f_832_4,plain,
( c_Orderings_Oord__class_Oless(U_2423,c_Rings_Oinverse__class_Odivide(U_2423,U_2424,U_2427),c_Rings_Oinverse__class_Odivide(U_2423,U_2425,U_2426))
| ~ c_Orderings_Oord__class_Oless(U_2423,U_2426,U_2427)
| ~ c_Orderings_Oord__class_Oless(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2426)
| ~ c_Orderings_Oord__class_Oless__eq(U_2423,U_2424,U_2425)
| ~ c_Orderings_Oord__class_Oless(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2424)
| ~ class_Fields_Olinordered__field(U_2423) ),
inference(clausify,[status(thm)],[f_832_3]) ).
fof(f_833_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_833_2,plain,
! [U_2432,U_2431,U_2430,U_2429,U_2428] :
( c_Orderings_Oord__class_Oless(U_2428,c_Rings_Oinverse__class_Odivide(U_2428,U_2429,U_2432),c_Rings_Oinverse__class_Odivide(U_2428,U_2430,U_2431))
| ~ c_Orderings_Oord__class_Oless__eq(U_2428,U_2431,U_2432)
| ~ c_Orderings_Oord__class_Oless(U_2428,c_Groups_Ozero__class_Ozero(U_2428),U_2431)
| ~ c_Orderings_Oord__class_Oless(U_2428,U_2429,U_2430)
| ~ c_Orderings_Oord__class_Oless__eq(U_2428,c_Groups_Ozero__class_Ozero(U_2428),U_2429)
| ~ class_Fields_Olinordered__field(U_2428) ),
inference(variable_rename,[status(thm)],[f_833_1]) ).
fof(f_833_3,plain,
! [U_2432,U_2428,U_2431,U_2429,U_2430] :
( c_Orderings_Oord__class_Oless(U_2428,c_Rings_Oinverse__class_Odivide(U_2428,U_2429,U_2432),c_Rings_Oinverse__class_Odivide(U_2428,U_2430,U_2431))
| ~ c_Orderings_Oord__class_Oless__eq(U_2428,U_2431,U_2432)
| ~ c_Orderings_Oord__class_Oless(U_2428,c_Groups_Ozero__class_Ozero(U_2428),U_2431)
| ~ c_Orderings_Oord__class_Oless(U_2428,U_2429,U_2430)
| ~ c_Orderings_Oord__class_Oless__eq(U_2428,c_Groups_Ozero__class_Ozero(U_2428),U_2429)
| ~ class_Fields_Olinordered__field(U_2428) ),
inference(definitional_conversion,[status(esa)],[f_833_2]) ).
cnf(f_833_4,plain,
( c_Orderings_Oord__class_Oless(U_2428,c_Rings_Oinverse__class_Odivide(U_2428,U_2429,U_2432),c_Rings_Oinverse__class_Odivide(U_2428,U_2430,U_2431))
| ~ c_Orderings_Oord__class_Oless__eq(U_2428,U_2431,U_2432)
| ~ c_Orderings_Oord__class_Oless(U_2428,c_Groups_Ozero__class_Ozero(U_2428),U_2431)
| ~ c_Orderings_Oord__class_Oless(U_2428,U_2429,U_2430)
| ~ c_Orderings_Oord__class_Oless__eq(U_2428,c_Groups_Ozero__class_Ozero(U_2428),U_2429)
| ~ class_Fields_Olinordered__field(U_2428) ),
inference(clausify,[status(thm)],[f_833_3]) ).
fof(f_834_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_834_2,plain,
! [U_2437,U_2436,U_2435,U_2434,U_2433] :
( c_Orderings_Oord__class_Oless__eq(U_2433,c_Rings_Oinverse__class_Odivide(U_2433,U_2434,U_2437),c_Rings_Oinverse__class_Odivide(U_2433,U_2435,U_2436))
| ~ c_Orderings_Oord__class_Oless__eq(U_2433,U_2436,U_2437)
| ~ c_Orderings_Oord__class_Oless(U_2433,c_Groups_Ozero__class_Ozero(U_2433),U_2436)
| ~ c_Orderings_Oord__class_Oless__eq(U_2433,U_2434,U_2435)
| ~ c_Orderings_Oord__class_Oless__eq(U_2433,c_Groups_Ozero__class_Ozero(U_2433),U_2434)
| ~ class_Fields_Olinordered__field(U_2433) ),
inference(variable_rename,[status(thm)],[f_834_1]) ).
fof(f_834_3,plain,
! [U_2437,U_2434,U_2436,U_2433,U_2435] :
( c_Orderings_Oord__class_Oless__eq(U_2433,c_Rings_Oinverse__class_Odivide(U_2433,U_2434,U_2437),c_Rings_Oinverse__class_Odivide(U_2433,U_2435,U_2436))
| ~ c_Orderings_Oord__class_Oless__eq(U_2433,U_2436,U_2437)
| ~ c_Orderings_Oord__class_Oless(U_2433,c_Groups_Ozero__class_Ozero(U_2433),U_2436)
| ~ c_Orderings_Oord__class_Oless__eq(U_2433,U_2434,U_2435)
| ~ c_Orderings_Oord__class_Oless__eq(U_2433,c_Groups_Ozero__class_Ozero(U_2433),U_2434)
| ~ class_Fields_Olinordered__field(U_2433) ),
inference(definitional_conversion,[status(esa)],[f_834_2]) ).
cnf(f_834_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2433,c_Rings_Oinverse__class_Odivide(U_2433,U_2434,U_2437),c_Rings_Oinverse__class_Odivide(U_2433,U_2435,U_2436))
| ~ c_Orderings_Oord__class_Oless__eq(U_2433,U_2436,U_2437)
| ~ c_Orderings_Oord__class_Oless(U_2433,c_Groups_Ozero__class_Ozero(U_2433),U_2436)
| ~ c_Orderings_Oord__class_Oless__eq(U_2433,U_2434,U_2435)
| ~ c_Orderings_Oord__class_Oless__eq(U_2433,c_Groups_Ozero__class_Ozero(U_2433),U_2434)
| ~ class_Fields_Olinordered__field(U_2433) ),
inference(clausify,[status(thm)],[f_834_3]) ).
fof(f_835_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_835_2,plain,
! [U_2440,U_2439,U_2438] :
( c_Orderings_Oord__class_Oless__eq(U_2438,c_Rings_Oinverse__class_Odivide(U_2438,U_2439,U_2440),c_Groups_Ozero__class_Ozero(U_2438))
| ~ c_Orderings_Oord__class_Oless(U_2438,c_Groups_Ozero__class_Ozero(U_2438),U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(U_2438,U_2439,c_Groups_Ozero__class_Ozero(U_2438))
| ~ class_Fields_Olinordered__field(U_2438) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
fof(f_835_3,plain,
! [U_2438,U_2440,U_2439] :
( c_Orderings_Oord__class_Oless__eq(U_2438,c_Rings_Oinverse__class_Odivide(U_2438,U_2439,U_2440),c_Groups_Ozero__class_Ozero(U_2438))
| ~ c_Orderings_Oord__class_Oless(U_2438,c_Groups_Ozero__class_Ozero(U_2438),U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(U_2438,U_2439,c_Groups_Ozero__class_Ozero(U_2438))
| ~ class_Fields_Olinordered__field(U_2438) ),
inference(definitional_conversion,[status(esa)],[f_835_2]) ).
cnf(f_835_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2438,c_Rings_Oinverse__class_Odivide(U_2438,U_2439,U_2440),c_Groups_Ozero__class_Ozero(U_2438))
| ~ c_Orderings_Oord__class_Oless(U_2438,c_Groups_Ozero__class_Ozero(U_2438),U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(U_2438,U_2439,c_Groups_Ozero__class_Ozero(U_2438))
| ~ class_Fields_Olinordered__field(U_2438) ),
inference(clausify,[status(thm)],[f_835_3]) ).
fof(f_836_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_836_2,plain,
! [U_2443,U_2442,U_2441] :
( c_Orderings_Oord__class_Oless__eq(U_2441,c_Groups_Ozero__class_Ozero(U_2441),c_Rings_Oinverse__class_Odivide(U_2441,U_2442,U_2443))
| ~ c_Orderings_Oord__class_Oless(U_2441,U_2443,c_Groups_Ozero__class_Ozero(U_2441))
| ~ c_Orderings_Oord__class_Oless__eq(U_2441,U_2442,c_Groups_Ozero__class_Ozero(U_2441))
| ~ class_Fields_Olinordered__field(U_2441) ),
inference(variable_rename,[status(thm)],[f_836_1]) ).
fof(f_836_3,plain,
! [U_2442,U_2441,U_2443] :
( c_Orderings_Oord__class_Oless__eq(U_2441,c_Groups_Ozero__class_Ozero(U_2441),c_Rings_Oinverse__class_Odivide(U_2441,U_2442,U_2443))
| ~ c_Orderings_Oord__class_Oless(U_2441,U_2443,c_Groups_Ozero__class_Ozero(U_2441))
| ~ c_Orderings_Oord__class_Oless__eq(U_2441,U_2442,c_Groups_Ozero__class_Ozero(U_2441))
| ~ class_Fields_Olinordered__field(U_2441) ),
inference(definitional_conversion,[status(esa)],[f_836_2]) ).
cnf(f_836_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2441,c_Groups_Ozero__class_Ozero(U_2441),c_Rings_Oinverse__class_Odivide(U_2441,U_2442,U_2443))
| ~ c_Orderings_Oord__class_Oless(U_2441,U_2443,c_Groups_Ozero__class_Ozero(U_2441))
| ~ c_Orderings_Oord__class_Oless__eq(U_2441,U_2442,c_Groups_Ozero__class_Ozero(U_2441))
| ~ class_Fields_Olinordered__field(U_2441) ),
inference(clausify,[status(thm)],[f_836_3]) ).
fof(f_837_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff2]) ).
fof(f_837_2,plain,
! [U_2449,U_2448,U_2447,U_2446,U_2445,U_2444] :
( ( ( c_Orderings_Oord__class_Oless(U_2444,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2445),U_2446),U_2447),c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2448),U_2446),U_2449))
| ~ c_Orderings_Oord__class_Oless(U_2444,U_2447,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),c_Groups_Ominus__class_Ominus(U_2444,U_2448,U_2445)),U_2446),U_2449)) )
& ( c_Orderings_Oord__class_Oless(U_2444,U_2447,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),c_Groups_Ominus__class_Ominus(U_2444,U_2448,U_2445)),U_2446),U_2449))
| ~ c_Orderings_Oord__class_Oless(U_2444,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2445),U_2446),U_2447),c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2448),U_2446),U_2449)) ) )
| ~ class_Rings_Oordered__ring(U_2444) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
fof(f_837_3,plain,
( ! [U_2444,U_2445,U_2446,U_2447,U_2448,U_2449] :
( c_Orderings_Oord__class_Oless(U_2444,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2445),U_2446),U_2447),c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2448),U_2446),U_2449))
| ~ c_Orderings_Oord__class_Oless(U_2444,U_2447,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),c_Groups_Ominus__class_Ominus(U_2444,U_2448,U_2445)),U_2446),U_2449))
| ~ sP207(U_2444,U_2445,U_2446,U_2447,U_2448,U_2449) )
& ! [U_2444,U_2445,U_2446,U_2447,U_2448,U_2449] :
( c_Orderings_Oord__class_Oless(U_2444,U_2447,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),c_Groups_Ominus__class_Ominus(U_2444,U_2448,U_2445)),U_2446),U_2449))
| ~ c_Orderings_Oord__class_Oless(U_2444,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2445),U_2446),U_2447),c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2448),U_2446),U_2449))
| ~ sP207(U_2444,U_2445,U_2446,U_2447,U_2448,U_2449) )
& ! [U_2444,U_2445,U_2446,U_2447,U_2448,U_2449] :
( sP207(U_2444,U_2445,U_2446,U_2447,U_2448,U_2449)
| ~ class_Rings_Oordered__ring(U_2444) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_837_2]) ).
cnf(f_837_4,plain,
( sP207(U_2444,U_2445,U_2446,U_2447,U_2448,U_2449)
| ~ class_Rings_Oordered__ring(U_2444) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_5,plain,
( c_Orderings_Oord__class_Oless(U_2444,U_2447,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),c_Groups_Ominus__class_Ominus(U_2444,U_2448,U_2445)),U_2446),U_2449))
| ~ c_Orderings_Oord__class_Oless(U_2444,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2445),U_2446),U_2447),c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2448),U_2446),U_2449))
| ~ sP207(U_2444,U_2445,U_2446,U_2447,U_2448,U_2449) ),
inference(clausify,[status(thm)],[f_837_3]) ).
cnf(f_837_6,plain,
( c_Orderings_Oord__class_Oless(U_2444,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2445),U_2446),U_2447),c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),U_2448),U_2446),U_2449))
| ~ c_Orderings_Oord__class_Oless(U_2444,U_2447,c_Groups_Oplus__class_Oplus(U_2444,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2444),c_Groups_Ominus__class_Ominus(U_2444,U_2448,U_2445)),U_2446),U_2449))
| ~ sP207(U_2444,U_2445,U_2446,U_2447,U_2448,U_2449) ),
inference(clausify,[status(thm)],[f_837_3]) ).
fof(f_838_1,plain,
! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2),V_c_2),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2),V_d_2)) ) )
| ~ class_Rings_Oordered__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__add__iff1]) ).
fof(f_838_2,plain,
! [U_2455,U_2454,U_2453,U_2452,U_2451,U_2450] :
( ( ( c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2451),U_2452),U_2453),c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2454),U_2452),U_2455))
| ~ c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),c_Groups_Ominus__class_Ominus(U_2450,U_2451,U_2454)),U_2452),U_2453),U_2455) )
& ( c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),c_Groups_Ominus__class_Ominus(U_2450,U_2451,U_2454)),U_2452),U_2453),U_2455)
| ~ c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2451),U_2452),U_2453),c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2454),U_2452),U_2455)) ) )
| ~ class_Rings_Oordered__ring(U_2450) ),
inference(variable_rename,[status(thm)],[f_838_1]) ).
fof(f_838_3,plain,
( ! [U_2453,U_2454,U_2450,U_2452,U_2451,U_2455] :
( c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2451),U_2452),U_2453),c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2454),U_2452),U_2455))
| ~ c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),c_Groups_Ominus__class_Ominus(U_2450,U_2451,U_2454)),U_2452),U_2453),U_2455)
| ~ sP208(U_2453,U_2454,U_2450,U_2452,U_2451,U_2455) )
& ! [U_2453,U_2454,U_2450,U_2452,U_2451,U_2455] :
( c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),c_Groups_Ominus__class_Ominus(U_2450,U_2451,U_2454)),U_2452),U_2453),U_2455)
| ~ c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2451),U_2452),U_2453),c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2454),U_2452),U_2455))
| ~ sP208(U_2453,U_2454,U_2450,U_2452,U_2451,U_2455) )
& ! [U_2453,U_2454,U_2450,U_2452,U_2451,U_2455] :
( sP208(U_2453,U_2454,U_2450,U_2452,U_2451,U_2455)
| ~ class_Rings_Oordered__ring(U_2450) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_838_2]) ).
cnf(f_838_4,plain,
( sP208(U_2453,U_2454,U_2450,U_2452,U_2451,U_2455)
| ~ class_Rings_Oordered__ring(U_2450) ),
inference(clausify,[status(thm)],[f_838_3]) ).
cnf(f_838_5,plain,
( c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),c_Groups_Ominus__class_Ominus(U_2450,U_2451,U_2454)),U_2452),U_2453),U_2455)
| ~ c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2451),U_2452),U_2453),c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2454),U_2452),U_2455))
| ~ sP208(U_2453,U_2454,U_2450,U_2452,U_2451,U_2455) ),
inference(clausify,[status(thm)],[f_838_3]) ).
cnf(f_838_6,plain,
( c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2451),U_2452),U_2453),c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),U_2454),U_2452),U_2455))
| ~ c_Orderings_Oord__class_Oless(U_2450,c_Groups_Oplus__class_Oplus(U_2450,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2450),c_Groups_Ominus__class_Ominus(U_2450,U_2451,U_2454)),U_2452),U_2453),U_2455)
| ~ sP208(U_2453,U_2454,U_2450,U_2452,U_2451,U_2455) ),
inference(clausify,[status(thm)],[f_838_3]) ).
fof(f_839_1,plain,
! [V_c_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_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_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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_a_2,c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq]) ).
fof(f_839_2,plain,
! [U_2459,U_2458,U_2457,U_2456] :
( ( ( c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Rings_Oinverse__class_Odivide(U_2456,U_2458,U_2459))
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Groups_Ozero__class_Ozero(U_2456))
& ~ c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456)) )
| ( ~ c_Orderings_Oord__class_Oless(U_2456,U_2458,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459))
& c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459) )
| ( ~ c_Orderings_Oord__class_Oless(U_2456,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459),U_2458)
& c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Groups_Ozero__class_Ozero(U_2456))
| c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456)) )
& ( c_Orderings_Oord__class_Oless(U_2456,U_2458,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459))
| ~ c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456)) ) )
| c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459) )
& ( c_Orderings_Oord__class_Oless(U_2456,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459),U_2458)
| ~ c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459) ) )
| ~ c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Rings_Oinverse__class_Odivide(U_2456,U_2458,U_2459)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_2456) ),
inference(variable_rename,[status(thm)],[f_839_1]) ).
fof(f_839_3,plain,
( ! [U_2456,U_2457,U_2459] :
( ~ c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP213(U_2456,U_2457,U_2459) )
& ! [U_2456,U_2457,U_2459] :
( ~ c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP213(U_2456,U_2457,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( ~ c_Orderings_Oord__class_Oless(U_2456,U_2458,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459))
| ~ sP212(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP212(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( sP213(U_2456,U_2457,U_2459)
| sP212(U_2456,U_2457,U_2458,U_2459)
| ~ sP214(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( ~ c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459)
| ~ sP214(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( ~ c_Orderings_Oord__class_Oless(U_2456,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459),U_2458)
| ~ sP211(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459)
| ~ sP211(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Groups_Ozero__class_Ozero(U_2456))
| c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP209(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( c_Orderings_Oord__class_Oless(U_2456,U_2458,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459))
| ~ c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP209(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( sP209(U_2456,U_2457,U_2458,U_2459)
| c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459)
| ~ sP210(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( c_Orderings_Oord__class_Oless(U_2456,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459),U_2458)
| ~ c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459)
| ~ sP210(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Rings_Oinverse__class_Odivide(U_2456,U_2458,U_2459))
| sP214(U_2456,U_2457,U_2458,U_2459)
| sP211(U_2456,U_2457,U_2458,U_2459)
| ~ sP215(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( sP210(U_2456,U_2457,U_2458,U_2459)
| ~ c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Rings_Oinverse__class_Odivide(U_2456,U_2458,U_2459))
| ~ sP215(U_2456,U_2457,U_2458,U_2459) )
& ! [U_2456,U_2457,U_2458,U_2459] :
( sP215(U_2456,U_2457,U_2458,U_2459)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2456) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209,sP210,sP211,sP212,sP213,sP214,sP215])],[f_839_2]) ).
cnf(f_839_4,plain,
( sP215(U_2456,U_2457,U_2458,U_2459)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2456) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_5,plain,
( sP210(U_2456,U_2457,U_2458,U_2459)
| ~ c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Rings_Oinverse__class_Odivide(U_2456,U_2458,U_2459))
| ~ sP215(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_6,plain,
( c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Rings_Oinverse__class_Odivide(U_2456,U_2458,U_2459))
| sP214(U_2456,U_2457,U_2458,U_2459)
| sP211(U_2456,U_2457,U_2458,U_2459)
| ~ sP215(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_7,plain,
( c_Orderings_Oord__class_Oless(U_2456,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459),U_2458)
| ~ c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459)
| ~ sP210(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_8,plain,
( sP209(U_2456,U_2457,U_2458,U_2459)
| c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459)
| ~ sP210(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_9,plain,
( c_Orderings_Oord__class_Oless(U_2456,U_2458,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459))
| ~ c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP209(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_10,plain,
( c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Groups_Ozero__class_Ozero(U_2456))
| c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP209(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_11,plain,
( c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459)
| ~ sP211(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_2456,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459),U_2458)
| ~ sP211(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2456,c_Groups_Ozero__class_Ozero(U_2456),U_2459)
| ~ sP214(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_14,plain,
( sP213(U_2456,U_2457,U_2459)
| sP212(U_2456,U_2457,U_2458,U_2459)
| ~ sP214(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_15,plain,
( c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP212(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_16,plain,
( ~ c_Orderings_Oord__class_Oless(U_2456,U_2458,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2456),U_2457),U_2459))
| ~ sP212(U_2456,U_2457,U_2458,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2456,U_2459,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP213(U_2456,U_2457,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
cnf(f_839_18,plain,
( ~ c_Orderings_Oord__class_Oless(U_2456,U_2457,c_Groups_Ozero__class_Ozero(U_2456))
| ~ sP213(U_2456,U_2457,U_2459) ),
inference(clausify,[status(thm)],[f_839_3]) ).
fof(f_840_1,plain,
! [V_a_2,V_c_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_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,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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_Ozero__class_Ozero(T_a),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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq]) ).
fof(f_840_2,plain,
! [U_2463,U_2462,U_2461,U_2460] :
( ( ( c_Orderings_Oord__class_Oless(U_2460,c_Rings_Oinverse__class_Odivide(U_2460,U_2461,U_2462),U_2463)
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2463)
& ~ c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460)) )
| ( ~ c_Orderings_Oord__class_Oless(U_2460,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462),U_2461)
& c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462) )
| ( ~ c_Orderings_Oord__class_Oless(U_2460,U_2461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462))
& c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2463)
| c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460)) )
& ( c_Orderings_Oord__class_Oless(U_2460,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462),U_2461)
| ~ c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460)) ) )
| c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462) )
& ( c_Orderings_Oord__class_Oless(U_2460,U_2461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462))
| ~ c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462) ) )
| ~ c_Orderings_Oord__class_Oless(U_2460,c_Rings_Oinverse__class_Odivide(U_2460,U_2461,U_2462),U_2463) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_2460) ),
inference(variable_rename,[status(thm)],[f_840_1]) ).
fof(f_840_3,plain,
( ! [U_2462,U_2460,U_2463] :
( ~ c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2463)
| ~ sP220(U_2462,U_2460,U_2463) )
& ! [U_2462,U_2460,U_2463] :
( ~ c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460))
| ~ sP220(U_2462,U_2460,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( ~ c_Orderings_Oord__class_Oless(U_2460,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462),U_2461)
| ~ sP219(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460))
| ~ sP219(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( sP220(U_2462,U_2460,U_2463)
| sP219(U_2462,U_2460,U_2461,U_2463)
| ~ sP221(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( ~ c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462)
| ~ sP221(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( ~ c_Orderings_Oord__class_Oless(U_2460,U_2461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462))
| ~ sP218(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462)
| ~ sP218(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2463)
| c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460))
| ~ sP216(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( c_Orderings_Oord__class_Oless(U_2460,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462),U_2461)
| ~ c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460))
| ~ sP216(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( sP216(U_2462,U_2460,U_2461,U_2463)
| c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462)
| ~ sP217(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( c_Orderings_Oord__class_Oless(U_2460,U_2461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462))
| ~ c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462)
| ~ sP217(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( c_Orderings_Oord__class_Oless(U_2460,c_Rings_Oinverse__class_Odivide(U_2460,U_2461,U_2462),U_2463)
| sP221(U_2462,U_2460,U_2461,U_2463)
| sP218(U_2462,U_2460,U_2461,U_2463)
| ~ sP222(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( sP217(U_2462,U_2460,U_2461,U_2463)
| ~ c_Orderings_Oord__class_Oless(U_2460,c_Rings_Oinverse__class_Odivide(U_2460,U_2461,U_2462),U_2463)
| ~ sP222(U_2462,U_2460,U_2461,U_2463) )
& ! [U_2462,U_2460,U_2461,U_2463] :
( sP222(U_2462,U_2460,U_2461,U_2463)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2460) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216,sP217,sP218,sP219,sP220,sP221,sP222])],[f_840_2]) ).
cnf(f_840_4,plain,
( sP222(U_2462,U_2460,U_2461,U_2463)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2460) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_5,plain,
( sP217(U_2462,U_2460,U_2461,U_2463)
| ~ c_Orderings_Oord__class_Oless(U_2460,c_Rings_Oinverse__class_Odivide(U_2460,U_2461,U_2462),U_2463)
| ~ sP222(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_6,plain,
( c_Orderings_Oord__class_Oless(U_2460,c_Rings_Oinverse__class_Odivide(U_2460,U_2461,U_2462),U_2463)
| sP221(U_2462,U_2460,U_2461,U_2463)
| sP218(U_2462,U_2460,U_2461,U_2463)
| ~ sP222(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_7,plain,
( c_Orderings_Oord__class_Oless(U_2460,U_2461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462))
| ~ c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462)
| ~ sP217(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_8,plain,
( sP216(U_2462,U_2460,U_2461,U_2463)
| c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462)
| ~ sP217(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_9,plain,
( c_Orderings_Oord__class_Oless(U_2460,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462),U_2461)
| ~ c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460))
| ~ sP216(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_10,plain,
( c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2463)
| c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460))
| ~ sP216(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_11,plain,
( c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462)
| ~ sP218(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_2460,U_2461,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462))
| ~ sP218(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2462)
| ~ sP221(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_14,plain,
( sP220(U_2462,U_2460,U_2463)
| sP219(U_2462,U_2460,U_2461,U_2463)
| ~ sP221(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_15,plain,
( c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460))
| ~ sP219(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_16,plain,
( ~ c_Orderings_Oord__class_Oless(U_2460,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2460),U_2463),U_2462),U_2461)
| ~ sP219(U_2462,U_2460,U_2461,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2460,U_2462,c_Groups_Ozero__class_Ozero(U_2460))
| ~ sP220(U_2462,U_2460,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
cnf(f_840_18,plain,
( ~ c_Orderings_Oord__class_Oless(U_2460,c_Groups_Ozero__class_Ozero(U_2460),U_2463)
| ~ sP220(U_2462,U_2460,U_2463) ),
inference(clausify,[status(thm)],[f_840_3]) ).
fof(f_841_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__less__divide__eq]) ).
fof(f_841_2,plain,
! [U_2467,U_2466,U_2465,U_2464] :
( ( ( c_Orderings_Oord__class_Oless(U_2464,U_2466,c_Rings_Oinverse__class_Odivide(U_2464,U_2467,U_2465))
| ~ c_Orderings_Oord__class_Oless(U_2464,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2464),U_2466),U_2465),U_2467) )
& ( c_Orderings_Oord__class_Oless(U_2464,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2464),U_2466),U_2465),U_2467)
| ~ c_Orderings_Oord__class_Oless(U_2464,U_2466,c_Rings_Oinverse__class_Odivide(U_2464,U_2467,U_2465)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2464,c_Groups_Ozero__class_Ozero(U_2464),U_2465)
| ~ class_Fields_Olinordered__field(U_2464) ),
inference(variable_rename,[status(thm)],[f_841_1]) ).
fof(f_841_3,plain,
( ! [U_2466,U_2467,U_2465,U_2464] :
( c_Orderings_Oord__class_Oless(U_2464,U_2466,c_Rings_Oinverse__class_Odivide(U_2464,U_2467,U_2465))
| ~ c_Orderings_Oord__class_Oless(U_2464,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2464),U_2466),U_2465),U_2467)
| ~ sP223(U_2466,U_2467,U_2465,U_2464) )
& ! [U_2466,U_2467,U_2465,U_2464] :
( c_Orderings_Oord__class_Oless(U_2464,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2464),U_2466),U_2465),U_2467)
| ~ c_Orderings_Oord__class_Oless(U_2464,U_2466,c_Rings_Oinverse__class_Odivide(U_2464,U_2467,U_2465))
| ~ sP223(U_2466,U_2467,U_2465,U_2464) )
& ! [U_2466,U_2467,U_2465,U_2464] :
( sP223(U_2466,U_2467,U_2465,U_2464)
| ~ c_Orderings_Oord__class_Oless(U_2464,c_Groups_Ozero__class_Ozero(U_2464),U_2465)
| ~ class_Fields_Olinordered__field(U_2464) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223])],[f_841_2]) ).
cnf(f_841_4,plain,
( sP223(U_2466,U_2467,U_2465,U_2464)
| ~ c_Orderings_Oord__class_Oless(U_2464,c_Groups_Ozero__class_Ozero(U_2464),U_2465)
| ~ class_Fields_Olinordered__field(U_2464) ),
inference(clausify,[status(thm)],[f_841_3]) ).
cnf(f_841_5,plain,
( c_Orderings_Oord__class_Oless(U_2464,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2464),U_2466),U_2465),U_2467)
| ~ c_Orderings_Oord__class_Oless(U_2464,U_2466,c_Rings_Oinverse__class_Odivide(U_2464,U_2467,U_2465))
| ~ sP223(U_2466,U_2467,U_2465,U_2464) ),
inference(clausify,[status(thm)],[f_841_3]) ).
cnf(f_841_6,plain,
( c_Orderings_Oord__class_Oless(U_2464,U_2466,c_Rings_Oinverse__class_Odivide(U_2464,U_2467,U_2465))
| ~ c_Orderings_Oord__class_Oless(U_2464,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2464),U_2466),U_2465),U_2467)
| ~ sP223(U_2466,U_2467,U_2465,U_2464) ),
inference(clausify,[status(thm)],[f_841_3]) ).
fof(f_842_1,plain,
! [V_a_2,V_b_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__less__eq]) ).
fof(f_842_2,plain,
! [U_2471,U_2470,U_2469,U_2468] :
( ( ( c_Orderings_Oord__class_Oless(U_2468,c_Rings_Oinverse__class_Odivide(U_2468,U_2470,U_2469),U_2471)
| ~ c_Orderings_Oord__class_Oless(U_2468,U_2470,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2468),U_2471),U_2469)) )
& ( c_Orderings_Oord__class_Oless(U_2468,U_2470,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2468),U_2471),U_2469))
| ~ c_Orderings_Oord__class_Oless(U_2468,c_Rings_Oinverse__class_Odivide(U_2468,U_2470,U_2469),U_2471) ) )
| ~ c_Orderings_Oord__class_Oless(U_2468,c_Groups_Ozero__class_Ozero(U_2468),U_2469)
| ~ class_Fields_Olinordered__field(U_2468) ),
inference(variable_rename,[status(thm)],[f_842_1]) ).
fof(f_842_3,plain,
( ! [U_2469,U_2470,U_2468,U_2471] :
( c_Orderings_Oord__class_Oless(U_2468,c_Rings_Oinverse__class_Odivide(U_2468,U_2470,U_2469),U_2471)
| ~ c_Orderings_Oord__class_Oless(U_2468,U_2470,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2468),U_2471),U_2469))
| ~ sP224(U_2469,U_2470,U_2468,U_2471) )
& ! [U_2469,U_2470,U_2468,U_2471] :
( c_Orderings_Oord__class_Oless(U_2468,U_2470,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2468),U_2471),U_2469))
| ~ c_Orderings_Oord__class_Oless(U_2468,c_Rings_Oinverse__class_Odivide(U_2468,U_2470,U_2469),U_2471)
| ~ sP224(U_2469,U_2470,U_2468,U_2471) )
& ! [U_2469,U_2470,U_2468,U_2471] :
( sP224(U_2469,U_2470,U_2468,U_2471)
| ~ c_Orderings_Oord__class_Oless(U_2468,c_Groups_Ozero__class_Ozero(U_2468),U_2469)
| ~ class_Fields_Olinordered__field(U_2468) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224])],[f_842_2]) ).
cnf(f_842_4,plain,
( sP224(U_2469,U_2470,U_2468,U_2471)
| ~ c_Orderings_Oord__class_Oless(U_2468,c_Groups_Ozero__class_Ozero(U_2468),U_2469)
| ~ class_Fields_Olinordered__field(U_2468) ),
inference(clausify,[status(thm)],[f_842_3]) ).
cnf(f_842_5,plain,
( c_Orderings_Oord__class_Oless(U_2468,U_2470,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2468),U_2471),U_2469))
| ~ c_Orderings_Oord__class_Oless(U_2468,c_Rings_Oinverse__class_Odivide(U_2468,U_2470,U_2469),U_2471)
| ~ sP224(U_2469,U_2470,U_2468,U_2471) ),
inference(clausify,[status(thm)],[f_842_3]) ).
cnf(f_842_6,plain,
( c_Orderings_Oord__class_Oless(U_2468,c_Rings_Oinverse__class_Odivide(U_2468,U_2470,U_2469),U_2471)
| ~ c_Orderings_Oord__class_Oless(U_2468,U_2470,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2468),U_2471),U_2469))
| ~ sP224(U_2469,U_2470,U_2468,U_2471) ),
inference(clausify,[status(thm)],[f_842_3]) ).
fof(f_843_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__less]) ).
fof(f_843_2,plain,
! [U_2475,U_2474,U_2473,U_2472] :
( c_Orderings_Oord__class_Oless(U_2472,c_Rings_Oinverse__class_Odivide(U_2472,U_2474,U_2473),U_2475)
| ~ c_Orderings_Oord__class_Oless(U_2472,U_2474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2472),U_2475),U_2473))
| ~ c_Orderings_Oord__class_Oless(U_2472,c_Groups_Ozero__class_Ozero(U_2472),U_2473)
| ~ class_Fields_Olinordered__field(U_2472) ),
inference(variable_rename,[status(thm)],[f_843_1]) ).
fof(f_843_3,plain,
! [U_2472,U_2473,U_2475,U_2474] :
( c_Orderings_Oord__class_Oless(U_2472,c_Rings_Oinverse__class_Odivide(U_2472,U_2474,U_2473),U_2475)
| ~ c_Orderings_Oord__class_Oless(U_2472,U_2474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2472),U_2475),U_2473))
| ~ c_Orderings_Oord__class_Oless(U_2472,c_Groups_Ozero__class_Ozero(U_2472),U_2473)
| ~ class_Fields_Olinordered__field(U_2472) ),
inference(definitional_conversion,[status(esa)],[f_843_2]) ).
cnf(f_843_4,plain,
( c_Orderings_Oord__class_Oless(U_2472,c_Rings_Oinverse__class_Odivide(U_2472,U_2474,U_2473),U_2475)
| ~ c_Orderings_Oord__class_Oless(U_2472,U_2474,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2472),U_2475),U_2473))
| ~ c_Orderings_Oord__class_Oless(U_2472,c_Groups_Ozero__class_Ozero(U_2472),U_2473)
| ~ class_Fields_Olinordered__field(U_2472) ),
inference(clausify,[status(thm)],[f_843_3]) ).
fof(f_844_1,plain,
! [V_x,V_z,V_y,T_a] :
( c_Orderings_Oord__class_Oless(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__less__div__pos]) ).
fof(f_844_2,plain,
! [U_2479,U_2478,U_2477,U_2476] :
( c_Orderings_Oord__class_Oless(U_2476,U_2478,c_Rings_Oinverse__class_Odivide(U_2476,U_2479,U_2477))
| ~ c_Orderings_Oord__class_Oless(U_2476,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2476),U_2478),U_2477),U_2479)
| ~ c_Orderings_Oord__class_Oless(U_2476,c_Groups_Ozero__class_Ozero(U_2476),U_2477)
| ~ class_Fields_Olinordered__field(U_2476) ),
inference(variable_rename,[status(thm)],[f_844_1]) ).
fof(f_844_3,plain,
! [U_2476,U_2477,U_2478,U_2479] :
( c_Orderings_Oord__class_Oless(U_2476,U_2478,c_Rings_Oinverse__class_Odivide(U_2476,U_2479,U_2477))
| ~ c_Orderings_Oord__class_Oless(U_2476,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2476),U_2478),U_2477),U_2479)
| ~ c_Orderings_Oord__class_Oless(U_2476,c_Groups_Ozero__class_Ozero(U_2476),U_2477)
| ~ class_Fields_Olinordered__field(U_2476) ),
inference(definitional_conversion,[status(esa)],[f_844_2]) ).
cnf(f_844_4,plain,
( c_Orderings_Oord__class_Oless(U_2476,U_2478,c_Rings_Oinverse__class_Odivide(U_2476,U_2479,U_2477))
| ~ c_Orderings_Oord__class_Oless(U_2476,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2476),U_2478),U_2477),U_2479)
| ~ c_Orderings_Oord__class_Oless(U_2476,c_Groups_Ozero__class_Ozero(U_2476),U_2477)
| ~ class_Fields_Olinordered__field(U_2476) ),
inference(clausify,[status(thm)],[f_844_3]) ).
fof(f_845_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__divide__eq]) ).
fof(f_845_2,plain,
! [U_2483,U_2482,U_2481,U_2480] :
( ( ( c_Orderings_Oord__class_Oless(U_2480,U_2482,c_Rings_Oinverse__class_Odivide(U_2480,U_2483,U_2481))
| ~ c_Orderings_Oord__class_Oless(U_2480,U_2483,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2480),U_2482),U_2481)) )
& ( c_Orderings_Oord__class_Oless(U_2480,U_2483,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2480),U_2482),U_2481))
| ~ c_Orderings_Oord__class_Oless(U_2480,U_2482,c_Rings_Oinverse__class_Odivide(U_2480,U_2483,U_2481)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2480,U_2481,c_Groups_Ozero__class_Ozero(U_2480))
| ~ class_Fields_Olinordered__field(U_2480) ),
inference(variable_rename,[status(thm)],[f_845_1]) ).
fof(f_845_3,plain,
( ! [U_2483,U_2480,U_2481,U_2482] :
( c_Orderings_Oord__class_Oless(U_2480,U_2482,c_Rings_Oinverse__class_Odivide(U_2480,U_2483,U_2481))
| ~ c_Orderings_Oord__class_Oless(U_2480,U_2483,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2480),U_2482),U_2481))
| ~ sP225(U_2483,U_2480,U_2481,U_2482) )
& ! [U_2483,U_2480,U_2481,U_2482] :
( c_Orderings_Oord__class_Oless(U_2480,U_2483,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2480),U_2482),U_2481))
| ~ c_Orderings_Oord__class_Oless(U_2480,U_2482,c_Rings_Oinverse__class_Odivide(U_2480,U_2483,U_2481))
| ~ sP225(U_2483,U_2480,U_2481,U_2482) )
& ! [U_2483,U_2480,U_2481,U_2482] :
( sP225(U_2483,U_2480,U_2481,U_2482)
| ~ c_Orderings_Oord__class_Oless(U_2480,U_2481,c_Groups_Ozero__class_Ozero(U_2480))
| ~ class_Fields_Olinordered__field(U_2480) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225])],[f_845_2]) ).
cnf(f_845_4,plain,
( sP225(U_2483,U_2480,U_2481,U_2482)
| ~ c_Orderings_Oord__class_Oless(U_2480,U_2481,c_Groups_Ozero__class_Ozero(U_2480))
| ~ class_Fields_Olinordered__field(U_2480) ),
inference(clausify,[status(thm)],[f_845_3]) ).
cnf(f_845_5,plain,
( c_Orderings_Oord__class_Oless(U_2480,U_2483,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2480),U_2482),U_2481))
| ~ c_Orderings_Oord__class_Oless(U_2480,U_2482,c_Rings_Oinverse__class_Odivide(U_2480,U_2483,U_2481))
| ~ sP225(U_2483,U_2480,U_2481,U_2482) ),
inference(clausify,[status(thm)],[f_845_3]) ).
cnf(f_845_6,plain,
( c_Orderings_Oord__class_Oless(U_2480,U_2482,c_Rings_Oinverse__class_Odivide(U_2480,U_2483,U_2481))
| ~ c_Orderings_Oord__class_Oless(U_2480,U_2483,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2480),U_2482),U_2481))
| ~ sP225(U_2483,U_2480,U_2481,U_2482) ),
inference(clausify,[status(thm)],[f_845_3]) ).
fof(f_846_1,plain,
! [V_a_2,V_b_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__less__eq]) ).
fof(f_846_2,plain,
! [U_2487,U_2486,U_2485,U_2484] :
( ( ( c_Orderings_Oord__class_Oless(U_2484,c_Rings_Oinverse__class_Odivide(U_2484,U_2486,U_2485),U_2487)
| ~ c_Orderings_Oord__class_Oless(U_2484,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2487),U_2485),U_2486) )
& ( c_Orderings_Oord__class_Oless(U_2484,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2487),U_2485),U_2486)
| ~ c_Orderings_Oord__class_Oless(U_2484,c_Rings_Oinverse__class_Odivide(U_2484,U_2486,U_2485),U_2487) ) )
| ~ c_Orderings_Oord__class_Oless(U_2484,U_2485,c_Groups_Ozero__class_Ozero(U_2484))
| ~ class_Fields_Olinordered__field(U_2484) ),
inference(variable_rename,[status(thm)],[f_846_1]) ).
fof(f_846_3,plain,
( ! [U_2485,U_2487,U_2486,U_2484] :
( c_Orderings_Oord__class_Oless(U_2484,c_Rings_Oinverse__class_Odivide(U_2484,U_2486,U_2485),U_2487)
| ~ c_Orderings_Oord__class_Oless(U_2484,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2487),U_2485),U_2486)
| ~ sP226(U_2485,U_2487,U_2486,U_2484) )
& ! [U_2485,U_2487,U_2486,U_2484] :
( c_Orderings_Oord__class_Oless(U_2484,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2487),U_2485),U_2486)
| ~ c_Orderings_Oord__class_Oless(U_2484,c_Rings_Oinverse__class_Odivide(U_2484,U_2486,U_2485),U_2487)
| ~ sP226(U_2485,U_2487,U_2486,U_2484) )
& ! [U_2485,U_2487,U_2486,U_2484] :
( sP226(U_2485,U_2487,U_2486,U_2484)
| ~ c_Orderings_Oord__class_Oless(U_2484,U_2485,c_Groups_Ozero__class_Ozero(U_2484))
| ~ class_Fields_Olinordered__field(U_2484) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_846_2]) ).
cnf(f_846_4,plain,
( sP226(U_2485,U_2487,U_2486,U_2484)
| ~ c_Orderings_Oord__class_Oless(U_2484,U_2485,c_Groups_Ozero__class_Ozero(U_2484))
| ~ class_Fields_Olinordered__field(U_2484) ),
inference(clausify,[status(thm)],[f_846_3]) ).
cnf(f_846_5,plain,
( c_Orderings_Oord__class_Oless(U_2484,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2487),U_2485),U_2486)
| ~ c_Orderings_Oord__class_Oless(U_2484,c_Rings_Oinverse__class_Odivide(U_2484,U_2486,U_2485),U_2487)
| ~ sP226(U_2485,U_2487,U_2486,U_2484) ),
inference(clausify,[status(thm)],[f_846_3]) ).
cnf(f_846_6,plain,
( c_Orderings_Oord__class_Oless(U_2484,c_Rings_Oinverse__class_Odivide(U_2484,U_2486,U_2485),U_2487)
| ~ c_Orderings_Oord__class_Oless(U_2484,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2484),U_2487),U_2485),U_2486)
| ~ sP226(U_2485,U_2487,U_2486,U_2484) ),
inference(clausify,[status(thm)],[f_846_3]) ).
fof(f_847_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_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_c)
| ~ 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__left__mono]) ).
fof(f_847_2,plain,
! [U_2491,U_2490,U_2489,U_2488] :
( c_Orderings_Oord__class_Oless(U_2488,c_Rings_Oinverse__class_Odivide(U_2488,U_2491,U_2490),c_Rings_Oinverse__class_Odivide(U_2488,U_2491,U_2489))
| ~ c_Orderings_Oord__class_Oless(U_2488,c_Groups_Ozero__class_Ozero(U_2488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2488),U_2490),U_2489))
| ~ c_Orderings_Oord__class_Oless(U_2488,c_Groups_Ozero__class_Ozero(U_2488),U_2491)
| ~ c_Orderings_Oord__class_Oless(U_2488,U_2489,U_2490)
| ~ class_Fields_Olinordered__field(U_2488) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
fof(f_847_3,plain,
! [U_2490,U_2491,U_2488,U_2489] :
( c_Orderings_Oord__class_Oless(U_2488,c_Rings_Oinverse__class_Odivide(U_2488,U_2491,U_2490),c_Rings_Oinverse__class_Odivide(U_2488,U_2491,U_2489))
| ~ c_Orderings_Oord__class_Oless(U_2488,c_Groups_Ozero__class_Ozero(U_2488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2488),U_2490),U_2489))
| ~ c_Orderings_Oord__class_Oless(U_2488,c_Groups_Ozero__class_Ozero(U_2488),U_2491)
| ~ c_Orderings_Oord__class_Oless(U_2488,U_2489,U_2490)
| ~ class_Fields_Olinordered__field(U_2488) ),
inference(definitional_conversion,[status(esa)],[f_847_2]) ).
cnf(f_847_4,plain,
( c_Orderings_Oord__class_Oless(U_2488,c_Rings_Oinverse__class_Odivide(U_2488,U_2491,U_2490),c_Rings_Oinverse__class_Odivide(U_2488,U_2491,U_2489))
| ~ c_Orderings_Oord__class_Oless(U_2488,c_Groups_Ozero__class_Ozero(U_2488),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2488),U_2490),U_2489))
| ~ c_Orderings_Oord__class_Oless(U_2488,c_Groups_Ozero__class_Ozero(U_2488),U_2491)
| ~ c_Orderings_Oord__class_Oless(U_2488,U_2489,U_2490)
| ~ class_Fields_Olinordered__field(U_2488) ),
inference(clausify,[status(thm)],[f_847_3]) ).
fof(f_848_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_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),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_a,V_b)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__strict__left__mono__neg]) ).
fof(f_848_2,plain,
! [U_2495,U_2494,U_2493,U_2492] :
( c_Orderings_Oord__class_Oless(U_2492,c_Rings_Oinverse__class_Odivide(U_2492,U_2495,U_2493),c_Rings_Oinverse__class_Odivide(U_2492,U_2495,U_2494))
| ~ c_Orderings_Oord__class_Oless(U_2492,c_Groups_Ozero__class_Ozero(U_2492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2492),U_2493),U_2494))
| ~ c_Orderings_Oord__class_Oless(U_2492,U_2495,c_Groups_Ozero__class_Ozero(U_2492))
| ~ c_Orderings_Oord__class_Oless(U_2492,U_2493,U_2494)
| ~ class_Fields_Olinordered__field(U_2492) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
fof(f_848_3,plain,
! [U_2493,U_2494,U_2492,U_2495] :
( c_Orderings_Oord__class_Oless(U_2492,c_Rings_Oinverse__class_Odivide(U_2492,U_2495,U_2493),c_Rings_Oinverse__class_Odivide(U_2492,U_2495,U_2494))
| ~ c_Orderings_Oord__class_Oless(U_2492,c_Groups_Ozero__class_Ozero(U_2492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2492),U_2493),U_2494))
| ~ c_Orderings_Oord__class_Oless(U_2492,U_2495,c_Groups_Ozero__class_Ozero(U_2492))
| ~ c_Orderings_Oord__class_Oless(U_2492,U_2493,U_2494)
| ~ class_Fields_Olinordered__field(U_2492) ),
inference(definitional_conversion,[status(esa)],[f_848_2]) ).
cnf(f_848_4,plain,
( c_Orderings_Oord__class_Oless(U_2492,c_Rings_Oinverse__class_Odivide(U_2492,U_2495,U_2493),c_Rings_Oinverse__class_Odivide(U_2492,U_2495,U_2494))
| ~ c_Orderings_Oord__class_Oless(U_2492,c_Groups_Ozero__class_Ozero(U_2492),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2492),U_2493),U_2494))
| ~ c_Orderings_Oord__class_Oless(U_2492,U_2495,c_Groups_Ozero__class_Ozero(U_2492))
| ~ c_Orderings_Oord__class_Oless(U_2492,U_2493,U_2494)
| ~ class_Fields_Olinordered__field(U_2492) ),
inference(clausify,[status(thm)],[f_848_3]) ).
fof(f_849_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(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__gt1__lemma]) ).
fof(f_849_2,plain,
! [U_2498,U_2497,U_2496] :
( c_Orderings_Oord__class_Oless(U_2496,c_Groups_Oone__class_Oone(U_2496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2496),U_2497),hAPP(hAPP(c_Power_Opower__class_Opower(U_2496),U_2497),U_2498)))
| ~ c_Orderings_Oord__class_Oless(U_2496,c_Groups_Oone__class_Oone(U_2496),U_2497)
| ~ class_Rings_Olinordered__semidom(U_2496) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
fof(f_849_3,plain,
! [U_2497,U_2498,U_2496] :
( c_Orderings_Oord__class_Oless(U_2496,c_Groups_Oone__class_Oone(U_2496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2496),U_2497),hAPP(hAPP(c_Power_Opower__class_Opower(U_2496),U_2497),U_2498)))
| ~ c_Orderings_Oord__class_Oless(U_2496,c_Groups_Oone__class_Oone(U_2496),U_2497)
| ~ class_Rings_Olinordered__semidom(U_2496) ),
inference(definitional_conversion,[status(esa)],[f_849_2]) ).
cnf(f_849_4,plain,
( c_Orderings_Oord__class_Oless(U_2496,c_Groups_Oone__class_Oone(U_2496),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2496),U_2497),hAPP(hAPP(c_Power_Opower__class_Opower(U_2496),U_2497),U_2498)))
| ~ c_Orderings_Oord__class_Oless(U_2496,c_Groups_Oone__class_Oone(U_2496),U_2497)
| ~ class_Rings_Olinordered__semidom(U_2496) ),
inference(clausify,[status(thm)],[f_849_3]) ).
fof(f_850_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(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__power__Suc]) ).
fof(f_850_2,plain,
! [U_2501,U_2500,U_2499] :
( c_Orderings_Oord__class_Oless(U_2499,hAPP(hAPP(c_Power_Opower__class_Opower(U_2499),U_2500),U_2501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2500),hAPP(hAPP(c_Power_Opower__class_Opower(U_2499),U_2500),U_2501)))
| ~ c_Orderings_Oord__class_Oless(U_2499,c_Groups_Oone__class_Oone(U_2499),U_2500)
| ~ class_Rings_Olinordered__semidom(U_2499) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
fof(f_850_3,plain,
! [U_2499,U_2500,U_2501] :
( c_Orderings_Oord__class_Oless(U_2499,hAPP(hAPP(c_Power_Opower__class_Opower(U_2499),U_2500),U_2501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2500),hAPP(hAPP(c_Power_Opower__class_Opower(U_2499),U_2500),U_2501)))
| ~ c_Orderings_Oord__class_Oless(U_2499,c_Groups_Oone__class_Oone(U_2499),U_2500)
| ~ class_Rings_Olinordered__semidom(U_2499) ),
inference(definitional_conversion,[status(esa)],[f_850_2]) ).
cnf(f_850_4,plain,
( c_Orderings_Oord__class_Oless(U_2499,hAPP(hAPP(c_Power_Opower__class_Opower(U_2499),U_2500),U_2501),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2499),U_2500),hAPP(hAPP(c_Power_Opower__class_Opower(U_2499),U_2500),U_2501)))
| ~ c_Orderings_Oord__class_Oless(U_2499,c_Groups_Oone__class_Oone(U_2499),U_2500)
| ~ class_Rings_Olinordered__semidom(U_2499) ),
inference(clausify,[status(thm)],[f_850_3]) ).
fof(f_851_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_851_2,plain,
! [U_2504,U_2503,U_2502] :
( c_Orderings_Oord__class_Oless(U_2502,U_2503,c_Rings_Oinverse__class_Odivide(U_2502,c_Groups_Oplus__class_Oplus(U_2502,U_2503,U_2504),c_Groups_Oplus__class_Oplus(U_2502,c_Groups_Oone__class_Oone(U_2502),c_Groups_Oone__class_Oone(U_2502))))
| ~ c_Orderings_Oord__class_Oless(U_2502,U_2503,U_2504)
| ~ class_Fields_Olinordered__field(U_2502) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
fof(f_851_3,plain,
! [U_2503,U_2502,U_2504] :
( c_Orderings_Oord__class_Oless(U_2502,U_2503,c_Rings_Oinverse__class_Odivide(U_2502,c_Groups_Oplus__class_Oplus(U_2502,U_2503,U_2504),c_Groups_Oplus__class_Oplus(U_2502,c_Groups_Oone__class_Oone(U_2502),c_Groups_Oone__class_Oone(U_2502))))
| ~ c_Orderings_Oord__class_Oless(U_2502,U_2503,U_2504)
| ~ class_Fields_Olinordered__field(U_2502) ),
inference(definitional_conversion,[status(esa)],[f_851_2]) ).
cnf(f_851_4,plain,
( c_Orderings_Oord__class_Oless(U_2502,U_2503,c_Rings_Oinverse__class_Odivide(U_2502,c_Groups_Oplus__class_Oplus(U_2502,U_2503,U_2504),c_Groups_Oplus__class_Oplus(U_2502,c_Groups_Oone__class_Oone(U_2502),c_Groups_Oone__class_Oone(U_2502))))
| ~ c_Orderings_Oord__class_Oless(U_2502,U_2503,U_2504)
| ~ class_Fields_Olinordered__field(U_2502) ),
inference(clausify,[status(thm)],[f_851_3]) ).
fof(f_852_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_852_2,plain,
! [U_2507,U_2506,U_2505] :
( c_Orderings_Oord__class_Oless(U_2505,c_Rings_Oinverse__class_Odivide(U_2505,c_Groups_Oplus__class_Oplus(U_2505,U_2506,U_2507),c_Groups_Oplus__class_Oplus(U_2505,c_Groups_Oone__class_Oone(U_2505),c_Groups_Oone__class_Oone(U_2505))),U_2507)
| ~ c_Orderings_Oord__class_Oless(U_2505,U_2506,U_2507)
| ~ class_Fields_Olinordered__field(U_2505) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
fof(f_852_3,plain,
! [U_2506,U_2505,U_2507] :
( c_Orderings_Oord__class_Oless(U_2505,c_Rings_Oinverse__class_Odivide(U_2505,c_Groups_Oplus__class_Oplus(U_2505,U_2506,U_2507),c_Groups_Oplus__class_Oplus(U_2505,c_Groups_Oone__class_Oone(U_2505),c_Groups_Oone__class_Oone(U_2505))),U_2507)
| ~ c_Orderings_Oord__class_Oless(U_2505,U_2506,U_2507)
| ~ class_Fields_Olinordered__field(U_2505) ),
inference(definitional_conversion,[status(esa)],[f_852_2]) ).
cnf(f_852_4,plain,
( c_Orderings_Oord__class_Oless(U_2505,c_Rings_Oinverse__class_Odivide(U_2505,c_Groups_Oplus__class_Oplus(U_2505,U_2506,U_2507),c_Groups_Oplus__class_Oplus(U_2505,c_Groups_Oone__class_Oone(U_2505),c_Groups_Oone__class_Oone(U_2505))),U_2507)
| ~ c_Orderings_Oord__class_Oless(U_2505,U_2506,U_2507)
| ~ class_Fields_Olinordered__field(U_2505) ),
inference(clausify,[status(thm)],[f_852_3]) ).
fof(f_853_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),hAPP(hAPP(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_853_2,plain,
! [U_2510,U_2509,U_2508] :
( c_Orderings_Oord__class_Oless(U_2508,c_Groups_Oone__class_Oone(U_2508),hAPP(hAPP(c_Power_Opower__class_Opower(U_2508),U_2509),c_Nat_OSuc(U_2510)))
| ~ c_Orderings_Oord__class_Oless(U_2508,c_Groups_Oone__class_Oone(U_2508),U_2509)
| ~ class_Rings_Olinordered__semidom(U_2508) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
fof(f_853_3,plain,
! [U_2508,U_2509,U_2510] :
( c_Orderings_Oord__class_Oless(U_2508,c_Groups_Oone__class_Oone(U_2508),hAPP(hAPP(c_Power_Opower__class_Opower(U_2508),U_2509),c_Nat_OSuc(U_2510)))
| ~ c_Orderings_Oord__class_Oless(U_2508,c_Groups_Oone__class_Oone(U_2508),U_2509)
| ~ class_Rings_Olinordered__semidom(U_2508) ),
inference(definitional_conversion,[status(esa)],[f_853_2]) ).
cnf(f_853_4,plain,
( c_Orderings_Oord__class_Oless(U_2508,c_Groups_Oone__class_Oone(U_2508),hAPP(hAPP(c_Power_Opower__class_Opower(U_2508),U_2509),c_Nat_OSuc(U_2510)))
| ~ c_Orderings_Oord__class_Oless(U_2508,c_Groups_Oone__class_Oone(U_2508),U_2509)
| ~ class_Rings_Olinordered__semidom(U_2508) ),
inference(clausify,[status(thm)],[f_853_3]) ).
fof(f_854_1,plain,
! [V_r_2,V_a_2,V_xa_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_xa_2,V_a_2)),V_r_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_xa_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_r_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_r_2),V_xa_2) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_xa_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_r_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_r_2),V_xa_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_xa_2,V_a_2)),V_r_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff]) ).
fof(f_854_2,plain,
! [U_2514,U_2513,U_2512,U_2511] :
( ( ( c_Orderings_Oord__class_Oless(U_2511,c_Groups_Oabs__class_Oabs(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2512,U_2513)),U_2514)
| ~ c_Orderings_Oord__class_Oless(U_2511,U_2512,c_Groups_Oplus__class_Oplus(U_2511,U_2513,U_2514))
| ~ c_Orderings_Oord__class_Oless(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2513,U_2514),U_2512) )
& ( ( c_Orderings_Oord__class_Oless(U_2511,U_2512,c_Groups_Oplus__class_Oplus(U_2511,U_2513,U_2514))
& c_Orderings_Oord__class_Oless(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2513,U_2514),U_2512) )
| ~ c_Orderings_Oord__class_Oless(U_2511,c_Groups_Oabs__class_Oabs(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2512,U_2513)),U_2514) ) )
| ~ class_Rings_Olinordered__idom(U_2511) ),
inference(variable_rename,[status(thm)],[f_854_1]) ).
fof(f_854_3,plain,
( ! [U_2512,U_2511,U_2513,U_2514] :
( c_Orderings_Oord__class_Oless(U_2511,U_2512,c_Groups_Oplus__class_Oplus(U_2511,U_2513,U_2514))
| ~ sP227(U_2512,U_2511,U_2513,U_2514) )
& ! [U_2512,U_2511,U_2513,U_2514] :
( c_Orderings_Oord__class_Oless(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2513,U_2514),U_2512)
| ~ sP227(U_2512,U_2511,U_2513,U_2514) )
& ! [U_2512,U_2511,U_2513,U_2514] :
( c_Orderings_Oord__class_Oless(U_2511,c_Groups_Oabs__class_Oabs(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2512,U_2513)),U_2514)
| ~ c_Orderings_Oord__class_Oless(U_2511,U_2512,c_Groups_Oplus__class_Oplus(U_2511,U_2513,U_2514))
| ~ c_Orderings_Oord__class_Oless(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2513,U_2514),U_2512)
| ~ sP228(U_2512,U_2511,U_2513,U_2514) )
& ! [U_2512,U_2511,U_2513,U_2514] :
( sP227(U_2512,U_2511,U_2513,U_2514)
| ~ c_Orderings_Oord__class_Oless(U_2511,c_Groups_Oabs__class_Oabs(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2512,U_2513)),U_2514)
| ~ sP228(U_2512,U_2511,U_2513,U_2514) )
& ! [U_2512,U_2511,U_2513,U_2514] :
( sP228(U_2512,U_2511,U_2513,U_2514)
| ~ class_Rings_Olinordered__idom(U_2511) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227,sP228])],[f_854_2]) ).
cnf(f_854_4,plain,
( sP228(U_2512,U_2511,U_2513,U_2514)
| ~ class_Rings_Olinordered__idom(U_2511) ),
inference(clausify,[status(thm)],[f_854_3]) ).
cnf(f_854_5,plain,
( sP227(U_2512,U_2511,U_2513,U_2514)
| ~ c_Orderings_Oord__class_Oless(U_2511,c_Groups_Oabs__class_Oabs(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2512,U_2513)),U_2514)
| ~ sP228(U_2512,U_2511,U_2513,U_2514) ),
inference(clausify,[status(thm)],[f_854_3]) ).
cnf(f_854_6,plain,
( c_Orderings_Oord__class_Oless(U_2511,c_Groups_Oabs__class_Oabs(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2512,U_2513)),U_2514)
| ~ c_Orderings_Oord__class_Oless(U_2511,U_2512,c_Groups_Oplus__class_Oplus(U_2511,U_2513,U_2514))
| ~ c_Orderings_Oord__class_Oless(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2513,U_2514),U_2512)
| ~ sP228(U_2512,U_2511,U_2513,U_2514) ),
inference(clausify,[status(thm)],[f_854_3]) ).
cnf(f_854_7,plain,
( c_Orderings_Oord__class_Oless(U_2511,c_Groups_Ominus__class_Ominus(U_2511,U_2513,U_2514),U_2512)
| ~ sP227(U_2512,U_2511,U_2513,U_2514) ),
inference(clausify,[status(thm)],[f_854_3]) ).
cnf(f_854_8,plain,
( c_Orderings_Oord__class_Oless(U_2511,U_2512,c_Groups_Oplus__class_Oplus(U_2511,U_2513,U_2514))
| ~ sP227(U_2512,U_2511,U_2513,U_2514) ),
inference(clausify,[status(thm)],[f_854_3]) ).
fof(f_855_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_855_2,plain,
! [U_2517,U_2516,U_2515] :
( c_Rings_Oinverse__class_Odivide(U_2515,c_Groups_Oabs__class_Oabs(U_2515,U_2517),U_2516) = c_Groups_Oabs__class_Oabs(U_2515,c_Rings_Oinverse__class_Odivide(U_2515,U_2517,U_2516))
| ~ c_Orderings_Oord__class_Oless(U_2515,c_Groups_Ozero__class_Ozero(U_2515),U_2516)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2515) ),
inference(variable_rename,[status(thm)],[f_855_1]) ).
fof(f_855_3,plain,
! [U_2517,U_2515,U_2516] :
( c_Rings_Oinverse__class_Odivide(U_2515,c_Groups_Oabs__class_Oabs(U_2515,U_2517),U_2516) = c_Groups_Oabs__class_Oabs(U_2515,c_Rings_Oinverse__class_Odivide(U_2515,U_2517,U_2516))
| ~ c_Orderings_Oord__class_Oless(U_2515,c_Groups_Ozero__class_Ozero(U_2515),U_2516)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2515) ),
inference(definitional_conversion,[status(esa)],[f_855_2]) ).
cnf(f_855_4,plain,
( c_Rings_Oinverse__class_Odivide(U_2515,c_Groups_Oabs__class_Oabs(U_2515,U_2517),U_2516) = c_Groups_Oabs__class_Oabs(U_2515,c_Rings_Oinverse__class_Odivide(U_2515,U_2517,U_2516))
| ~ c_Orderings_Oord__class_Oless(U_2515,c_Groups_Ozero__class_Ozero(U_2515),U_2516)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2515) ),
inference(clausify,[status(thm)],[f_855_3]) ).
fof(f_856_1,plain,
! [V_xa_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_xa_2))
| V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_xa_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_xa_2)) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff]) ).
fof(f_856_2,plain,
! [U_2519,U_2518] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2518,U_2519))
| U_2519 = c_Groups_Ozero__class_Ozero(U_2518) )
& ( U_2519 != c_Groups_Ozero__class_Ozero(U_2518)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2518,U_2519)) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2518) ),
inference(variable_rename,[status(thm)],[f_856_1]) ).
fof(f_856_3,plain,
( ! [U_2518,U_2519] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2518,U_2519))
| U_2519 = c_Groups_Ozero__class_Ozero(U_2518)
| ~ sP229(U_2518,U_2519) )
& ! [U_2518,U_2519] :
( U_2519 != c_Groups_Ozero__class_Ozero(U_2518)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2518,U_2519))
| ~ sP229(U_2518,U_2519) )
& ! [U_2518,U_2519] :
( sP229(U_2518,U_2519)
| ~ class_RealVector_Oreal__normed__vector(U_2518) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_856_2]) ).
cnf(f_856_4,plain,
( sP229(U_2518,U_2519)
| ~ class_RealVector_Oreal__normed__vector(U_2518) ),
inference(clausify,[status(thm)],[f_856_3]) ).
cnf(f_856_5,plain,
( U_2519 != c_Groups_Ozero__class_Ozero(U_2518)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2518,U_2519))
| ~ sP229(U_2518,U_2519) ),
inference(clausify,[status(thm)],[f_856_3]) ).
cnf(f_856_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2518,U_2519))
| U_2519 = c_Groups_Ozero__class_Ozero(U_2518)
| ~ sP229(U_2518,U_2519) ),
inference(clausify,[status(thm)],[f_856_3]) ).
fof(f_857_1,plain,
! [V_ya_2,V_xa_2,V_za_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_2),V_za_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_xa_2),V_za_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ya_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__le__cancel__iff1]) ).
fof(f_857_2,plain,
! [U_2522,U_2521,U_2520] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2521),U_2520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2522),U_2520))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2521,U_2522) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2521,U_2522)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2521),U_2520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2522),U_2520)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2520) ),
inference(variable_rename,[status(thm)],[f_857_1]) ).
fof(f_857_3,plain,
( ! [U_2521,U_2522,U_2520] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2521),U_2520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2522),U_2520))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2521,U_2522)
| ~ sP230(U_2521,U_2522,U_2520) )
& ! [U_2521,U_2522,U_2520] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2521,U_2522)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2521),U_2520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2522),U_2520))
| ~ sP230(U_2521,U_2522,U_2520) )
& ! [U_2521,U_2522,U_2520] :
( sP230(U_2521,U_2522,U_2520)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2520) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_857_2]) ).
cnf(f_857_4,plain,
( sP230(U_2521,U_2522,U_2520)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2520) ),
inference(clausify,[status(thm)],[f_857_3]) ).
cnf(f_857_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2521,U_2522)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2521),U_2520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2522),U_2520))
| ~ sP230(U_2521,U_2522,U_2520) ),
inference(clausify,[status(thm)],[f_857_3]) ).
cnf(f_857_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2521),U_2520),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2522),U_2520))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2521,U_2522)
| ~ sP230(U_2521,U_2522,U_2520) ),
inference(clausify,[status(thm)],[f_857_3]) ).
fof(f_858_1,plain,
! [V_ya_2,V_xa_2,V_za_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_ya_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_xa_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_za_2),V_ya_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__le__cancel__iff2]) ).
fof(f_858_2,plain,
! [U_2525,U_2524,U_2523] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2525))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2524,U_2525) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2524,U_2525)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2525)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2523) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
fof(f_858_3,plain,
( ! [U_2525,U_2524,U_2523] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2525))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2524,U_2525)
| ~ sP231(U_2525,U_2524,U_2523) )
& ! [U_2525,U_2524,U_2523] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2524,U_2525)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2525))
| ~ sP231(U_2525,U_2524,U_2523) )
& ! [U_2525,U_2524,U_2523] :
( sP231(U_2525,U_2524,U_2523)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2523) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231])],[f_858_2]) ).
cnf(f_858_4,plain,
( sP231(U_2525,U_2524,U_2523)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2523) ),
inference(clausify,[status(thm)],[f_858_3]) ).
cnf(f_858_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2524,U_2525)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2525))
| ~ sP231(U_2525,U_2524,U_2523) ),
inference(clausify,[status(thm)],[f_858_3]) ).
cnf(f_858_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2524),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2523),U_2525))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2524,U_2525)
| ~ sP231(U_2525,U_2524,U_2523) ),
inference(clausify,[status(thm)],[f_858_3]) ).
fof(f_859_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(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_859_2,plain,
! [U_2530,U_2529,U_2528,U_2527,U_2526] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2526,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2526),U_2527),U_2529)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2528),U_2530))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2526,U_2529),U_2530)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2526,U_2527),U_2528)
| ~ class_RealVector_Oreal__normed__algebra(U_2526) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
fof(f_859_3,plain,
! [U_2528,U_2527,U_2526,U_2529,U_2530] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2526,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2526),U_2527),U_2529)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2528),U_2530))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2526,U_2529),U_2530)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2526,U_2527),U_2528)
| ~ class_RealVector_Oreal__normed__algebra(U_2526) ),
inference(definitional_conversion,[status(esa)],[f_859_2]) ).
cnf(f_859_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2526,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2526),U_2527),U_2529)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2528),U_2530))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2526,U_2529),U_2530)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2526,U_2527),U_2528)
| ~ class_RealVector_Oreal__normed__algebra(U_2526) ),
inference(clausify,[status(thm)],[f_859_3]) ).
fof(f_860_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_860_2,plain,
! [U_2535,U_2534,U_2533,U_2532,U_2531] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,c_Groups_Oplus__class_Oplus(U_2531,U_2532,U_2534)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2533,U_2535))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,U_2534),U_2535)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,U_2532),U_2533)
| ~ class_RealVector_Oreal__normed__vector(U_2531) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
fof(f_860_3,plain,
! [U_2533,U_2534,U_2535,U_2532,U_2531] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,c_Groups_Oplus__class_Oplus(U_2531,U_2532,U_2534)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2533,U_2535))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,U_2534),U_2535)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,U_2532),U_2533)
| ~ class_RealVector_Oreal__normed__vector(U_2531) ),
inference(definitional_conversion,[status(esa)],[f_860_2]) ).
cnf(f_860_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,c_Groups_Oplus__class_Oplus(U_2531,U_2532,U_2534)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2533,U_2535))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,U_2534),U_2535)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2531,U_2532),U_2533)
| ~ class_RealVector_Oreal__normed__vector(U_2531) ),
inference(clausify,[status(thm)],[f_860_3]) ).
fof(f_861_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_861_2,plain,
! [U_2536] : ~ 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_2536),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2536),
inference(variable_rename,[status(thm)],[f_861_1]) ).
fof(f_861_3,plain,
! [U_2536] : ~ 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_2536),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2536),
inference(definitional_conversion,[status(esa)],[f_861_2]) ).
cnf(f_861_4,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_2536),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_2536),
inference(clausify,[status(thm)],[f_861_3]) ).
fof(f_862_1,plain,
! [V_y,V_x] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oarctan(V_x),c_Transcendental_Oarctan(V_y)) = c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_y))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_y),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(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_arctan__add]) ).
fof(f_862_2,plain,
! [U_2538,U_2537] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oarctan(U_2537),c_Transcendental_Oarctan(U_2538)) = c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2537,U_2538),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2537),U_2538))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2538),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2537),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_862_1]) ).
fof(f_862_3,plain,
! [U_2537,U_2538] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oarctan(U_2537),c_Transcendental_Oarctan(U_2538)) = c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2537,U_2538),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2537),U_2538))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2538),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2537),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(definitional_conversion,[status(esa)],[f_862_2]) ).
cnf(f_862_4,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Transcendental_Oarctan(U_2537),c_Transcendental_Oarctan(U_2538)) = c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2537,U_2538),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2537),U_2538))))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2538),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_2537),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_862_3]) ).
fof(f_863_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_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,V_a,V_b)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__left__mono__neg]) ).
fof(f_863_2,plain,
! [U_2542,U_2541,U_2540,U_2539] :
( c_Orderings_Oord__class_Oless__eq(U_2539,c_Rings_Oinverse__class_Odivide(U_2539,U_2542,U_2540),c_Rings_Oinverse__class_Odivide(U_2539,U_2542,U_2541))
| ~ c_Orderings_Oord__class_Oless(U_2539,c_Groups_Ozero__class_Ozero(U_2539),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2539),U_2540),U_2541))
| ~ c_Orderings_Oord__class_Oless__eq(U_2539,U_2542,c_Groups_Ozero__class_Ozero(U_2539))
| ~ c_Orderings_Oord__class_Oless__eq(U_2539,U_2540,U_2541)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2539) ),
inference(variable_rename,[status(thm)],[f_863_1]) ).
fof(f_863_3,plain,
! [U_2540,U_2539,U_2541,U_2542] :
( c_Orderings_Oord__class_Oless__eq(U_2539,c_Rings_Oinverse__class_Odivide(U_2539,U_2542,U_2540),c_Rings_Oinverse__class_Odivide(U_2539,U_2542,U_2541))
| ~ c_Orderings_Oord__class_Oless(U_2539,c_Groups_Ozero__class_Ozero(U_2539),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2539),U_2540),U_2541))
| ~ c_Orderings_Oord__class_Oless__eq(U_2539,U_2542,c_Groups_Ozero__class_Ozero(U_2539))
| ~ c_Orderings_Oord__class_Oless__eq(U_2539,U_2540,U_2541)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2539) ),
inference(definitional_conversion,[status(esa)],[f_863_2]) ).
cnf(f_863_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2539,c_Rings_Oinverse__class_Odivide(U_2539,U_2542,U_2540),c_Rings_Oinverse__class_Odivide(U_2539,U_2542,U_2541))
| ~ c_Orderings_Oord__class_Oless(U_2539,c_Groups_Ozero__class_Ozero(U_2539),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2539),U_2540),U_2541))
| ~ c_Orderings_Oord__class_Oless__eq(U_2539,U_2542,c_Groups_Ozero__class_Ozero(U_2539))
| ~ c_Orderings_Oord__class_Oless__eq(U_2539,U_2540,U_2541)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2539) ),
inference(clausify,[status(thm)],[f_863_3]) ).
fof(f_864_1,plain,
! [V_c,V_a,V_b,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_c,V_a),c_Rings_Oinverse__class_Odivide(T_a,V_c,V_b))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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_c)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__left__mono]) ).
fof(f_864_2,plain,
! [U_2546,U_2545,U_2544,U_2543] :
( c_Orderings_Oord__class_Oless__eq(U_2543,c_Rings_Oinverse__class_Odivide(U_2543,U_2546,U_2545),c_Rings_Oinverse__class_Odivide(U_2543,U_2546,U_2544))
| ~ c_Orderings_Oord__class_Oless(U_2543,c_Groups_Ozero__class_Ozero(U_2543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2543),U_2545),U_2544))
| ~ c_Orderings_Oord__class_Oless__eq(U_2543,c_Groups_Ozero__class_Ozero(U_2543),U_2546)
| ~ c_Orderings_Oord__class_Oless__eq(U_2543,U_2544,U_2545)
| ~ class_Fields_Olinordered__field(U_2543) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
fof(f_864_3,plain,
! [U_2544,U_2546,U_2543,U_2545] :
( c_Orderings_Oord__class_Oless__eq(U_2543,c_Rings_Oinverse__class_Odivide(U_2543,U_2546,U_2545),c_Rings_Oinverse__class_Odivide(U_2543,U_2546,U_2544))
| ~ c_Orderings_Oord__class_Oless(U_2543,c_Groups_Ozero__class_Ozero(U_2543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2543),U_2545),U_2544))
| ~ c_Orderings_Oord__class_Oless__eq(U_2543,c_Groups_Ozero__class_Ozero(U_2543),U_2546)
| ~ c_Orderings_Oord__class_Oless__eq(U_2543,U_2544,U_2545)
| ~ class_Fields_Olinordered__field(U_2543) ),
inference(definitional_conversion,[status(esa)],[f_864_2]) ).
cnf(f_864_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2543,c_Rings_Oinverse__class_Odivide(U_2543,U_2546,U_2545),c_Rings_Oinverse__class_Odivide(U_2543,U_2546,U_2544))
| ~ c_Orderings_Oord__class_Oless(U_2543,c_Groups_Ozero__class_Ozero(U_2543),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2543),U_2545),U_2544))
| ~ c_Orderings_Oord__class_Oless__eq(U_2543,c_Groups_Ozero__class_Ozero(U_2543),U_2546)
| ~ c_Orderings_Oord__class_Oless__eq(U_2543,U_2544,U_2545)
| ~ class_Fields_Olinordered__field(U_2543) ),
inference(clausify,[status(thm)],[f_864_3]) ).
fof(f_865_1,plain,
! [V_a_2,V_b_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__divide__le__eq]) ).
fof(f_865_2,plain,
! [U_2550,U_2549,U_2548,U_2547] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2547,c_Rings_Oinverse__class_Odivide(U_2547,U_2549,U_2548),U_2550)
| ~ c_Orderings_Oord__class_Oless__eq(U_2547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2547),U_2550),U_2548),U_2549) )
& ( c_Orderings_Oord__class_Oless__eq(U_2547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2547),U_2550),U_2548),U_2549)
| ~ c_Orderings_Oord__class_Oless__eq(U_2547,c_Rings_Oinverse__class_Odivide(U_2547,U_2549,U_2548),U_2550) ) )
| ~ c_Orderings_Oord__class_Oless(U_2547,U_2548,c_Groups_Ozero__class_Ozero(U_2547))
| ~ class_Fields_Olinordered__field(U_2547) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
fof(f_865_3,plain,
( ! [U_2548,U_2549,U_2550,U_2547] :
( c_Orderings_Oord__class_Oless__eq(U_2547,c_Rings_Oinverse__class_Odivide(U_2547,U_2549,U_2548),U_2550)
| ~ c_Orderings_Oord__class_Oless__eq(U_2547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2547),U_2550),U_2548),U_2549)
| ~ sP232(U_2548,U_2549,U_2550,U_2547) )
& ! [U_2548,U_2549,U_2550,U_2547] :
( c_Orderings_Oord__class_Oless__eq(U_2547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2547),U_2550),U_2548),U_2549)
| ~ c_Orderings_Oord__class_Oless__eq(U_2547,c_Rings_Oinverse__class_Odivide(U_2547,U_2549,U_2548),U_2550)
| ~ sP232(U_2548,U_2549,U_2550,U_2547) )
& ! [U_2548,U_2549,U_2550,U_2547] :
( sP232(U_2548,U_2549,U_2550,U_2547)
| ~ c_Orderings_Oord__class_Oless(U_2547,U_2548,c_Groups_Ozero__class_Ozero(U_2547))
| ~ class_Fields_Olinordered__field(U_2547) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_865_2]) ).
cnf(f_865_4,plain,
( sP232(U_2548,U_2549,U_2550,U_2547)
| ~ c_Orderings_Oord__class_Oless(U_2547,U_2548,c_Groups_Ozero__class_Ozero(U_2547))
| ~ class_Fields_Olinordered__field(U_2547) ),
inference(clausify,[status(thm)],[f_865_3]) ).
cnf(f_865_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2547),U_2550),U_2548),U_2549)
| ~ c_Orderings_Oord__class_Oless__eq(U_2547,c_Rings_Oinverse__class_Odivide(U_2547,U_2549,U_2548),U_2550)
| ~ sP232(U_2548,U_2549,U_2550,U_2547) ),
inference(clausify,[status(thm)],[f_865_3]) ).
cnf(f_865_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2547,c_Rings_Oinverse__class_Odivide(U_2547,U_2549,U_2548),U_2550)
| ~ c_Orderings_Oord__class_Oless__eq(U_2547,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2547),U_2550),U_2548),U_2549)
| ~ sP232(U_2548,U_2549,U_2550,U_2547) ),
inference(clausify,[status(thm)],[f_865_3]) ).
fof(f_866_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__divide__eq]) ).
fof(f_866_2,plain,
! [U_2554,U_2553,U_2552,U_2551] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2551,U_2553,c_Rings_Oinverse__class_Odivide(U_2551,U_2554,U_2552))
| ~ c_Orderings_Oord__class_Oless__eq(U_2551,U_2554,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2551),U_2553),U_2552)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2551,U_2554,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2551),U_2553),U_2552))
| ~ c_Orderings_Oord__class_Oless__eq(U_2551,U_2553,c_Rings_Oinverse__class_Odivide(U_2551,U_2554,U_2552)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2551,U_2552,c_Groups_Ozero__class_Ozero(U_2551))
| ~ class_Fields_Olinordered__field(U_2551) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
fof(f_866_3,plain,
( ! [U_2551,U_2552,U_2554,U_2553] :
( c_Orderings_Oord__class_Oless__eq(U_2551,U_2553,c_Rings_Oinverse__class_Odivide(U_2551,U_2554,U_2552))
| ~ c_Orderings_Oord__class_Oless__eq(U_2551,U_2554,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2551),U_2553),U_2552))
| ~ sP233(U_2551,U_2552,U_2554,U_2553) )
& ! [U_2551,U_2552,U_2554,U_2553] :
( c_Orderings_Oord__class_Oless__eq(U_2551,U_2554,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2551),U_2553),U_2552))
| ~ c_Orderings_Oord__class_Oless__eq(U_2551,U_2553,c_Rings_Oinverse__class_Odivide(U_2551,U_2554,U_2552))
| ~ sP233(U_2551,U_2552,U_2554,U_2553) )
& ! [U_2551,U_2552,U_2554,U_2553] :
( sP233(U_2551,U_2552,U_2554,U_2553)
| ~ c_Orderings_Oord__class_Oless(U_2551,U_2552,c_Groups_Ozero__class_Ozero(U_2551))
| ~ class_Fields_Olinordered__field(U_2551) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_866_2]) ).
cnf(f_866_4,plain,
( sP233(U_2551,U_2552,U_2554,U_2553)
| ~ c_Orderings_Oord__class_Oless(U_2551,U_2552,c_Groups_Ozero__class_Ozero(U_2551))
| ~ class_Fields_Olinordered__field(U_2551) ),
inference(clausify,[status(thm)],[f_866_3]) ).
cnf(f_866_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2551,U_2554,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2551),U_2553),U_2552))
| ~ c_Orderings_Oord__class_Oless__eq(U_2551,U_2553,c_Rings_Oinverse__class_Odivide(U_2551,U_2554,U_2552))
| ~ sP233(U_2551,U_2552,U_2554,U_2553) ),
inference(clausify,[status(thm)],[f_866_3]) ).
cnf(f_866_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2551,U_2553,c_Rings_Oinverse__class_Odivide(U_2551,U_2554,U_2552))
| ~ c_Orderings_Oord__class_Oless__eq(U_2551,U_2554,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2551),U_2553),U_2552))
| ~ sP233(U_2551,U_2552,U_2554,U_2553) ),
inference(clausify,[status(thm)],[f_866_3]) ).
fof(f_867_1,plain,
! [V_x,V_z,V_y,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_z,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y),V_x)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__le__div__pos]) ).
fof(f_867_2,plain,
! [U_2558,U_2557,U_2556,U_2555] :
( c_Orderings_Oord__class_Oless__eq(U_2555,U_2557,c_Rings_Oinverse__class_Odivide(U_2555,U_2558,U_2556))
| ~ c_Orderings_Oord__class_Oless__eq(U_2555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2555),U_2557),U_2556),U_2558)
| ~ c_Orderings_Oord__class_Oless(U_2555,c_Groups_Ozero__class_Ozero(U_2555),U_2556)
| ~ class_Fields_Olinordered__field(U_2555) ),
inference(variable_rename,[status(thm)],[f_867_1]) ).
fof(f_867_3,plain,
! [U_2558,U_2555,U_2556,U_2557] :
( c_Orderings_Oord__class_Oless__eq(U_2555,U_2557,c_Rings_Oinverse__class_Odivide(U_2555,U_2558,U_2556))
| ~ c_Orderings_Oord__class_Oless__eq(U_2555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2555),U_2557),U_2556),U_2558)
| ~ c_Orderings_Oord__class_Oless(U_2555,c_Groups_Ozero__class_Ozero(U_2555),U_2556)
| ~ class_Fields_Olinordered__field(U_2555) ),
inference(definitional_conversion,[status(esa)],[f_867_2]) ).
cnf(f_867_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2555,U_2557,c_Rings_Oinverse__class_Odivide(U_2555,U_2558,U_2556))
| ~ c_Orderings_Oord__class_Oless__eq(U_2555,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2555),U_2557),U_2556),U_2558)
| ~ c_Orderings_Oord__class_Oless(U_2555,c_Groups_Ozero__class_Ozero(U_2555),U_2556)
| ~ class_Fields_Olinordered__field(U_2555) ),
inference(clausify,[status(thm)],[f_867_3]) ).
fof(f_868_1,plain,
! [V_z,V_x,V_y,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_x,V_y),V_z)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__imp__div__pos__le]) ).
fof(f_868_2,plain,
! [U_2562,U_2561,U_2560,U_2559] :
( c_Orderings_Oord__class_Oless__eq(U_2559,c_Rings_Oinverse__class_Odivide(U_2559,U_2561,U_2560),U_2562)
| ~ c_Orderings_Oord__class_Oless__eq(U_2559,U_2561,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2559),U_2562),U_2560))
| ~ c_Orderings_Oord__class_Oless(U_2559,c_Groups_Ozero__class_Ozero(U_2559),U_2560)
| ~ class_Fields_Olinordered__field(U_2559) ),
inference(variable_rename,[status(thm)],[f_868_1]) ).
fof(f_868_3,plain,
! [U_2559,U_2560,U_2562,U_2561] :
( c_Orderings_Oord__class_Oless__eq(U_2559,c_Rings_Oinverse__class_Odivide(U_2559,U_2561,U_2560),U_2562)
| ~ c_Orderings_Oord__class_Oless__eq(U_2559,U_2561,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2559),U_2562),U_2560))
| ~ c_Orderings_Oord__class_Oless(U_2559,c_Groups_Ozero__class_Ozero(U_2559),U_2560)
| ~ class_Fields_Olinordered__field(U_2559) ),
inference(definitional_conversion,[status(esa)],[f_868_2]) ).
cnf(f_868_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2559,c_Rings_Oinverse__class_Odivide(U_2559,U_2561,U_2560),U_2562)
| ~ c_Orderings_Oord__class_Oless__eq(U_2559,U_2561,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2559),U_2562),U_2560))
| ~ c_Orderings_Oord__class_Oless(U_2559,c_Groups_Ozero__class_Ozero(U_2559),U_2560)
| ~ class_Fields_Olinordered__field(U_2559) ),
inference(clausify,[status(thm)],[f_868_3]) ).
fof(f_869_1,plain,
! [V_a_2,V_b_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__divide__le__eq]) ).
fof(f_869_2,plain,
! [U_2566,U_2565,U_2564,U_2563] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2563,c_Rings_Oinverse__class_Odivide(U_2563,U_2565,U_2564),U_2566)
| ~ c_Orderings_Oord__class_Oless__eq(U_2563,U_2565,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2563),U_2566),U_2564)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2563,U_2565,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2563),U_2566),U_2564))
| ~ c_Orderings_Oord__class_Oless__eq(U_2563,c_Rings_Oinverse__class_Odivide(U_2563,U_2565,U_2564),U_2566) ) )
| ~ c_Orderings_Oord__class_Oless(U_2563,c_Groups_Ozero__class_Ozero(U_2563),U_2564)
| ~ class_Fields_Olinordered__field(U_2563) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
fof(f_869_3,plain,
( ! [U_2564,U_2565,U_2566,U_2563] :
( c_Orderings_Oord__class_Oless__eq(U_2563,c_Rings_Oinverse__class_Odivide(U_2563,U_2565,U_2564),U_2566)
| ~ c_Orderings_Oord__class_Oless__eq(U_2563,U_2565,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2563),U_2566),U_2564))
| ~ sP234(U_2564,U_2565,U_2566,U_2563) )
& ! [U_2564,U_2565,U_2566,U_2563] :
( c_Orderings_Oord__class_Oless__eq(U_2563,U_2565,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2563),U_2566),U_2564))
| ~ c_Orderings_Oord__class_Oless__eq(U_2563,c_Rings_Oinverse__class_Odivide(U_2563,U_2565,U_2564),U_2566)
| ~ sP234(U_2564,U_2565,U_2566,U_2563) )
& ! [U_2564,U_2565,U_2566,U_2563] :
( sP234(U_2564,U_2565,U_2566,U_2563)
| ~ c_Orderings_Oord__class_Oless(U_2563,c_Groups_Ozero__class_Ozero(U_2563),U_2564)
| ~ class_Fields_Olinordered__field(U_2563) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234])],[f_869_2]) ).
cnf(f_869_4,plain,
( sP234(U_2564,U_2565,U_2566,U_2563)
| ~ c_Orderings_Oord__class_Oless(U_2563,c_Groups_Ozero__class_Ozero(U_2563),U_2564)
| ~ class_Fields_Olinordered__field(U_2563) ),
inference(clausify,[status(thm)],[f_869_3]) ).
cnf(f_869_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2563,U_2565,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2563),U_2566),U_2564))
| ~ c_Orderings_Oord__class_Oless__eq(U_2563,c_Rings_Oinverse__class_Odivide(U_2563,U_2565,U_2564),U_2566)
| ~ sP234(U_2564,U_2565,U_2566,U_2563) ),
inference(clausify,[status(thm)],[f_869_3]) ).
cnf(f_869_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2563,c_Rings_Oinverse__class_Odivide(U_2563,U_2565,U_2564),U_2566)
| ~ c_Orderings_Oord__class_Oless__eq(U_2563,U_2565,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2563),U_2566),U_2564))
| ~ sP234(U_2564,U_2565,U_2566,U_2563) ),
inference(clausify,[status(thm)],[f_869_3]) ).
fof(f_870_1,plain,
! [V_b_2,V_a_2,V_c_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2)
| ~ class_Fields_Olinordered__field(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__le__divide__eq]) ).
fof(f_870_2,plain,
! [U_2570,U_2569,U_2568,U_2567] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2567,U_2569,c_Rings_Oinverse__class_Odivide(U_2567,U_2570,U_2568))
| ~ c_Orderings_Oord__class_Oless__eq(U_2567,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2567),U_2569),U_2568),U_2570) )
& ( c_Orderings_Oord__class_Oless__eq(U_2567,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2567),U_2569),U_2568),U_2570)
| ~ c_Orderings_Oord__class_Oless__eq(U_2567,U_2569,c_Rings_Oinverse__class_Odivide(U_2567,U_2570,U_2568)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2567,c_Groups_Ozero__class_Ozero(U_2567),U_2568)
| ~ class_Fields_Olinordered__field(U_2567) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
fof(f_870_3,plain,
( ! [U_2569,U_2570,U_2568,U_2567] :
( c_Orderings_Oord__class_Oless__eq(U_2567,U_2569,c_Rings_Oinverse__class_Odivide(U_2567,U_2570,U_2568))
| ~ c_Orderings_Oord__class_Oless__eq(U_2567,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2567),U_2569),U_2568),U_2570)
| ~ sP235(U_2569,U_2570,U_2568,U_2567) )
& ! [U_2569,U_2570,U_2568,U_2567] :
( c_Orderings_Oord__class_Oless__eq(U_2567,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2567),U_2569),U_2568),U_2570)
| ~ c_Orderings_Oord__class_Oless__eq(U_2567,U_2569,c_Rings_Oinverse__class_Odivide(U_2567,U_2570,U_2568))
| ~ sP235(U_2569,U_2570,U_2568,U_2567) )
& ! [U_2569,U_2570,U_2568,U_2567] :
( sP235(U_2569,U_2570,U_2568,U_2567)
| ~ c_Orderings_Oord__class_Oless(U_2567,c_Groups_Ozero__class_Ozero(U_2567),U_2568)
| ~ class_Fields_Olinordered__field(U_2567) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235])],[f_870_2]) ).
cnf(f_870_4,plain,
( sP235(U_2569,U_2570,U_2568,U_2567)
| ~ c_Orderings_Oord__class_Oless(U_2567,c_Groups_Ozero__class_Ozero(U_2567),U_2568)
| ~ class_Fields_Olinordered__field(U_2567) ),
inference(clausify,[status(thm)],[f_870_3]) ).
cnf(f_870_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2567,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2567),U_2569),U_2568),U_2570)
| ~ c_Orderings_Oord__class_Oless__eq(U_2567,U_2569,c_Rings_Oinverse__class_Odivide(U_2567,U_2570,U_2568))
| ~ sP235(U_2569,U_2570,U_2568,U_2567) ),
inference(clausify,[status(thm)],[f_870_3]) ).
cnf(f_870_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2567,U_2569,c_Rings_Oinverse__class_Odivide(U_2567,U_2570,U_2568))
| ~ c_Orderings_Oord__class_Oless__eq(U_2567,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2567),U_2569),U_2568),U_2570)
| ~ sP235(U_2569,U_2570,U_2568,U_2567) ),
inference(clausify,[status(thm)],[f_870_3]) ).
fof(f_871_1,plain,
! [V_a_2,V_c_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_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(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),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__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),V_a_2) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq]) ).
fof(f_871_2,plain,
! [U_2574,U_2573,U_2572,U_2571] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2571,c_Rings_Oinverse__class_Odivide(U_2571,U_2572,U_2573),U_2574)
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2574)
& ~ c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2571,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573),U_2572)
& c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2571,U_2572,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573))
& c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2574)
| c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2571,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573),U_2572)
| ~ c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571)) ) )
| c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573) )
& ( c_Orderings_Oord__class_Oless__eq(U_2571,U_2572,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573))
| ~ c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2571,c_Rings_Oinverse__class_Odivide(U_2571,U_2572,U_2573),U_2574) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_2571) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
fof(f_871_3,plain,
( ! [U_2573,U_2571,U_2574] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2574)
| ~ sP240(U_2573,U_2571,U_2574) )
& ! [U_2573,U_2571,U_2574] :
( ~ c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571))
| ~ sP240(U_2573,U_2571,U_2574) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2571,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573),U_2572)
| ~ sP239(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571))
| ~ sP239(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( sP240(U_2573,U_2571,U_2574)
| sP239(U_2573,U_2571,U_2574,U_2572)
| ~ sP241(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( ~ c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573)
| ~ sP241(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2571,U_2572,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573))
| ~ sP238(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573)
| ~ sP238(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( c_Orderings_Oord__class_Oless__eq(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2574)
| c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571))
| ~ sP236(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( c_Orderings_Oord__class_Oless__eq(U_2571,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573),U_2572)
| ~ c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571))
| ~ sP236(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( sP236(U_2573,U_2571,U_2574,U_2572)
| c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573)
| ~ sP237(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( c_Orderings_Oord__class_Oless__eq(U_2571,U_2572,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573))
| ~ c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573)
| ~ sP237(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( c_Orderings_Oord__class_Oless__eq(U_2571,c_Rings_Oinverse__class_Odivide(U_2571,U_2572,U_2573),U_2574)
| sP241(U_2573,U_2571,U_2574,U_2572)
| sP238(U_2573,U_2571,U_2574,U_2572)
| ~ sP242(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( sP237(U_2573,U_2571,U_2574,U_2572)
| ~ c_Orderings_Oord__class_Oless__eq(U_2571,c_Rings_Oinverse__class_Odivide(U_2571,U_2572,U_2573),U_2574)
| ~ sP242(U_2573,U_2571,U_2574,U_2572) )
& ! [U_2573,U_2571,U_2574,U_2572] :
( sP242(U_2573,U_2571,U_2574,U_2572)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2571) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236,sP237,sP238,sP239,sP240,sP241,sP242])],[f_871_2]) ).
cnf(f_871_4,plain,
( sP242(U_2573,U_2571,U_2574,U_2572)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2571) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_5,plain,
( sP237(U_2573,U_2571,U_2574,U_2572)
| ~ c_Orderings_Oord__class_Oless__eq(U_2571,c_Rings_Oinverse__class_Odivide(U_2571,U_2572,U_2573),U_2574)
| ~ sP242(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2571,c_Rings_Oinverse__class_Odivide(U_2571,U_2572,U_2573),U_2574)
| sP241(U_2573,U_2571,U_2574,U_2572)
| sP238(U_2573,U_2571,U_2574,U_2572)
| ~ sP242(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2571,U_2572,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573))
| ~ c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573)
| ~ sP237(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_8,plain,
( sP236(U_2573,U_2571,U_2574,U_2572)
| c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573)
| ~ sP237(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_2571,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573),U_2572)
| ~ c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571))
| ~ sP236(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2574)
| c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571))
| ~ sP236(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_11,plain,
( c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573)
| ~ sP238(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2571,U_2572,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573))
| ~ sP238(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2573)
| ~ sP241(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_14,plain,
( sP240(U_2573,U_2571,U_2574)
| sP239(U_2573,U_2571,U_2574,U_2572)
| ~ sP241(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_15,plain,
( c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571))
| ~ sP239(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_16,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2571,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2571),U_2574),U_2573),U_2572)
| ~ sP239(U_2573,U_2571,U_2574,U_2572) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2571,U_2573,c_Groups_Ozero__class_Ozero(U_2571))
| ~ sP240(U_2573,U_2571,U_2574) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_18,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2571,c_Groups_Ozero__class_Ozero(U_2571),U_2574)
| ~ sP240(U_2573,U_2571,U_2574) ),
inference(clausify,[status(thm)],[f_871_3]) ).
fof(f_872_1,plain,
! [V_c_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
& ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_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__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq]) ).
fof(f_872_2,plain,
! [U_2578,U_2577,U_2576,U_2575] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Rings_Oinverse__class_Odivide(U_2575,U_2577,U_2578))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Groups_Ozero__class_Ozero(U_2575))
& ~ c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2575,U_2577,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578))
& c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2575,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578),U_2577)
& c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Groups_Ozero__class_Ozero(U_2575))
| c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2575,U_2577,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578))
| ~ c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575)) ) )
| c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578) )
& ( c_Orderings_Oord__class_Oless__eq(U_2575,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578),U_2577)
| ~ c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Rings_Oinverse__class_Odivide(U_2575,U_2577,U_2578)) ) )
| ~ class_Fields_Olinordered__field__inverse__zero(U_2575) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
fof(f_872_3,plain,
( ! [U_2576,U_2575,U_2578] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP247(U_2576,U_2575,U_2578) )
& ! [U_2576,U_2575,U_2578] :
( ~ c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP247(U_2576,U_2575,U_2578) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2575,U_2577,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578))
| ~ sP246(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP246(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( sP247(U_2576,U_2575,U_2578)
| sP246(U_2576,U_2575,U_2578,U_2577)
| ~ sP248(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( ~ c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578)
| ~ sP248(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2575,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578),U_2577)
| ~ sP245(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578)
| ~ sP245(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Groups_Ozero__class_Ozero(U_2575))
| c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP243(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( c_Orderings_Oord__class_Oless__eq(U_2575,U_2577,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578))
| ~ c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP243(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( sP243(U_2576,U_2575,U_2578,U_2577)
| c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578)
| ~ sP244(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( c_Orderings_Oord__class_Oless__eq(U_2575,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578),U_2577)
| ~ c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578)
| ~ sP244(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Rings_Oinverse__class_Odivide(U_2575,U_2577,U_2578))
| sP248(U_2576,U_2575,U_2578,U_2577)
| sP245(U_2576,U_2575,U_2578,U_2577)
| ~ sP249(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( sP244(U_2576,U_2575,U_2578,U_2577)
| ~ c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Rings_Oinverse__class_Odivide(U_2575,U_2577,U_2578))
| ~ sP249(U_2576,U_2575,U_2578,U_2577) )
& ! [U_2576,U_2575,U_2578,U_2577] :
( sP249(U_2576,U_2575,U_2578,U_2577)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2575) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243,sP244,sP245,sP246,sP247,sP248,sP249])],[f_872_2]) ).
cnf(f_872_4,plain,
( sP249(U_2576,U_2575,U_2578,U_2577)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2575) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_5,plain,
( sP244(U_2576,U_2575,U_2578,U_2577)
| ~ c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Rings_Oinverse__class_Odivide(U_2575,U_2577,U_2578))
| ~ sP249(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Rings_Oinverse__class_Odivide(U_2575,U_2577,U_2578))
| sP248(U_2576,U_2575,U_2578,U_2577)
| sP245(U_2576,U_2575,U_2578,U_2577)
| ~ sP249(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2575,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578),U_2577)
| ~ c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578)
| ~ sP244(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_8,plain,
( sP243(U_2576,U_2575,U_2578,U_2577)
| c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578)
| ~ sP244(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_2575,U_2577,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578))
| ~ c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP243(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Groups_Ozero__class_Ozero(U_2575))
| c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP243(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_11,plain,
( c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578)
| ~ sP245(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2575,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578),U_2577)
| ~ sP245(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2575,c_Groups_Ozero__class_Ozero(U_2575),U_2578)
| ~ sP248(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_14,plain,
( sP247(U_2576,U_2575,U_2578)
| sP246(U_2576,U_2575,U_2578,U_2577)
| ~ sP248(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_15,plain,
( c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP246(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_16,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2575,U_2577,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2575),U_2576),U_2578))
| ~ sP246(U_2576,U_2575,U_2578,U_2577) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2575,U_2578,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP247(U_2576,U_2575,U_2578) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_18,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2575,U_2576,c_Groups_Ozero__class_Ozero(U_2575))
| ~ sP247(U_2576,U_2575,U_2578) ),
inference(clausify,[status(thm)],[f_872_3]) ).
fof(f_873_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(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)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__Suc__less]) ).
fof(f_873_2,plain,
! [U_2581,U_2580,U_2579] :
( c_Orderings_Oord__class_Oless(U_2579,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2579),U_2580),hAPP(hAPP(c_Power_Opower__class_Opower(U_2579),U_2580),U_2581)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2579),U_2580),U_2581))
| ~ c_Orderings_Oord__class_Oless(U_2579,U_2580,c_Groups_Oone__class_Oone(U_2579))
| ~ c_Orderings_Oord__class_Oless(U_2579,c_Groups_Ozero__class_Ozero(U_2579),U_2580)
| ~ class_Rings_Olinordered__semidom(U_2579) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
fof(f_873_3,plain,
! [U_2581,U_2580,U_2579] :
( c_Orderings_Oord__class_Oless(U_2579,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2579),U_2580),hAPP(hAPP(c_Power_Opower__class_Opower(U_2579),U_2580),U_2581)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2579),U_2580),U_2581))
| ~ c_Orderings_Oord__class_Oless(U_2579,U_2580,c_Groups_Oone__class_Oone(U_2579))
| ~ c_Orderings_Oord__class_Oless(U_2579,c_Groups_Ozero__class_Ozero(U_2579),U_2580)
| ~ class_Rings_Olinordered__semidom(U_2579) ),
inference(definitional_conversion,[status(esa)],[f_873_2]) ).
cnf(f_873_4,plain,
( c_Orderings_Oord__class_Oless(U_2579,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2579),U_2580),hAPP(hAPP(c_Power_Opower__class_Opower(U_2579),U_2580),U_2581)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2579),U_2580),U_2581))
| ~ c_Orderings_Oord__class_Oless(U_2579,U_2580,c_Groups_Oone__class_Oone(U_2579))
| ~ c_Orderings_Oord__class_Oless(U_2579,c_Groups_Ozero__class_Ozero(U_2579),U_2580)
| ~ class_Rings_Olinordered__semidom(U_2579) ),
inference(clausify,[status(thm)],[f_873_3]) ).
fof(f_874_1,plain,
! [V_a_2,V_w_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_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_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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_w_2)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_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_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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_w_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_a_2) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of1]) ).
fof(f_874_2,plain,
! [U_2585,U_2584,U_2583,U_2582] :
( ( ( c_Orderings_Oord__class_Oless(U_2582,c_Rings_Oinverse__class_Odivide(U_2582,U_2583,c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2585)
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),U_2585)
& ~ c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582)) )
| ( ~ c_Orderings_Oord__class_Oless(U_2582,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2583)
& c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)) )
| ( ~ c_Orderings_Oord__class_Oless(U_2582,U_2583,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)))
& c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),U_2585)
| c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582)) )
& ( c_Orderings_Oord__class_Oless(U_2582,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2583)
| ~ c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582)) ) )
| c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)) )
& ( c_Orderings_Oord__class_Oless(U_2582,U_2583,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)))
| ~ c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2582,c_Rings_Oinverse__class_Odivide(U_2582,U_2583,c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2585) ) )
| ~ class_Int_Onumber(U_2582)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2582) ),
inference(variable_rename,[status(thm)],[f_874_1]) ).
fof(f_874_3,plain,
( ! [U_2582,U_2585,U_2584] :
( ~ c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),U_2585)
| ~ sP254(U_2582,U_2585,U_2584) )
& ! [U_2582,U_2585,U_2584] :
( ~ c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582))
| ~ sP254(U_2582,U_2585,U_2584) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( ~ c_Orderings_Oord__class_Oless(U_2582,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2583)
| ~ sP253(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582))
| ~ sP253(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( sP254(U_2582,U_2585,U_2584)
| sP253(U_2582,U_2585,U_2584,U_2583)
| ~ sP255(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( ~ c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584))
| ~ sP255(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( ~ c_Orderings_Oord__class_Oless(U_2582,U_2583,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)))
| ~ sP252(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584))
| ~ sP252(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),U_2585)
| c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582))
| ~ sP250(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( c_Orderings_Oord__class_Oless(U_2582,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2583)
| ~ c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582))
| ~ sP250(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( sP250(U_2582,U_2585,U_2584,U_2583)
| c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584))
| ~ sP251(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( c_Orderings_Oord__class_Oless(U_2582,U_2583,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)))
| ~ c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584))
| ~ sP251(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( c_Orderings_Oord__class_Oless(U_2582,c_Rings_Oinverse__class_Odivide(U_2582,U_2583,c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2585)
| sP255(U_2582,U_2585,U_2584,U_2583)
| sP252(U_2582,U_2585,U_2584,U_2583)
| ~ sP256(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( sP251(U_2582,U_2585,U_2584,U_2583)
| ~ c_Orderings_Oord__class_Oless(U_2582,c_Rings_Oinverse__class_Odivide(U_2582,U_2583,c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2585)
| ~ sP256(U_2582,U_2585,U_2584,U_2583) )
& ! [U_2582,U_2585,U_2584,U_2583] :
( sP256(U_2582,U_2585,U_2584,U_2583)
| ~ class_Int_Onumber(U_2582)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2582) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP250,sP251,sP252,sP253,sP254,sP255,sP256])],[f_874_2]) ).
cnf(f_874_4,plain,
( sP256(U_2582,U_2585,U_2584,U_2583)
| ~ class_Int_Onumber(U_2582)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2582) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_5,plain,
( sP251(U_2582,U_2585,U_2584,U_2583)
| ~ c_Orderings_Oord__class_Oless(U_2582,c_Rings_Oinverse__class_Odivide(U_2582,U_2583,c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2585)
| ~ sP256(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_6,plain,
( c_Orderings_Oord__class_Oless(U_2582,c_Rings_Oinverse__class_Odivide(U_2582,U_2583,c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2585)
| sP255(U_2582,U_2585,U_2584,U_2583)
| sP252(U_2582,U_2585,U_2584,U_2583)
| ~ sP256(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_7,plain,
( c_Orderings_Oord__class_Oless(U_2582,U_2583,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)))
| ~ c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584))
| ~ sP251(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_8,plain,
( sP250(U_2582,U_2585,U_2584,U_2583)
| c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584))
| ~ sP251(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_9,plain,
( c_Orderings_Oord__class_Oless(U_2582,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2583)
| ~ c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582))
| ~ sP250(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_10,plain,
( c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),U_2585)
| c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582))
| ~ sP250(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_11,plain,
( c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584))
| ~ sP252(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_2582,U_2583,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)))
| ~ sP252(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),c_Int_Onumber__class_Onumber__of(U_2582,U_2584))
| ~ sP255(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_14,plain,
( sP254(U_2582,U_2585,U_2584)
| sP253(U_2582,U_2585,U_2584,U_2583)
| ~ sP255(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_15,plain,
( c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582))
| ~ sP253(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_16,plain,
( ~ c_Orderings_Oord__class_Oless(U_2582,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2582),U_2585),c_Int_Onumber__class_Onumber__of(U_2582,U_2584)),U_2583)
| ~ sP253(U_2582,U_2585,U_2584,U_2583) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2582,c_Int_Onumber__class_Onumber__of(U_2582,U_2584),c_Groups_Ozero__class_Ozero(U_2582))
| ~ sP254(U_2582,U_2585,U_2584) ),
inference(clausify,[status(thm)],[f_874_3]) ).
cnf(f_874_18,plain,
( ~ c_Orderings_Oord__class_Oless(U_2582,c_Groups_Ozero__class_Ozero(U_2582),U_2585)
| ~ sP254(U_2582,U_2585,U_2584) ),
inference(clausify,[status(thm)],[f_874_3]) ).
fof(f_875_1,plain,
! [V_w_2,V_c_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2))
| ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__less__eq__number__of]) ).
fof(f_875_2,plain,
! [U_2589,U_2588,U_2587,U_2586] :
( ( ( c_Orderings_Oord__class_Oless(U_2586,c_Rings_Oinverse__class_Odivide(U_2586,U_2587,U_2588),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
& ~ c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586)) )
| ( ~ c_Orderings_Oord__class_Oless(U_2586,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588),U_2587)
& c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588) )
| ( ~ c_Orderings_Oord__class_Oless(U_2586,U_2587,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588))
& c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586)) )
& ( c_Orderings_Oord__class_Oless(U_2586,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588),U_2587)
| ~ c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586)) ) )
| c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588) )
& ( c_Orderings_Oord__class_Oless(U_2586,U_2587,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588))
| ~ c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588) ) )
| ~ c_Orderings_Oord__class_Oless(U_2586,c_Rings_Oinverse__class_Odivide(U_2586,U_2587,U_2588),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)) ) )
| ~ class_Int_Onumber(U_2586)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2586) ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
fof(f_875_3,plain,
( ! [U_2589,U_2586,U_2588] :
( ~ c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| ~ sP261(U_2589,U_2586,U_2588) )
& ! [U_2589,U_2586,U_2588] :
( ~ c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586))
| ~ sP261(U_2589,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( ~ c_Orderings_Oord__class_Oless(U_2586,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588),U_2587)
| ~ sP260(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586))
| ~ sP260(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( sP261(U_2589,U_2586,U_2588)
| sP260(U_2589,U_2587,U_2586,U_2588)
| ~ sP262(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( ~ c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588)
| ~ sP262(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( ~ c_Orderings_Oord__class_Oless(U_2586,U_2587,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588))
| ~ sP259(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588)
| ~ sP259(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586))
| ~ sP257(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( c_Orderings_Oord__class_Oless(U_2586,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588),U_2587)
| ~ c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586))
| ~ sP257(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( sP257(U_2589,U_2587,U_2586,U_2588)
| c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588)
| ~ sP258(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( c_Orderings_Oord__class_Oless(U_2586,U_2587,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588))
| ~ c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588)
| ~ sP258(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( c_Orderings_Oord__class_Oless(U_2586,c_Rings_Oinverse__class_Odivide(U_2586,U_2587,U_2588),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| sP262(U_2589,U_2587,U_2586,U_2588)
| sP259(U_2589,U_2587,U_2586,U_2588)
| ~ sP263(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( sP258(U_2589,U_2587,U_2586,U_2588)
| ~ c_Orderings_Oord__class_Oless(U_2586,c_Rings_Oinverse__class_Odivide(U_2586,U_2587,U_2588),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| ~ sP263(U_2589,U_2587,U_2586,U_2588) )
& ! [U_2589,U_2587,U_2586,U_2588] :
( sP263(U_2589,U_2587,U_2586,U_2588)
| ~ class_Int_Onumber(U_2586)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2586) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP257,sP258,sP259,sP260,sP261,sP262,sP263])],[f_875_2]) ).
cnf(f_875_4,plain,
( sP263(U_2589,U_2587,U_2586,U_2588)
| ~ class_Int_Onumber(U_2586)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2586) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_5,plain,
( sP258(U_2589,U_2587,U_2586,U_2588)
| ~ c_Orderings_Oord__class_Oless(U_2586,c_Rings_Oinverse__class_Odivide(U_2586,U_2587,U_2588),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| ~ sP263(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_6,plain,
( c_Orderings_Oord__class_Oless(U_2586,c_Rings_Oinverse__class_Odivide(U_2586,U_2587,U_2588),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| sP262(U_2589,U_2587,U_2586,U_2588)
| sP259(U_2589,U_2587,U_2586,U_2588)
| ~ sP263(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_7,plain,
( c_Orderings_Oord__class_Oless(U_2586,U_2587,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588))
| ~ c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588)
| ~ sP258(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_8,plain,
( sP257(U_2589,U_2587,U_2586,U_2588)
| c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588)
| ~ sP258(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_9,plain,
( c_Orderings_Oord__class_Oless(U_2586,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588),U_2587)
| ~ c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586))
| ~ sP257(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_10,plain,
( c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586))
| ~ sP257(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_11,plain,
( c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588)
| ~ sP259(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_2586,U_2587,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588))
| ~ sP259(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),U_2588)
| ~ sP262(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_14,plain,
( sP261(U_2589,U_2586,U_2588)
| sP260(U_2589,U_2587,U_2586,U_2588)
| ~ sP262(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_15,plain,
( c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586))
| ~ sP260(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_16,plain,
( ~ c_Orderings_Oord__class_Oless(U_2586,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589)),U_2588),U_2587)
| ~ sP260(U_2589,U_2587,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2586,U_2588,c_Groups_Ozero__class_Ozero(U_2586))
| ~ sP261(U_2589,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
cnf(f_875_18,plain,
( ~ c_Orderings_Oord__class_Oless(U_2586,c_Groups_Ozero__class_Ozero(U_2586),c_Int_Onumber__class_Onumber__of(U_2586,U_2589))
| ~ sP261(U_2589,U_2586,U_2588) ),
inference(clausify,[status(thm)],[f_875_3]) ).
fof(f_876_1,plain,
! [V_c_2,V_b_2,V_w_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
| ( ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of]) ).
fof(f_876_2,plain,
! [U_2593,U_2592,U_2591,U_2590] :
( ( ( c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Rings_Oinverse__class_Odivide(U_2590,U_2592,U_2593))
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Groups_Ozero__class_Ozero(U_2590))
& ~ c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590)) )
| ( ~ c_Orderings_Oord__class_Oless(U_2590,U_2592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593))
& c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593) )
| ( ~ c_Orderings_Oord__class_Oless(U_2590,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593),U_2592)
& c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Groups_Ozero__class_Ozero(U_2590))
| c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590)) )
& ( c_Orderings_Oord__class_Oless(U_2590,U_2592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593))
| ~ c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590)) ) )
| c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593) )
& ( c_Orderings_Oord__class_Oless(U_2590,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593),U_2592)
| ~ c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593) ) )
| ~ c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Rings_Oinverse__class_Odivide(U_2590,U_2592,U_2593)) ) )
| ~ class_Int_Onumber(U_2590)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2590) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
fof(f_876_3,plain,
( ! [U_2591,U_2590,U_2593] :
( ~ c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP268(U_2591,U_2590,U_2593) )
& ! [U_2591,U_2590,U_2593] :
( ~ c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP268(U_2591,U_2590,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( ~ c_Orderings_Oord__class_Oless(U_2590,U_2592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593))
| ~ sP267(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP267(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( sP268(U_2591,U_2590,U_2593)
| sP267(U_2591,U_2590,U_2592,U_2593)
| ~ sP269(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( ~ c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593)
| ~ sP269(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( ~ c_Orderings_Oord__class_Oless(U_2590,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593),U_2592)
| ~ sP266(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593)
| ~ sP266(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Groups_Ozero__class_Ozero(U_2590))
| c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP264(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( c_Orderings_Oord__class_Oless(U_2590,U_2592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593))
| ~ c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP264(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( sP264(U_2591,U_2590,U_2592,U_2593)
| c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593)
| ~ sP265(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( c_Orderings_Oord__class_Oless(U_2590,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593),U_2592)
| ~ c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593)
| ~ sP265(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Rings_Oinverse__class_Odivide(U_2590,U_2592,U_2593))
| sP269(U_2591,U_2590,U_2592,U_2593)
| sP266(U_2591,U_2590,U_2592,U_2593)
| ~ sP270(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( sP265(U_2591,U_2590,U_2592,U_2593)
| ~ c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Rings_Oinverse__class_Odivide(U_2590,U_2592,U_2593))
| ~ sP270(U_2591,U_2590,U_2592,U_2593) )
& ! [U_2591,U_2590,U_2592,U_2593] :
( sP270(U_2591,U_2590,U_2592,U_2593)
| ~ class_Int_Onumber(U_2590)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2590) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP264,sP265,sP266,sP267,sP268,sP269,sP270])],[f_876_2]) ).
cnf(f_876_4,plain,
( sP270(U_2591,U_2590,U_2592,U_2593)
| ~ class_Int_Onumber(U_2590)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2590) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_5,plain,
( sP265(U_2591,U_2590,U_2592,U_2593)
| ~ c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Rings_Oinverse__class_Odivide(U_2590,U_2592,U_2593))
| ~ sP270(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_6,plain,
( c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Rings_Oinverse__class_Odivide(U_2590,U_2592,U_2593))
| sP269(U_2591,U_2590,U_2592,U_2593)
| sP266(U_2591,U_2590,U_2592,U_2593)
| ~ sP270(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_7,plain,
( c_Orderings_Oord__class_Oless(U_2590,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593),U_2592)
| ~ c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593)
| ~ sP265(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_8,plain,
( sP264(U_2591,U_2590,U_2592,U_2593)
| c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593)
| ~ sP265(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_9,plain,
( c_Orderings_Oord__class_Oless(U_2590,U_2592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593))
| ~ c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP264(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_10,plain,
( c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Groups_Ozero__class_Ozero(U_2590))
| c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP264(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_11,plain,
( c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593)
| ~ sP266(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_2590,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593),U_2592)
| ~ sP266(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2590,c_Groups_Ozero__class_Ozero(U_2590),U_2593)
| ~ sP269(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_14,plain,
( sP268(U_2591,U_2590,U_2593)
| sP267(U_2591,U_2590,U_2592,U_2593)
| ~ sP269(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_15,plain,
( c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP267(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_16,plain,
( ~ c_Orderings_Oord__class_Oless(U_2590,U_2592,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2590),c_Int_Onumber__class_Onumber__of(U_2590,U_2591)),U_2593))
| ~ sP267(U_2591,U_2590,U_2592,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2590,U_2593,c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP268(U_2591,U_2590,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
cnf(f_876_18,plain,
( ~ c_Orderings_Oord__class_Oless(U_2590,c_Int_Onumber__class_Onumber__of(U_2590,U_2591),c_Groups_Ozero__class_Ozero(U_2590))
| ~ sP268(U_2591,U_2590,U_2593) ),
inference(clausify,[status(thm)],[f_876_3]) ).
fof(f_877_1,plain,
! [V_w_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_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,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
& c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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_w_2)) )
| ( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_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,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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_w_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__divide__eq__number__of1]) ).
fof(f_877_2,plain,
! [U_2597,U_2596,U_2595,U_2594] :
( ( ( c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Rings_Oinverse__class_Odivide(U_2594,U_2596,c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| ( ( ( ~ c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Groups_Ozero__class_Ozero(U_2594))
& ~ c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594)) )
| ( ~ c_Orderings_Oord__class_Oless(U_2594,U_2596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
& c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)) )
| ( ~ c_Orderings_Oord__class_Oless(U_2594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)),U_2596)
& c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Groups_Ozero__class_Ozero(U_2594))
| c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594)) )
& ( c_Orderings_Oord__class_Oless(U_2594,U_2596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| ~ c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594)) ) )
| c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)) )
& ( c_Orderings_Oord__class_Oless(U_2594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)),U_2596)
| ~ c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Rings_Oinverse__class_Odivide(U_2594,U_2596,c_Int_Onumber__class_Onumber__of(U_2594,U_2597))) ) )
| ~ class_Int_Onumber(U_2594)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2594) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
fof(f_877_3,plain,
( ! [U_2595,U_2597,U_2594] :
( ~ c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP275(U_2595,U_2597,U_2594) )
& ! [U_2595,U_2597,U_2594] :
( ~ c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP275(U_2595,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( ~ c_Orderings_Oord__class_Oless(U_2594,U_2596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| ~ sP274(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP274(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( sP275(U_2595,U_2597,U_2594)
| sP274(U_2595,U_2596,U_2597,U_2594)
| ~ sP276(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( ~ c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597))
| ~ sP276(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( ~ c_Orderings_Oord__class_Oless(U_2594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)),U_2596)
| ~ sP273(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597))
| ~ sP273(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Groups_Ozero__class_Ozero(U_2594))
| c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP271(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( c_Orderings_Oord__class_Oless(U_2594,U_2596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| ~ c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP271(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( sP271(U_2595,U_2596,U_2597,U_2594)
| c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597))
| ~ sP272(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( c_Orderings_Oord__class_Oless(U_2594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)),U_2596)
| ~ c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597))
| ~ sP272(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Rings_Oinverse__class_Odivide(U_2594,U_2596,c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| sP276(U_2595,U_2596,U_2597,U_2594)
| sP273(U_2595,U_2596,U_2597,U_2594)
| ~ sP277(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( sP272(U_2595,U_2596,U_2597,U_2594)
| ~ c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Rings_Oinverse__class_Odivide(U_2594,U_2596,c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| ~ sP277(U_2595,U_2596,U_2597,U_2594) )
& ! [U_2595,U_2596,U_2597,U_2594] :
( sP277(U_2595,U_2596,U_2597,U_2594)
| ~ class_Int_Onumber(U_2594)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2594) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271,sP272,sP273,sP274,sP275,sP276,sP277])],[f_877_2]) ).
cnf(f_877_4,plain,
( sP277(U_2595,U_2596,U_2597,U_2594)
| ~ class_Int_Onumber(U_2594)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_5,plain,
( sP272(U_2595,U_2596,U_2597,U_2594)
| ~ c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Rings_Oinverse__class_Odivide(U_2594,U_2596,c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| ~ sP277(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_6,plain,
( c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Rings_Oinverse__class_Odivide(U_2594,U_2596,c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| sP276(U_2595,U_2596,U_2597,U_2594)
| sP273(U_2595,U_2596,U_2597,U_2594)
| ~ sP277(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_7,plain,
( c_Orderings_Oord__class_Oless(U_2594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)),U_2596)
| ~ c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597))
| ~ sP272(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_8,plain,
( sP271(U_2595,U_2596,U_2597,U_2594)
| c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597))
| ~ sP272(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_9,plain,
( c_Orderings_Oord__class_Oless(U_2594,U_2596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| ~ c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP271(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_10,plain,
( c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Groups_Ozero__class_Ozero(U_2594))
| c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP271(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_11,plain,
( c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597))
| ~ sP273(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_2594,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)),U_2596)
| ~ sP273(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2594,c_Groups_Ozero__class_Ozero(U_2594),c_Int_Onumber__class_Onumber__of(U_2594,U_2597))
| ~ sP276(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_14,plain,
( sP275(U_2595,U_2597,U_2594)
| sP274(U_2595,U_2596,U_2597,U_2594)
| ~ sP276(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_15,plain,
( c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP274(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_16,plain,
( ~ c_Orderings_Oord__class_Oless(U_2594,U_2596,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2594),U_2595),c_Int_Onumber__class_Onumber__of(U_2594,U_2597)))
| ~ sP274(U_2595,U_2596,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2594,c_Int_Onumber__class_Onumber__of(U_2594,U_2597),c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP275(U_2595,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
cnf(f_877_18,plain,
( ~ c_Orderings_Oord__class_Oless(U_2594,U_2595,c_Groups_Ozero__class_Ozero(U_2594))
| ~ sP275(U_2595,U_2597,U_2594) ),
inference(clausify,[status(thm)],[f_877_3]) ).
fof(f_878_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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_878_2,plain,
! [U_2600,U_2599,U_2598] :
( c_Orderings_Oord__class_Oless(U_2598,hAPP(hAPP(c_Power_Opower__class_Opower(U_2598),U_2599),c_Nat_OSuc(U_2600)),c_Groups_Oone__class_Oone(U_2598))
| ~ c_Orderings_Oord__class_Oless(U_2598,U_2599,c_Groups_Oone__class_Oone(U_2598))
| ~ c_Orderings_Oord__class_Oless(U_2598,c_Groups_Ozero__class_Ozero(U_2598),U_2599)
| ~ class_Rings_Olinordered__semidom(U_2598) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
fof(f_878_3,plain,
! [U_2598,U_2600,U_2599] :
( c_Orderings_Oord__class_Oless(U_2598,hAPP(hAPP(c_Power_Opower__class_Opower(U_2598),U_2599),c_Nat_OSuc(U_2600)),c_Groups_Oone__class_Oone(U_2598))
| ~ c_Orderings_Oord__class_Oless(U_2598,U_2599,c_Groups_Oone__class_Oone(U_2598))
| ~ c_Orderings_Oord__class_Oless(U_2598,c_Groups_Ozero__class_Ozero(U_2598),U_2599)
| ~ class_Rings_Olinordered__semidom(U_2598) ),
inference(definitional_conversion,[status(esa)],[f_878_2]) ).
cnf(f_878_4,plain,
( c_Orderings_Oord__class_Oless(U_2598,hAPP(hAPP(c_Power_Opower__class_Opower(U_2598),U_2599),c_Nat_OSuc(U_2600)),c_Groups_Oone__class_Oone(U_2598))
| ~ c_Orderings_Oord__class_Oless(U_2598,U_2599,c_Groups_Oone__class_Oone(U_2598))
| ~ c_Orderings_Oord__class_Oless(U_2598,c_Groups_Ozero__class_Ozero(U_2598),U_2599)
| ~ class_Rings_Olinordered__semidom(U_2598) ),
inference(clausify,[status(thm)],[f_878_3]) ).
fof(f_879_1,plain,
! [V_ya_2,V_xa_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_xa_2,V_ya_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_xa_2,V_ya_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_xa_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_ya_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_879_2,plain,
! [U_2604,U_2603,U_2602,U_2601] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2601,hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2603),hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2604))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2603,U_2604) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2603,U_2604)
| ~ c_Orderings_Oord__class_Oless__eq(U_2601,hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2603),hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2604)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2601,c_Groups_Oone__class_Oone(U_2601),U_2602)
| ~ class_Rings_Olinordered__semidom(U_2601) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
fof(f_879_3,plain,
( ! [U_2602,U_2603,U_2601,U_2604] :
( c_Orderings_Oord__class_Oless__eq(U_2601,hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2603),hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2604))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2603,U_2604)
| ~ sP278(U_2602,U_2603,U_2601,U_2604) )
& ! [U_2602,U_2603,U_2601,U_2604] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2603,U_2604)
| ~ c_Orderings_Oord__class_Oless__eq(U_2601,hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2603),hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2604))
| ~ sP278(U_2602,U_2603,U_2601,U_2604) )
& ! [U_2602,U_2603,U_2601,U_2604] :
( sP278(U_2602,U_2603,U_2601,U_2604)
| ~ c_Orderings_Oord__class_Oless(U_2601,c_Groups_Oone__class_Oone(U_2601),U_2602)
| ~ class_Rings_Olinordered__semidom(U_2601) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP278])],[f_879_2]) ).
cnf(f_879_4,plain,
( sP278(U_2602,U_2603,U_2601,U_2604)
| ~ c_Orderings_Oord__class_Oless(U_2601,c_Groups_Oone__class_Oone(U_2601),U_2602)
| ~ class_Rings_Olinordered__semidom(U_2601) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2603,U_2604)
| ~ c_Orderings_Oord__class_Oless__eq(U_2601,hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2603),hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2604))
| ~ sP278(U_2602,U_2603,U_2601,U_2604) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2601,hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2603),hAPP(hAPP(c_Power_Opower__class_Opower(U_2601),U_2602),U_2604))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2603,U_2604)
| ~ sP278(U_2602,U_2603,U_2601,U_2604) ),
inference(clausify,[status(thm)],[f_879_3]) ).
fof(f_880_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),hAPP(hAPP(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_880_2,plain,
! [U_2608,U_2607,U_2606,U_2605] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2607,U_2608)
| ~ c_Orderings_Oord__class_Oless__eq(U_2605,hAPP(hAPP(c_Power_Opower__class_Opower(U_2605),U_2606),U_2607),hAPP(hAPP(c_Power_Opower__class_Opower(U_2605),U_2606),U_2608))
| ~ c_Orderings_Oord__class_Oless(U_2605,c_Groups_Oone__class_Oone(U_2605),U_2606)
| ~ class_Rings_Olinordered__semidom(U_2605) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
fof(f_880_3,plain,
! [U_2607,U_2606,U_2605,U_2608] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2607,U_2608)
| ~ c_Orderings_Oord__class_Oless__eq(U_2605,hAPP(hAPP(c_Power_Opower__class_Opower(U_2605),U_2606),U_2607),hAPP(hAPP(c_Power_Opower__class_Opower(U_2605),U_2606),U_2608))
| ~ c_Orderings_Oord__class_Oless(U_2605,c_Groups_Oone__class_Oone(U_2605),U_2606)
| ~ class_Rings_Olinordered__semidom(U_2605) ),
inference(definitional_conversion,[status(esa)],[f_880_2]) ).
cnf(f_880_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2607,U_2608)
| ~ c_Orderings_Oord__class_Oless__eq(U_2605,hAPP(hAPP(c_Power_Opower__class_Opower(U_2605),U_2606),U_2607),hAPP(hAPP(c_Power_Opower__class_Opower(U_2605),U_2606),U_2608))
| ~ c_Orderings_Oord__class_Oless(U_2605,c_Groups_Oone__class_Oone(U_2605),U_2606)
| ~ class_Rings_Olinordered__semidom(U_2605) ),
inference(clausify,[status(thm)],[f_880_3]) ).
fof(f_881_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_881_2,plain,
! [U_2609] : 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_2609))),
inference(variable_rename,[status(thm)],[f_881_1]) ).
fof(f_881_3,plain,
! [U_2609] : 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_2609))),
inference(definitional_conversion,[status(esa)],[f_881_2]) ).
cnf(f_881_4,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_2609))),
inference(clausify,[status(thm)],[f_881_3]) ).
fof(f_882_1,plain,
! [V_v,V_u,V_y,V_a,V_x,T_a] :
( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_u),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_v),V_y)),V_a)
| c_Groups_Oplus__class_Oplus(T_a,V_u,V_v) != c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_v)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_u)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x,V_a)
| ~ class_Rings_Olinordered__semiring__1__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_convex__bound__lt]) ).
fof(f_882_2,plain,
! [U_2615,U_2614,U_2613,U_2612,U_2611,U_2610] :
( c_Orderings_Oord__class_Oless(U_2610,c_Groups_Oplus__class_Oplus(U_2610,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2610),U_2614),U_2611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2610),U_2615),U_2613)),U_2612)
| c_Groups_Oplus__class_Oplus(U_2610,U_2614,U_2615) != c_Groups_Oone__class_Oone(U_2610)
| ~ c_Orderings_Oord__class_Oless__eq(U_2610,c_Groups_Ozero__class_Ozero(U_2610),U_2615)
| ~ c_Orderings_Oord__class_Oless__eq(U_2610,c_Groups_Ozero__class_Ozero(U_2610),U_2614)
| ~ c_Orderings_Oord__class_Oless(U_2610,U_2613,U_2612)
| ~ c_Orderings_Oord__class_Oless(U_2610,U_2611,U_2612)
| ~ class_Rings_Olinordered__semiring__1__strict(U_2610) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
fof(f_882_3,plain,
! [U_2611,U_2610,U_2612,U_2615,U_2614,U_2613] :
( c_Orderings_Oord__class_Oless(U_2610,c_Groups_Oplus__class_Oplus(U_2610,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2610),U_2614),U_2611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2610),U_2615),U_2613)),U_2612)
| c_Groups_Oplus__class_Oplus(U_2610,U_2614,U_2615) != c_Groups_Oone__class_Oone(U_2610)
| ~ c_Orderings_Oord__class_Oless__eq(U_2610,c_Groups_Ozero__class_Ozero(U_2610),U_2615)
| ~ c_Orderings_Oord__class_Oless__eq(U_2610,c_Groups_Ozero__class_Ozero(U_2610),U_2614)
| ~ c_Orderings_Oord__class_Oless(U_2610,U_2613,U_2612)
| ~ c_Orderings_Oord__class_Oless(U_2610,U_2611,U_2612)
| ~ class_Rings_Olinordered__semiring__1__strict(U_2610) ),
inference(definitional_conversion,[status(esa)],[f_882_2]) ).
cnf(f_882_4,plain,
( c_Orderings_Oord__class_Oless(U_2610,c_Groups_Oplus__class_Oplus(U_2610,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2610),U_2614),U_2611),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2610),U_2615),U_2613)),U_2612)
| c_Groups_Oplus__class_Oplus(U_2610,U_2614,U_2615) != c_Groups_Oone__class_Oone(U_2610)
| ~ c_Orderings_Oord__class_Oless__eq(U_2610,c_Groups_Ozero__class_Ozero(U_2610),U_2615)
| ~ c_Orderings_Oord__class_Oless__eq(U_2610,c_Groups_Ozero__class_Ozero(U_2610),U_2614)
| ~ c_Orderings_Oord__class_Oless(U_2610,U_2613,U_2612)
| ~ c_Orderings_Oord__class_Oless(U_2610,U_2611,U_2612)
| ~ class_Rings_Olinordered__semiring__1__strict(U_2610) ),
inference(clausify,[status(thm)],[f_882_3]) ).
fof(f_883_1,plain,
! [V_a_2,V_w_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_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(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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_w_2)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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_w_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_a_2) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of1]) ).
fof(f_883_2,plain,
! [U_2619,U_2618,U_2617,U_2616] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2616,c_Rings_Oinverse__class_Odivide(U_2616,U_2617,c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2619)
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2616,c_Groups_Ozero__class_Ozero(U_2616),U_2619)
& ~ c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2616,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2617)
& c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2616,U_2617,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)))
& c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_2616,c_Groups_Ozero__class_Ozero(U_2616),U_2619)
| c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2616,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2617)
| ~ c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616)) ) )
| c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2616,U_2617,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)))
| ~ c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2616,c_Rings_Oinverse__class_Odivide(U_2616,U_2617,c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2619) ) )
| ~ class_Int_Onumber(U_2616)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2616) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
fof(f_883_3,plain,
( ! [U_2618,U_2616,U_2619] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2616,c_Groups_Ozero__class_Ozero(U_2616),U_2619)
| ~ sP283(U_2618,U_2616,U_2619) )
& ! [U_2618,U_2616,U_2619] :
( ~ c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616))
| ~ sP283(U_2618,U_2616,U_2619) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2616,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2617)
| ~ sP282(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616))
| ~ sP282(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( sP283(U_2618,U_2616,U_2619)
| sP282(U_2618,U_2616,U_2619,U_2617)
| ~ sP284(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( ~ c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618))
| ~ sP284(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2616,U_2617,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)))
| ~ sP281(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618))
| ~ sP281(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( c_Orderings_Oord__class_Oless__eq(U_2616,c_Groups_Ozero__class_Ozero(U_2616),U_2619)
| c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616))
| ~ sP279(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( c_Orderings_Oord__class_Oless__eq(U_2616,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2617)
| ~ c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616))
| ~ sP279(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( sP279(U_2618,U_2616,U_2619,U_2617)
| c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618))
| ~ sP280(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( c_Orderings_Oord__class_Oless__eq(U_2616,U_2617,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)))
| ~ c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618))
| ~ sP280(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( c_Orderings_Oord__class_Oless__eq(U_2616,c_Rings_Oinverse__class_Odivide(U_2616,U_2617,c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2619)
| sP284(U_2618,U_2616,U_2619,U_2617)
| sP281(U_2618,U_2616,U_2619,U_2617)
| ~ sP285(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( sP280(U_2618,U_2616,U_2619,U_2617)
| ~ c_Orderings_Oord__class_Oless__eq(U_2616,c_Rings_Oinverse__class_Odivide(U_2616,U_2617,c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2619)
| ~ sP285(U_2618,U_2616,U_2619,U_2617) )
& ! [U_2618,U_2616,U_2619,U_2617] :
( sP285(U_2618,U_2616,U_2619,U_2617)
| ~ class_Int_Onumber(U_2616)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2616) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279,sP280,sP281,sP282,sP283,sP284,sP285])],[f_883_2]) ).
cnf(f_883_4,plain,
( sP285(U_2618,U_2616,U_2619,U_2617)
| ~ class_Int_Onumber(U_2616)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2616) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_5,plain,
( sP280(U_2618,U_2616,U_2619,U_2617)
| ~ c_Orderings_Oord__class_Oless__eq(U_2616,c_Rings_Oinverse__class_Odivide(U_2616,U_2617,c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2619)
| ~ sP285(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2616,c_Rings_Oinverse__class_Odivide(U_2616,U_2617,c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2619)
| sP284(U_2618,U_2616,U_2619,U_2617)
| sP281(U_2618,U_2616,U_2619,U_2617)
| ~ sP285(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2616,U_2617,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)))
| ~ c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618))
| ~ sP280(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_8,plain,
( sP279(U_2618,U_2616,U_2619,U_2617)
| c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618))
| ~ sP280(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_2616,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2617)
| ~ c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616))
| ~ sP279(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_2616,c_Groups_Ozero__class_Ozero(U_2616),U_2619)
| c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616))
| ~ sP279(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_11,plain,
( c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618))
| ~ sP281(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2616,U_2617,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)))
| ~ sP281(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2616,c_Groups_Ozero__class_Ozero(U_2616),c_Int_Onumber__class_Onumber__of(U_2616,U_2618))
| ~ sP284(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_14,plain,
( sP283(U_2618,U_2616,U_2619)
| sP282(U_2618,U_2616,U_2619,U_2617)
| ~ sP284(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_15,plain,
( c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616))
| ~ sP282(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_16,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2616,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2616),U_2619),c_Int_Onumber__class_Onumber__of(U_2616,U_2618)),U_2617)
| ~ sP282(U_2618,U_2616,U_2619,U_2617) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2616,c_Int_Onumber__class_Onumber__of(U_2616,U_2618),c_Groups_Ozero__class_Ozero(U_2616))
| ~ sP283(U_2618,U_2616,U_2619) ),
inference(clausify,[status(thm)],[f_883_3]) ).
cnf(f_883_18,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2616,c_Groups_Ozero__class_Ozero(U_2616),U_2619)
| ~ sP283(U_2618,U_2616,U_2619) ),
inference(clausify,[status(thm)],[f_883_3]) ).
fof(f_884_1,plain,
! [V_w_2,V_c_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_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_w_2))
& ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_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_w_2))
| c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2),V_b_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_c_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_divide__le__eq__number__of]) ).
fof(f_884_2,plain,
! [U_2623,U_2622,U_2621,U_2620] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2620,c_Rings_Oinverse__class_Odivide(U_2620,U_2621,U_2622),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2620,c_Groups_Ozero__class_Ozero(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
& ~ c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622),U_2621)
& c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2620,U_2621,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622))
& c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_2620,c_Groups_Ozero__class_Ozero(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622),U_2621)
| ~ c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620)) ) )
| c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622) )
& ( c_Orderings_Oord__class_Oless__eq(U_2620,U_2621,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622))
| ~ c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2620,c_Rings_Oinverse__class_Odivide(U_2620,U_2621,U_2622),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)) ) )
| ~ class_Int_Onumber(U_2620)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2620) ),
inference(variable_rename,[status(thm)],[f_884_1]) ).
fof(f_884_3,plain,
( ! [U_2620,U_2623,U_2622] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2620,c_Groups_Ozero__class_Ozero(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| ~ sP290(U_2620,U_2623,U_2622) )
& ! [U_2620,U_2623,U_2622] :
( ~ c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620))
| ~ sP290(U_2620,U_2623,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622),U_2621)
| ~ sP289(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620))
| ~ sP289(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( sP290(U_2620,U_2623,U_2622)
| sP289(U_2620,U_2623,U_2621,U_2622)
| ~ sP291(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( ~ c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622)
| ~ sP291(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2620,U_2621,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622))
| ~ sP288(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622)
| ~ sP288(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( c_Orderings_Oord__class_Oless__eq(U_2620,c_Groups_Ozero__class_Ozero(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620))
| ~ sP286(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( c_Orderings_Oord__class_Oless__eq(U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622),U_2621)
| ~ c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620))
| ~ sP286(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( sP286(U_2620,U_2623,U_2621,U_2622)
| c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622)
| ~ sP287(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( c_Orderings_Oord__class_Oless__eq(U_2620,U_2621,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622))
| ~ c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622)
| ~ sP287(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( c_Orderings_Oord__class_Oless__eq(U_2620,c_Rings_Oinverse__class_Odivide(U_2620,U_2621,U_2622),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| sP291(U_2620,U_2623,U_2621,U_2622)
| sP288(U_2620,U_2623,U_2621,U_2622)
| ~ sP292(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( sP287(U_2620,U_2623,U_2621,U_2622)
| ~ c_Orderings_Oord__class_Oless__eq(U_2620,c_Rings_Oinverse__class_Odivide(U_2620,U_2621,U_2622),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| ~ sP292(U_2620,U_2623,U_2621,U_2622) )
& ! [U_2620,U_2623,U_2621,U_2622] :
( sP292(U_2620,U_2623,U_2621,U_2622)
| ~ class_Int_Onumber(U_2620)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2620) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286,sP287,sP288,sP289,sP290,sP291,sP292])],[f_884_2]) ).
cnf(f_884_4,plain,
( sP292(U_2620,U_2623,U_2621,U_2622)
| ~ class_Int_Onumber(U_2620)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2620) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_5,plain,
( sP287(U_2620,U_2623,U_2621,U_2622)
| ~ c_Orderings_Oord__class_Oless__eq(U_2620,c_Rings_Oinverse__class_Odivide(U_2620,U_2621,U_2622),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| ~ sP292(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2620,c_Rings_Oinverse__class_Odivide(U_2620,U_2621,U_2622),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| sP291(U_2620,U_2623,U_2621,U_2622)
| sP288(U_2620,U_2623,U_2621,U_2622)
| ~ sP292(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2620,U_2621,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622))
| ~ c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622)
| ~ sP287(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_8,plain,
( sP286(U_2620,U_2623,U_2621,U_2622)
| c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622)
| ~ sP287(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622),U_2621)
| ~ c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620))
| ~ sP286(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_2620,c_Groups_Ozero__class_Ozero(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620))
| ~ sP286(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_11,plain,
( c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622)
| ~ sP288(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2620,U_2621,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622))
| ~ sP288(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2620,c_Groups_Ozero__class_Ozero(U_2620),U_2622)
| ~ sP291(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_14,plain,
( sP290(U_2620,U_2623,U_2622)
| sP289(U_2620,U_2623,U_2621,U_2622)
| ~ sP291(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_15,plain,
( c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620))
| ~ sP289(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_16,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2620,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623)),U_2622),U_2621)
| ~ sP289(U_2620,U_2623,U_2621,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2620,U_2622,c_Groups_Ozero__class_Ozero(U_2620))
| ~ sP290(U_2620,U_2623,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_18,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2620,c_Groups_Ozero__class_Ozero(U_2620),c_Int_Onumber__class_Onumber__of(U_2620,U_2623))
| ~ sP290(U_2620,U_2623,U_2622) ),
inference(clausify,[status(thm)],[f_884_3]) ).
fof(f_885_1,plain,
! [V_c_2,V_b_2,V_w_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
& ~ c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,V_c_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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,c_Groups_Ozero__class_Ozero(T_a),V_c_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_c_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__eq(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Rings_Oinverse__class_Odivide(T_a,V_b_2,V_c_2)) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of]) ).
fof(f_885_2,plain,
! [U_2627,U_2626,U_2625,U_2624] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Rings_Oinverse__class_Odivide(U_2624,U_2626,U_2627))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Groups_Ozero__class_Ozero(U_2624))
& ~ c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2624,U_2626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627))
& c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2624,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627),U_2626)
& c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Groups_Ozero__class_Ozero(U_2624))
| c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2624,U_2626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627))
| ~ c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624)) ) )
| c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627) )
& ( c_Orderings_Oord__class_Oless__eq(U_2624,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627),U_2626)
| ~ c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Rings_Oinverse__class_Odivide(U_2624,U_2626,U_2627)) ) )
| ~ class_Int_Onumber(U_2624)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2624) ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
fof(f_885_3,plain,
( ! [U_2625,U_2624,U_2627] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP297(U_2625,U_2624,U_2627) )
& ! [U_2625,U_2624,U_2627] :
( ~ c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP297(U_2625,U_2624,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2624,U_2626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627))
| ~ sP296(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP296(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( sP297(U_2625,U_2624,U_2627)
| sP296(U_2625,U_2624,U_2626,U_2627)
| ~ sP298(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( ~ c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627)
| ~ sP298(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2624,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627),U_2626)
| ~ sP295(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627)
| ~ sP295(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Groups_Ozero__class_Ozero(U_2624))
| c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP293(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( c_Orderings_Oord__class_Oless__eq(U_2624,U_2626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627))
| ~ c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP293(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( sP293(U_2625,U_2624,U_2626,U_2627)
| c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627)
| ~ sP294(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( c_Orderings_Oord__class_Oless__eq(U_2624,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627),U_2626)
| ~ c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627)
| ~ sP294(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Rings_Oinverse__class_Odivide(U_2624,U_2626,U_2627))
| sP298(U_2625,U_2624,U_2626,U_2627)
| sP295(U_2625,U_2624,U_2626,U_2627)
| ~ sP299(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( sP294(U_2625,U_2624,U_2626,U_2627)
| ~ c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Rings_Oinverse__class_Odivide(U_2624,U_2626,U_2627))
| ~ sP299(U_2625,U_2624,U_2626,U_2627) )
& ! [U_2625,U_2624,U_2626,U_2627] :
( sP299(U_2625,U_2624,U_2626,U_2627)
| ~ class_Int_Onumber(U_2624)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2624) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293,sP294,sP295,sP296,sP297,sP298,sP299])],[f_885_2]) ).
cnf(f_885_4,plain,
( sP299(U_2625,U_2624,U_2626,U_2627)
| ~ class_Int_Onumber(U_2624)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2624) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_5,plain,
( sP294(U_2625,U_2624,U_2626,U_2627)
| ~ c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Rings_Oinverse__class_Odivide(U_2624,U_2626,U_2627))
| ~ sP299(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Rings_Oinverse__class_Odivide(U_2624,U_2626,U_2627))
| sP298(U_2625,U_2624,U_2626,U_2627)
| sP295(U_2625,U_2624,U_2626,U_2627)
| ~ sP299(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2624,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627),U_2626)
| ~ c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627)
| ~ sP294(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_8,plain,
( sP293(U_2625,U_2624,U_2626,U_2627)
| c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627)
| ~ sP294(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_2624,U_2626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627))
| ~ c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP293(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Groups_Ozero__class_Ozero(U_2624))
| c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP293(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_11,plain,
( c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627)
| ~ sP295(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2624,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627),U_2626)
| ~ sP295(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2624,c_Groups_Ozero__class_Ozero(U_2624),U_2627)
| ~ sP298(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_14,plain,
( sP297(U_2625,U_2624,U_2627)
| sP296(U_2625,U_2624,U_2626,U_2627)
| ~ sP298(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_15,plain,
( c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP296(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_16,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2624,U_2626,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2624),c_Int_Onumber__class_Onumber__of(U_2624,U_2625)),U_2627))
| ~ sP296(U_2625,U_2624,U_2626,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2624,U_2627,c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP297(U_2625,U_2624,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_18,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2624,c_Int_Onumber__class_Onumber__of(U_2624,U_2625),c_Groups_Ozero__class_Ozero(U_2624))
| ~ sP297(U_2625,U_2624,U_2627) ),
inference(clausify,[status(thm)],[f_885_3]) ).
fof(f_886_1,plain,
! [V_w_2,V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
& ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
& c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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_w_2)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Int_Onumber__class_Onumber__of(T_a,V_w_2),c_Groups_Ozero__class_Ozero(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_w_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(T_a,V_w_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Rings_Oinverse__class_Odivide(T_a,V_b_2,c_Int_Onumber__class_Onumber__of(T_a,V_w_2))) ) )
| ~ class_Int_Onumber(T_a)
| ~ class_Fields_Olinordered__field__inverse__zero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__divide__eq__number__of1]) ).
fof(f_886_2,plain,
! [U_2631,U_2630,U_2629,U_2628] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Rings_Oinverse__class_Odivide(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| ( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Groups_Ozero__class_Ozero(U_2628))
& ~ c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2628,U_2630,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
& c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628)) ) )
& ~ c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_2628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)),U_2630)
& c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)) ) )
& ( ( ( ( ( c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Groups_Ozero__class_Ozero(U_2628))
| c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2628,U_2630,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| ~ c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628)) ) )
| c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)),U_2630)
| ~ c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Rings_Oinverse__class_Odivide(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(U_2628,U_2631))) ) )
| ~ class_Int_Onumber(U_2628)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2628) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
fof(f_886_3,plain,
( ! [U_2629,U_2628,U_2631] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP304(U_2629,U_2628,U_2631) )
& ! [U_2629,U_2628,U_2631] :
( ~ c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP304(U_2629,U_2628,U_2631) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2628,U_2630,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| ~ sP303(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP303(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( sP304(U_2629,U_2628,U_2631)
| sP303(U_2629,U_2628,U_2631,U_2630)
| ~ sP305(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( ~ c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631))
| ~ sP305(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( ~ c_Orderings_Oord__class_Oless__eq(U_2628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)),U_2630)
| ~ sP302(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631))
| ~ sP302(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Groups_Ozero__class_Ozero(U_2628))
| c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP300(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( c_Orderings_Oord__class_Oless__eq(U_2628,U_2630,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| ~ c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP300(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( sP300(U_2629,U_2628,U_2631,U_2630)
| c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631))
| ~ sP301(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( c_Orderings_Oord__class_Oless__eq(U_2628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)),U_2630)
| ~ c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631))
| ~ sP301(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Rings_Oinverse__class_Odivide(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| sP305(U_2629,U_2628,U_2631,U_2630)
| sP302(U_2629,U_2628,U_2631,U_2630)
| ~ sP306(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( sP301(U_2629,U_2628,U_2631,U_2630)
| ~ c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Rings_Oinverse__class_Odivide(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| ~ sP306(U_2629,U_2628,U_2631,U_2630) )
& ! [U_2629,U_2628,U_2631,U_2630] :
( sP306(U_2629,U_2628,U_2631,U_2630)
| ~ class_Int_Onumber(U_2628)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2628) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP300,sP301,sP302,sP303,sP304,sP305,sP306])],[f_886_2]) ).
cnf(f_886_4,plain,
( sP306(U_2629,U_2628,U_2631,U_2630)
| ~ class_Int_Onumber(U_2628)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2628) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_5,plain,
( sP301(U_2629,U_2628,U_2631,U_2630)
| ~ c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Rings_Oinverse__class_Odivide(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| ~ sP306(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Rings_Oinverse__class_Odivide(U_2628,U_2630,c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| sP305(U_2629,U_2628,U_2631,U_2630)
| sP302(U_2629,U_2628,U_2631,U_2630)
| ~ sP306(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_2628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)),U_2630)
| ~ c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631))
| ~ sP301(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_8,plain,
( sP300(U_2629,U_2628,U_2631,U_2630)
| c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631))
| ~ sP301(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_2628,U_2630,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| ~ c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP300(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Groups_Ozero__class_Ozero(U_2628))
| c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP300(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_11,plain,
( c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631))
| ~ sP302(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2628,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)),U_2630)
| ~ sP302(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_13,plain,
( ~ c_Orderings_Oord__class_Oless(U_2628,c_Groups_Ozero__class_Ozero(U_2628),c_Int_Onumber__class_Onumber__of(U_2628,U_2631))
| ~ sP305(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_14,plain,
( sP304(U_2629,U_2628,U_2631)
| sP303(U_2629,U_2628,U_2631,U_2630)
| ~ sP305(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_15,plain,
( c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP303(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_16,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2628,U_2630,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2628),U_2629),c_Int_Onumber__class_Onumber__of(U_2628,U_2631)))
| ~ sP303(U_2629,U_2628,U_2631,U_2630) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_17,plain,
( ~ c_Orderings_Oord__class_Oless(U_2628,c_Int_Onumber__class_Onumber__of(U_2628,U_2631),c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP304(U_2629,U_2628,U_2631) ),
inference(clausify,[status(thm)],[f_886_3]) ).
cnf(f_886_18,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_2628,U_2629,c_Groups_Ozero__class_Ozero(U_2628))
| ~ sP304(U_2629,U_2628,U_2631) ),
inference(clausify,[status(thm)],[f_886_3]) ).
fof(f_887_1,plain,
! [V_r_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_r_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_r_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_r_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Rings_Oinverse__class_Odivide(T_a,V_r_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_887_2,plain,
! [U_2633,U_2632] :
( ( ( c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),c_Rings_Oinverse__class_Odivide(U_2632,U_2633,c_Int_Onumber__class_Onumber__of(U_2632,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),U_2633) )
& ( c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),U_2633)
| ~ c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),c_Rings_Oinverse__class_Odivide(U_2632,U_2633,c_Int_Onumber__class_Onumber__of(U_2632,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Int_Onumber__ring(U_2632)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2632) ),
inference(variable_rename,[status(thm)],[f_887_1]) ).
fof(f_887_3,plain,
( ! [U_2633,U_2632] :
( c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),c_Rings_Oinverse__class_Odivide(U_2632,U_2633,c_Int_Onumber__class_Onumber__of(U_2632,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),U_2633)
| ~ sP307(U_2633,U_2632) )
& ! [U_2633,U_2632] :
( c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),U_2633)
| ~ c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),c_Rings_Oinverse__class_Odivide(U_2632,U_2633,c_Int_Onumber__class_Onumber__of(U_2632,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ sP307(U_2633,U_2632) )
& ! [U_2633,U_2632] :
( sP307(U_2633,U_2632)
| ~ class_Int_Onumber__ring(U_2632)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2632) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP307])],[f_887_2]) ).
cnf(f_887_4,plain,
( sP307(U_2633,U_2632)
| ~ class_Int_Onumber__ring(U_2632)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2632) ),
inference(clausify,[status(thm)],[f_887_3]) ).
cnf(f_887_5,plain,
( c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),U_2633)
| ~ c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),c_Rings_Oinverse__class_Odivide(U_2632,U_2633,c_Int_Onumber__class_Onumber__of(U_2632,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ sP307(U_2633,U_2632) ),
inference(clausify,[status(thm)],[f_887_3]) ).
cnf(f_887_6,plain,
( c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),c_Rings_Oinverse__class_Odivide(U_2632,U_2633,c_Int_Onumber__class_Onumber__of(U_2632,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2632,c_Groups_Ozero__class_Ozero(U_2632),U_2633)
| ~ sP307(U_2633,U_2632) ),
inference(clausify,[status(thm)],[f_887_3]) ).
fof(f_888_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_888_2,plain,
! [U_2635,U_2634] :
( c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),c_Rings_Oinverse__class_Odivide(U_2634,U_2635,c_Int_Onumber__class_Onumber__of(U_2634,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),U_2635)
| ~ class_Int_Onumber__ring(U_2634)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2634) ),
inference(variable_rename,[status(thm)],[f_888_1]) ).
fof(f_888_3,plain,
! [U_2635,U_2634] :
( c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),c_Rings_Oinverse__class_Odivide(U_2634,U_2635,c_Int_Onumber__class_Onumber__of(U_2634,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),U_2635)
| ~ class_Int_Onumber__ring(U_2634)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2634) ),
inference(definitional_conversion,[status(esa)],[f_888_2]) ).
cnf(f_888_4,plain,
( c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),c_Rings_Oinverse__class_Odivide(U_2634,U_2635,c_Int_Onumber__class_Onumber__of(U_2634,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ c_Orderings_Oord__class_Oless(U_2634,c_Groups_Ozero__class_Ozero(U_2634),U_2635)
| ~ class_Int_Onumber__ring(U_2634)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2634) ),
inference(clausify,[status(thm)],[f_888_3]) ).
fof(f_889_1,plain,
! [V_a,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(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_889_2,plain,
! [U_2637,U_2636] :
( ~ c_Orderings_Oord__class_Oless(U_2636,hAPP(hAPP(c_Power_Opower__class_Opower(U_2636),U_2637),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(U_2636))
| ~ class_Rings_Olinordered__idom(U_2636) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
fof(f_889_3,plain,
! [U_2637,U_2636] :
( ~ c_Orderings_Oord__class_Oless(U_2636,hAPP(hAPP(c_Power_Opower__class_Opower(U_2636),U_2637),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(U_2636))
| ~ class_Rings_Olinordered__idom(U_2636) ),
inference(definitional_conversion,[status(esa)],[f_889_2]) ).
cnf(f_889_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2636,hAPP(hAPP(c_Power_Opower__class_Opower(U_2636),U_2637),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Groups_Ozero__class_Ozero(U_2636))
| ~ class_Rings_Olinordered__idom(U_2636) ),
inference(clausify,[status(thm)],[f_889_3]) ).
fof(f_890_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(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),hAPP(hAPP(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_890_2,plain,
! [U_2639,U_2638] :
( ( ( c_Orderings_Oord__class_Oless(U_2638,c_Groups_Ozero__class_Ozero(U_2638),hAPP(hAPP(c_Power_Opower__class_Opower(U_2638),U_2639),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| U_2639 = c_Groups_Ozero__class_Ozero(U_2638) )
& ( U_2639 != c_Groups_Ozero__class_Ozero(U_2638)
| ~ c_Orderings_Oord__class_Oless(U_2638,c_Groups_Ozero__class_Ozero(U_2638),hAPP(hAPP(c_Power_Opower__class_Opower(U_2638),U_2639),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ) )
| ~ class_Rings_Olinordered__idom(U_2638) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
fof(f_890_3,plain,
( ! [U_2639,U_2638] :
( c_Orderings_Oord__class_Oless(U_2638,c_Groups_Ozero__class_Ozero(U_2638),hAPP(hAPP(c_Power_Opower__class_Opower(U_2638),U_2639),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| U_2639 = c_Groups_Ozero__class_Ozero(U_2638)
| ~ sP308(U_2639,U_2638) )
& ! [U_2639,U_2638] :
( U_2639 != c_Groups_Ozero__class_Ozero(U_2638)
| ~ c_Orderings_Oord__class_Oless(U_2638,c_Groups_Ozero__class_Ozero(U_2638),hAPP(hAPP(c_Power_Opower__class_Opower(U_2638),U_2639),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ sP308(U_2639,U_2638) )
& ! [U_2639,U_2638] :
( sP308(U_2639,U_2638)
| ~ class_Rings_Olinordered__idom(U_2638) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP308])],[f_890_2]) ).
cnf(f_890_4,plain,
( sP308(U_2639,U_2638)
| ~ class_Rings_Olinordered__idom(U_2638) ),
inference(clausify,[status(thm)],[f_890_3]) ).
cnf(f_890_5,plain,
( U_2639 != c_Groups_Ozero__class_Ozero(U_2638)
| ~ c_Orderings_Oord__class_Oless(U_2638,c_Groups_Ozero__class_Ozero(U_2638),hAPP(hAPP(c_Power_Opower__class_Opower(U_2638),U_2639),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ sP308(U_2639,U_2638) ),
inference(clausify,[status(thm)],[f_890_3]) ).
cnf(f_890_6,plain,
( c_Orderings_Oord__class_Oless(U_2638,c_Groups_Ozero__class_Ozero(U_2638),hAPP(hAPP(c_Power_Opower__class_Opower(U_2638),U_2639),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| U_2639 = c_Groups_Ozero__class_Ozero(U_2638)
| ~ sP308(U_2639,U_2638) ),
inference(clausify,[status(thm)],[f_890_3]) ).
fof(f_891_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]) ).
fof(f_891_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(definitional_conversion,[status(esa)],[f_891_1]) ).
cnf(f_891_3,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_891_2]) ).
fof(f_892_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_892_2,plain,
! [U_2641,U_2640] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2640,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2640,U_2641),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_2640,U_2641) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
fof(f_892_3,plain,
! [U_2641,U_2640] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2640,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2640,U_2641),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_2640,U_2641) ),
inference(definitional_conversion,[status(esa)],[f_892_2]) ).
cnf(f_892_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2640,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2640,U_2641),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_2640,U_2641) ),
inference(clausify,[status(thm)],[f_892_3]) ).
fof(f_893_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_893_2,plain,
! [U_2643,U_2642] :
( 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_2642,U_2643),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2643)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2642,U_2643) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
fof(f_893_3,plain,
! [U_2643,U_2642] :
( 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_2642,U_2643),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2643)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2642,U_2643) ),
inference(definitional_conversion,[status(esa)],[f_893_2]) ).
cnf(f_893_4,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_2642,U_2643),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_2643)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2642,U_2643) ),
inference(clausify,[status(thm)],[f_893_3]) ).
fof(f_894_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]) ).
fof(f_894_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(definitional_conversion,[status(esa)],[f_894_1]) ).
cnf(f_894_3,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_894_2]) ).
fof(f_895_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,hAPP(hAPP(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)))),hAPP(hAPP(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_895_2,plain,
! [U_2646,U_2645,U_2644] :
( c_Orderings_Oord__class_Oless(U_2644,U_2645,U_2646)
| ~ c_Orderings_Oord__class_Oless__eq(U_2644,c_Groups_Ozero__class_Ozero(U_2644),U_2646)
| ~ c_Orderings_Oord__class_Oless(U_2644,hAPP(hAPP(c_Power_Opower__class_Opower(U_2644),U_2645),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2644),U_2646),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_2644) ),
inference(variable_rename,[status(thm)],[f_895_1]) ).
fof(f_895_3,plain,
! [U_2645,U_2646,U_2644] :
( c_Orderings_Oord__class_Oless(U_2644,U_2645,U_2646)
| ~ c_Orderings_Oord__class_Oless__eq(U_2644,c_Groups_Ozero__class_Ozero(U_2644),U_2646)
| ~ c_Orderings_Oord__class_Oless(U_2644,hAPP(hAPP(c_Power_Opower__class_Opower(U_2644),U_2645),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2644),U_2646),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_2644) ),
inference(definitional_conversion,[status(esa)],[f_895_2]) ).
cnf(f_895_4,plain,
( c_Orderings_Oord__class_Oless(U_2644,U_2645,U_2646)
| ~ c_Orderings_Oord__class_Oless__eq(U_2644,c_Groups_Ozero__class_Ozero(U_2644),U_2646)
| ~ c_Orderings_Oord__class_Oless(U_2644,hAPP(hAPP(c_Power_Opower__class_Opower(U_2644),U_2645),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2644),U_2646),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Rings_Olinordered__semidom(U_2644) ),
inference(clausify,[status(thm)],[f_895_3]) ).
fof(f_896_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_896_2,plain,
! [U_2647] :
( c_Orderings_Oord__class_Oless(U_2647,c_Groups_Ozero__class_Ozero(U_2647),c_Rings_Oinverse__class_Odivide(U_2647,c_Groups_Oone__class_Oone(U_2647),c_Int_Onumber__class_Onumber__of(U_2647,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_2647)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2647) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
fof(f_896_3,plain,
! [U_2647] :
( c_Orderings_Oord__class_Oless(U_2647,c_Groups_Ozero__class_Ozero(U_2647),c_Rings_Oinverse__class_Odivide(U_2647,c_Groups_Oone__class_Oone(U_2647),c_Int_Onumber__class_Onumber__of(U_2647,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_2647)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2647) ),
inference(definitional_conversion,[status(esa)],[f_896_2]) ).
cnf(f_896_4,plain,
( c_Orderings_Oord__class_Oless(U_2647,c_Groups_Ozero__class_Ozero(U_2647),c_Rings_Oinverse__class_Odivide(U_2647,c_Groups_Oone__class_Oone(U_2647),c_Int_Onumber__class_Onumber__of(U_2647,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
| ~ class_Int_Onumber__ring(U_2647)
| ~ class_Fields_Olinordered__field__inverse__zero(U_2647) ),
inference(clausify,[status(thm)],[f_896_3]) ).
fof(f_897_1,plain,
! [V_y,V_x,T_a] :
( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(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)))),hAPP(hAPP(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_897_2,plain,
! [U_2650,U_2649,U_2648] :
( ~ c_Orderings_Oord__class_Oless(U_2648,c_Groups_Oplus__class_Oplus(U_2648,hAPP(hAPP(c_Power_Opower__class_Opower(U_2648),U_2649),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2648),U_2650),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2648))
| ~ class_Rings_Olinordered__idom(U_2648) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
fof(f_897_3,plain,
! [U_2648,U_2649,U_2650] :
( ~ c_Orderings_Oord__class_Oless(U_2648,c_Groups_Oplus__class_Oplus(U_2648,hAPP(hAPP(c_Power_Opower__class_Opower(U_2648),U_2649),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2648),U_2650),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2648))
| ~ class_Rings_Olinordered__idom(U_2648) ),
inference(definitional_conversion,[status(esa)],[f_897_2]) ).
cnf(f_897_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_2648,c_Groups_Oplus__class_Oplus(U_2648,hAPP(hAPP(c_Power_Opower__class_Opower(U_2648),U_2649),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2648),U_2650),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(U_2648))
| ~ class_Rings_Olinordered__idom(U_2648) ),
inference(clausify,[status(thm)],[f_897_3]) ).
fof(f_898_1,plain,
! [V_ya_2,V_xa_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ( V_ya_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_xa_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_ya_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_xa_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,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_xa_2),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_ya_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_898_2,plain,
! [U_2653,U_2652,U_2651] :
( ( ( c_Orderings_Oord__class_Oless(U_2651,c_Groups_Ozero__class_Ozero(U_2651),c_Groups_Oplus__class_Oplus(U_2651,hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2652),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2653),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ( U_2653 = c_Groups_Ozero__class_Ozero(U_2651)
& U_2652 = c_Groups_Ozero__class_Ozero(U_2651) ) )
& ( U_2653 != c_Groups_Ozero__class_Ozero(U_2651)
| U_2652 != c_Groups_Ozero__class_Ozero(U_2651)
| ~ c_Orderings_Oord__class_Oless(U_2651,c_Groups_Ozero__class_Ozero(U_2651),c_Groups_Oplus__class_Oplus(U_2651,hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2652),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2653),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
| ~ class_Rings_Olinordered__idom(U_2651) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
fof(f_898_3,plain,
( ! [U_2652,U_2651,U_2653] :
( U_2653 = c_Groups_Ozero__class_Ozero(U_2651)
| ~ sP309(U_2652,U_2651,U_2653) )
& ! [U_2652,U_2651,U_2653] :
( U_2652 = c_Groups_Ozero__class_Ozero(U_2651)
| ~ sP309(U_2652,U_2651,U_2653) )
& ! [U_2652,U_2651,U_2653] :
( c_Orderings_Oord__class_Oless(U_2651,c_Groups_Ozero__class_Ozero(U_2651),c_Groups_Oplus__class_Oplus(U_2651,hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2652),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2653),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| sP309(U_2652,U_2651,U_2653)
| ~ sP310(U_2652,U_2651,U_2653) )
& ! [U_2652,U_2651,U_2653] :
( U_2653 != c_Groups_Ozero__class_Ozero(U_2651)
| U_2652 != c_Groups_Ozero__class_Ozero(U_2651)
| ~ c_Orderings_Oord__class_Oless(U_2651,c_Groups_Ozero__class_Ozero(U_2651),c_Groups_Oplus__class_Oplus(U_2651,hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2652),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2653),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP310(U_2652,U_2651,U_2653) )
& ! [U_2652,U_2651,U_2653] :
( sP310(U_2652,U_2651,U_2653)
| ~ class_Rings_Olinordered__idom(U_2651) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP309,sP310])],[f_898_2]) ).
cnf(f_898_4,plain,
( sP310(U_2652,U_2651,U_2653)
| ~ class_Rings_Olinordered__idom(U_2651) ),
inference(clausify,[status(thm)],[f_898_3]) ).
cnf(f_898_5,plain,
( U_2653 != c_Groups_Ozero__class_Ozero(U_2651)
| U_2652 != c_Groups_Ozero__class_Ozero(U_2651)
| ~ c_Orderings_Oord__class_Oless(U_2651,c_Groups_Ozero__class_Ozero(U_2651),c_Groups_Oplus__class_Oplus(U_2651,hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2652),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2653),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ sP310(U_2652,U_2651,U_2653) ),
inference(clausify,[status(thm)],[f_898_3]) ).
cnf(f_898_6,plain,
( c_Orderings_Oord__class_Oless(U_2651,c_Groups_Ozero__class_Ozero(U_2651),c_Groups_Oplus__class_Oplus(U_2651,hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2652),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2651),U_2653),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| sP309(U_2652,U_2651,U_2653)
| ~ sP310(U_2652,U_2651,U_2653) ),
inference(clausify,[status(thm)],[f_898_3]) ).
cnf(f_898_7,plain,
( U_2652 = c_Groups_Ozero__class_Ozero(U_2651)
| ~ sP309(U_2652,U_2651,U_2653) ),
inference(clausify,[status(thm)],[f_898_3]) ).
cnf(f_898_8,plain,
( U_2653 = c_Groups_Ozero__class_Ozero(U_2651)
| ~ sP309(U_2652,U_2651,U_2653) ),
inference(clausify,[status(thm)],[f_898_3]) ).
fof(f_899_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(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_899_2,plain,
! [U_2654] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2654)),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_2654) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
fof(f_899_3,plain,
! [U_2654] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2654)),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_2654) ),
inference(definitional_conversion,[status(esa)],[f_899_2]) ).
cnf(f_899_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_NthRoot_Osqrt(U_2654)),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_2654) ),
inference(clausify,[status(thm)],[f_899_3]) ).
fof(f_900_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_900_2,plain,
! [U_2655] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2655,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),U_2655)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2655) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
fof(f_900_3,plain,
! [U_2655] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2655,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),U_2655)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2655) ),
inference(definitional_conversion,[status(esa)],[f_900_2]) ).
cnf(f_900_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,U_2655,c_NthRoot_Osqrt(c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),U_2655)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2655) ),
inference(clausify,[status(thm)],[f_900_3]) ).
fof(f_901_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(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_901_2,plain,
! [U_2656] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2656),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_2656),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
fof(f_901_3,plain,
! [U_2656] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2656),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_2656),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(definitional_conversion,[status(esa)],[f_901_2]) ).
cnf(f_901_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2656),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_2656),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_901_3]) ).
fof(f_902_1,plain,
! [V_n,V_a,T_a] :
( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Nat_OSuc(hAPP(hAPP(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_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_odd__power__less__zero]) ).
fof(f_902_2,plain,
! [U_2659,U_2658,U_2657] :
( c_Orderings_Oord__class_Oless(U_2657,hAPP(hAPP(c_Power_Opower__class_Opower(U_2657),U_2658),c_Nat_OSuc(hAPP(hAPP(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_2659))),c_Groups_Ozero__class_Ozero(U_2657))
| ~ c_Orderings_Oord__class_Oless(U_2657,U_2658,c_Groups_Ozero__class_Ozero(U_2657))
| ~ class_Rings_Olinordered__idom(U_2657) ),
inference(variable_rename,[status(thm)],[f_902_1]) ).
fof(f_902_3,plain,
! [U_2657,U_2658,U_2659] :
( c_Orderings_Oord__class_Oless(U_2657,hAPP(hAPP(c_Power_Opower__class_Opower(U_2657),U_2658),c_Nat_OSuc(hAPP(hAPP(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_2659))),c_Groups_Ozero__class_Ozero(U_2657))
| ~ c_Orderings_Oord__class_Oless(U_2657,U_2658,c_Groups_Ozero__class_Ozero(U_2657))
| ~ class_Rings_Olinordered__idom(U_2657) ),
inference(definitional_conversion,[status(esa)],[f_902_2]) ).
cnf(f_902_4,plain,
( c_Orderings_Oord__class_Oless(U_2657,hAPP(hAPP(c_Power_Opower__class_Opower(U_2657),U_2658),c_Nat_OSuc(hAPP(hAPP(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_2659))),c_Groups_Ozero__class_Ozero(U_2657))
| ~ c_Orderings_Oord__class_Oless(U_2657,U_2658,c_Groups_Ozero__class_Ozero(U_2657))
| ~ class_Rings_Olinordered__idom(U_2657) ),
inference(clausify,[status(thm)],[f_902_3]) ).
fof(f_903_1,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))))))))),
inference(fof_nnf,[status(thm)],[fact_machin]) ).
fof(f_903_2,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))))))))),
inference(definitional_conversion,[status(esa)],[f_903_1]) ).
cnf(f_903_3,plain,
c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Transcendental_Opi,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),c_Transcendental_Oarctan(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OBit0(c_Int_OBit1(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))))))))))),
inference(clausify,[status(thm)],[f_903_2]) ).
fof(f_904_1,plain,
! [V_real2_2,V_real1_2,V_f1_2,T_a] : c_Complex_Ocomplex_Ocomplex__rec(T_a,V_f1_2,c_Complex_Ocomplex_OComplex(V_real1_2,V_real2_2)) = hAPP(hAPP(V_f1_2,V_real1_2),V_real2_2),
inference(fof_nnf,[status(thm)],[fact_complex_Orecs]) ).
fof(f_904_2,plain,
! [U_2663,U_2662,U_2661,U_2660] : c_Complex_Ocomplex_Ocomplex__rec(U_2660,U_2661,c_Complex_Ocomplex_OComplex(U_2662,U_2663)) = hAPP(hAPP(U_2661,U_2662),U_2663),
inference(variable_rename,[status(thm)],[f_904_1]) ).
fof(f_904_3,plain,
! [U_2662,U_2663,U_2660,U_2661] : c_Complex_Ocomplex_Ocomplex__rec(U_2660,U_2661,c_Complex_Ocomplex_OComplex(U_2662,U_2663)) = hAPP(hAPP(U_2661,U_2662),U_2663),
inference(definitional_conversion,[status(esa)],[f_904_2]) ).
cnf(f_904_4,plain,
c_Complex_Ocomplex_Ocomplex__rec(U_2660,U_2661,c_Complex_Ocomplex_OComplex(U_2662,U_2663)) = hAPP(hAPP(U_2661,U_2662),U_2663),
inference(clausify,[status(thm)],[f_904_3]) ).
fof(f_905_1,plain,
! [V_x] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ 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_natceiling__add__one]) ).
fof(f_905_2,plain,
! [U_2664] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2664,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2664),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2664) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
fof(f_905_3,plain,
! [U_2664] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2664,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2664),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2664) ),
inference(definitional_conversion,[status(esa)],[f_905_2]) ).
cnf(f_905_4,plain,
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2664,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2664),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2664) ),
inference(clausify,[status(thm)],[f_905_3]) ).
fof(f_906_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_906_2,plain,
! [U_2665] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2665,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_906_1]) ).
fof(f_906_3,plain,
! [U_2665] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2665,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_906_2]) ).
cnf(f_906_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2665,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_906_3]) ).
fof(f_907_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_907_2,plain,
! [U_2667,U_2666] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2666),c_Nat_OSuc(U_2667))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2666,U_2667) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
fof(f_907_3,plain,
! [U_2666,U_2667] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2666),c_Nat_OSuc(U_2667))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2666,U_2667) ),
inference(definitional_conversion,[status(esa)],[f_907_2]) ).
cnf(f_907_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2666),c_Nat_OSuc(U_2667))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2666,U_2667) ),
inference(clausify,[status(thm)],[f_907_3]) ).
fof(f_908_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_908_2,plain,
! [U_2668] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2668,c_Nat_OSuc(U_2668)),
inference(variable_rename,[status(thm)],[f_908_1]) ).
fof(f_908_3,plain,
! [U_2668] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2668,c_Nat_OSuc(U_2668)),
inference(definitional_conversion,[status(esa)],[f_908_2]) ).
cnf(f_908_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2668,c_Nat_OSuc(U_2668)),
inference(clausify,[status(thm)],[f_908_3]) ).
fof(f_909_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_909_2,plain,
! [U_2669] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_2669)),
inference(variable_rename,[status(thm)],[f_909_1]) ).
fof(f_909_3,plain,
! [U_2669] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_2669)),
inference(definitional_conversion,[status(esa)],[f_909_2]) ).
cnf(f_909_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_2669)),
inference(clausify,[status(thm)],[f_909_3]) ).
fof(f_910_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_910_2,plain,
! [U_2672,U_2671,U_2670] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2670,U_2672)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2670,U_2671),U_2672) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
fof(f_910_3,plain,
! [U_2671,U_2670,U_2672] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2670,U_2672)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2670,U_2671),U_2672) ),
inference(definitional_conversion,[status(esa)],[f_910_2]) ).
cnf(f_910_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2670,U_2672)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2670,U_2671),U_2672) ),
inference(clausify,[status(thm)],[f_910_3]) ).
fof(f_911_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_911_2,plain,
! [U_2676,U_2675,U_2674,U_2673] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2675,U_2676)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2675,U_2674) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2673,U_2676)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2673,U_2674) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
fof(f_911_3,plain,
! [U_2673,U_2674,U_2675,U_2676] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2675,U_2676)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2675,U_2674) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2673,U_2676)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2673,U_2674) ),
inference(definitional_conversion,[status(esa)],[f_911_2]) ).
cnf(f_911_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2675,U_2676)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2675,U_2674) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2673,U_2676)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2673,U_2674) ),
inference(clausify,[status(thm)],[f_911_3]) ).
fof(f_912_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_912_2,plain,
! [U_2680,U_2679,U_2678,U_2677] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2677,U_2679),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2678,U_2680))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2679,U_2680)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2677,U_2678) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
fof(f_912_3,plain,
! [U_2679,U_2678,U_2677,U_2680] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2677,U_2679),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2678,U_2680))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2679,U_2680)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2677,U_2678) ),
inference(definitional_conversion,[status(esa)],[f_912_2]) ).
cnf(f_912_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2677,U_2679),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2678,U_2680))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2679,U_2680)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2677,U_2678) ),
inference(clausify,[status(thm)],[f_912_3]) ).
fof(f_913_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_913_2,plain,
! [U_2683,U_2682,U_2681] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2681,U_2683),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2682,U_2683))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2681,U_2682) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
fof(f_913_3,plain,
! [U_2683,U_2682,U_2681] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2681,U_2683),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2682,U_2683))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2681,U_2682) ),
inference(definitional_conversion,[status(esa)],[f_913_2]) ).
cnf(f_913_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2681,U_2683),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2682,U_2683))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2681,U_2682) ),
inference(clausify,[status(thm)],[f_913_3]) ).
fof(f_914_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_914_2,plain,
! [U_2686,U_2685,U_2684] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2684,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2686,U_2685))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2684,U_2685) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
fof(f_914_3,plain,
! [U_2685,U_2684,U_2686] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2684,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2686,U_2685))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2684,U_2685) ),
inference(definitional_conversion,[status(esa)],[f_914_2]) ).
cnf(f_914_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2684,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2686,U_2685))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2684,U_2685) ),
inference(clausify,[status(thm)],[f_914_3]) ).
fof(f_915_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_915_2,plain,
! [U_2689,U_2688,U_2687] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2687,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2688,U_2689))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2687,U_2688) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
fof(f_915_3,plain,
! [U_2688,U_2687,U_2689] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2687,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2688,U_2689))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2687,U_2688) ),
inference(definitional_conversion,[status(esa)],[f_915_2]) ).
cnf(f_915_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2687,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2688,U_2689))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2687,U_2688) ),
inference(clausify,[status(thm)],[f_915_3]) ).
fof(f_916_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_916_2,plain,
! [U_2692,U_2691,U_2690] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2690,U_2691),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2690,U_2692))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2691,U_2692) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2691,U_2692)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2690,U_2691),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2690,U_2692)) ) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
fof(f_916_3,plain,
( ! [U_2698,U_2696] :
( ! [U_2694] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2694,U_2696),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2694,U_2698))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2696,U_2698) )
& ! [U_2697,U_2695] :
( ! [U_2693] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2693,U_2695),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2693,U_2697))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2695,U_2697) ) ),
inference(miniscope,[status(thm)],[f_916_2]) ).
fof(f_916_4,plain,
( ! [U_2696,U_2694,U_2698] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2694,U_2696),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2694,U_2698))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2696,U_2698) )
& ! [U_2693,U_2695,U_2697] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2693,U_2695),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2693,U_2697))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2695,U_2697) ) ),
inference(definitional_conversion,[status(esa)],[f_916_3]) ).
cnf(f_916_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2693,U_2695),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2693,U_2697))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2695,U_2697) ),
inference(clausify,[status(thm)],[f_916_4]) ).
cnf(f_916_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2694,U_2696),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2694,U_2698))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2696,U_2698) ),
inference(clausify,[status(thm)],[f_916_4]) ).
fof(f_917_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_917_2,plain,
! [U_2700,U_2699] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2699,U_2700),U_2700),
inference(variable_rename,[status(thm)],[f_917_1]) ).
fof(f_917_3,plain,
! [U_2700,U_2699] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2699,U_2700),U_2700),
inference(definitional_conversion,[status(esa)],[f_917_2]) ).
cnf(f_917_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2699,U_2700),U_2700),
inference(clausify,[status(thm)],[f_917_3]) ).
fof(f_918_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_918_2,plain,
! [U_2702,U_2701] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2701,U_2702),U_2701),
inference(variable_rename,[status(thm)],[f_918_1]) ).
fof(f_918_3,plain,
! [U_2701,U_2702] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2701,U_2702),U_2701),
inference(definitional_conversion,[status(esa)],[f_918_2]) ).
cnf(f_918_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2701,U_2702),U_2701),
inference(clausify,[status(thm)],[f_918_3]) ).
fof(f_919_1,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Opi,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_pi__not__less__zero]) ).
fof(f_919_2,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Opi,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_919_1]) ).
cnf(f_919_3,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Transcendental_Opi,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_919_2]) ).
fof(f_920_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_920_2,plain,
! [U_2703] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_920_1]) ).
fof(f_920_3,plain,
! [U_2703] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_920_2]) ).
cnf(f_920_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2703,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_920_3]) ).
fof(f_921_1,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi),
inference(fof_nnf,[status(thm)],[fact_pi__gt__zero]) ).
fof(f_921_2,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi),
inference(definitional_conversion,[status(esa)],[f_921_1]) ).
cnf(f_921_3,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi),
inference(clausify,[status(thm)],[f_921_2]) ).
fof(f_922_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_922_2,plain,
! [U_2704] :
( ( U_2704 != 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_2704) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2704)
| U_2704 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_922_1]) ).
fof(f_922_3,plain,
( ! [U_2706] :
( U_2706 != 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_2706) )
& ! [U_2705] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2705)
| U_2705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_922_2]) ).
fof(f_922_4,plain,
( ! [U_2706] :
( U_2706 != 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_2706) )
& ! [U_2705] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2705)
| U_2705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_922_3]) ).
cnf(f_922_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2705)
| U_2705 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_922_4]) ).
cnf(f_922_6,plain,
( U_2706 != 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_2706) ),
inference(clausify,[status(thm)],[f_922_4]) ).
fof(f_923_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_923_2,plain,
! [U_2707] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2707,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_923_1]) ).
fof(f_923_3,plain,
! [U_2707] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2707,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_923_2]) ).
cnf(f_923_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2707,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_923_3]) ).
fof(f_924_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_924_2,plain,
! [U_2709,U_2708] :
( U_2709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2708,U_2709) ),
inference(variable_rename,[status(thm)],[f_924_1]) ).
fof(f_924_3,plain,
! [U_2709] :
( ! [U_2708] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2708,U_2709)
| U_2709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_924_2]) ).
fof(f_924_4,plain,
! [U_2708,U_2709] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2708,U_2709)
| U_2709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_924_3]) ).
cnf(f_924_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2708,U_2709)
| U_2709 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_924_4]) ).
fof(f_925_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_925_2,plain,
! [U_2712,U_2711,U_2710] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2710,U_2712),U_2711)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2710,U_2711) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
fof(f_925_3,plain,
! [U_2711,U_2710,U_2712] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2710,U_2712),U_2711)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2710,U_2711) ),
inference(definitional_conversion,[status(esa)],[f_925_2]) ).
cnf(f_925_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2710,U_2712),U_2711)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2710,U_2711) ),
inference(clausify,[status(thm)],[f_925_3]) ).
fof(f_926_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_926_2,plain,
! [U_2715,U_2714,U_2713] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2715,U_2714),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2715,U_2713))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2713,U_2715)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2713,U_2714) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
fof(f_926_3,plain,
! [U_2714,U_2713,U_2715] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2715,U_2714),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2715,U_2713))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2713,U_2715)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2713,U_2714) ),
inference(definitional_conversion,[status(esa)],[f_926_2]) ).
cnf(f_926_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2715,U_2714),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2715,U_2713))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2713,U_2715)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2713,U_2714) ),
inference(clausify,[status(thm)],[f_926_3]) ).
fof(f_927_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_927_2,plain,
! [U_2716] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2716)
| U_2716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_927_1]) ).
fof(f_927_3,plain,
! [U_2716] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2716)
| U_2716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_927_2]) ).
cnf(f_927_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2716)
| U_2716 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_927_3]) ).
fof(f_928_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_928_2,plain,
! [U_2718,U_2717] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2717,U_2718)
| U_2717 = U_2718
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2717,U_2718) )
& ( ( U_2717 != U_2718
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2717,U_2718) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2717,U_2718) ) ),
inference(variable_rename,[status(thm)],[f_928_1]) ).
fof(f_928_3,plain,
( ! [U_2722,U_2720] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2720,U_2722)
| U_2720 = U_2722
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2720,U_2722) )
& ! [U_2721,U_2719] :
( ( U_2719 != U_2721
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2719,U_2721) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2719,U_2721) ) ),
inference(miniscope,[status(thm)],[f_928_2]) ).
fof(f_928_4,plain,
( ! [U_2719,U_2721] :
( U_2719 != U_2721
| ~ sP311(U_2719,U_2721) )
& ! [U_2719,U_2721] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2719,U_2721)
| ~ sP311(U_2719,U_2721) )
& ! [U_2722,U_2720] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2720,U_2722)
| U_2720 = U_2722
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2720,U_2722) )
& ! [U_2719,U_2721] :
( sP311(U_2719,U_2721)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2719,U_2721) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP311])],[f_928_3]) ).
cnf(f_928_5,plain,
( sP311(U_2719,U_2721)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2719,U_2721) ),
inference(clausify,[status(thm)],[f_928_4]) ).
cnf(f_928_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2720,U_2722)
| U_2720 = U_2722
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2720,U_2722) ),
inference(clausify,[status(thm)],[f_928_4]) ).
cnf(f_928_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2719,U_2721)
| ~ sP311(U_2719,U_2721) ),
inference(clausify,[status(thm)],[f_928_4]) ).
cnf(f_928_8,plain,
( U_2719 != U_2721
| ~ sP311(U_2719,U_2721) ),
inference(clausify,[status(thm)],[f_928_4]) ).
fof(f_929_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_929_2,plain,
! [U_2724,U_2723] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2723,U_2724)
| ( U_2723 != U_2724
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2723,U_2724) ) )
& ( U_2723 = U_2724
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2723,U_2724)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2723,U_2724) ) ),
inference(variable_rename,[status(thm)],[f_929_1]) ).
fof(f_929_3,plain,
( ! [U_2728,U_2726] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2726,U_2728)
| ( U_2726 != U_2728
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2726,U_2728) ) )
& ! [U_2727,U_2725] :
( U_2725 = U_2727
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2725,U_2727)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2725,U_2727) ) ),
inference(miniscope,[status(thm)],[f_929_2]) ).
fof(f_929_4,plain,
( ! [U_2728,U_2726] :
( U_2726 != U_2728
| ~ sP312(U_2728,U_2726) )
& ! [U_2728,U_2726] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2726,U_2728)
| ~ sP312(U_2728,U_2726) )
& ! [U_2728,U_2726] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2726,U_2728)
| sP312(U_2728,U_2726) )
& ! [U_2727,U_2725] :
( U_2725 = U_2727
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2725,U_2727)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2725,U_2727) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP312])],[f_929_3]) ).
cnf(f_929_5,plain,
( U_2725 = U_2727
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2725,U_2727)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2725,U_2727) ),
inference(clausify,[status(thm)],[f_929_4]) ).
cnf(f_929_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2726,U_2728)
| sP312(U_2728,U_2726) ),
inference(clausify,[status(thm)],[f_929_4]) ).
cnf(f_929_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2726,U_2728)
| ~ sP312(U_2728,U_2726) ),
inference(clausify,[status(thm)],[f_929_4]) ).
cnf(f_929_8,plain,
( U_2726 != U_2728
| ~ sP312(U_2728,U_2726) ),
inference(clausify,[status(thm)],[f_929_4]) ).
fof(f_930_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_930_2,plain,
! [U_2730,U_2729] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2729,U_2730)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2729,U_2730) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
fof(f_930_3,plain,
! [U_2729,U_2730] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2729,U_2730)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2729,U_2730) ),
inference(definitional_conversion,[status(esa)],[f_930_2]) ).
cnf(f_930_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2729,U_2730)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2729,U_2730) ),
inference(clausify,[status(thm)],[f_930_3]) ).
fof(f_931_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_931_2,plain,
! [U_2732,U_2731] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2731,U_2732)
| U_2731 = U_2732
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2731,U_2732) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
fof(f_931_3,plain,
! [U_2731,U_2732] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2731,U_2732)
| U_2731 = U_2732
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2731,U_2732) ),
inference(definitional_conversion,[status(esa)],[f_931_2]) ).
cnf(f_931_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2731,U_2732)
| U_2731 = U_2732
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2731,U_2732) ),
inference(clausify,[status(thm)],[f_931_3]) ).
fof(f_932_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_932_2,plain,
! [U_2734,U_2733] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2733,U_2734)
| ( U_2733 != U_2734
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2733,U_2734) ) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
fof(f_932_3,plain,
( ! [U_2734,U_2733] :
( U_2733 != U_2734
| ~ sP313(U_2734,U_2733) )
& ! [U_2734,U_2733] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2733,U_2734)
| ~ sP313(U_2734,U_2733) )
& ! [U_2734,U_2733] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2733,U_2734)
| sP313(U_2734,U_2733) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP313])],[f_932_2]) ).
cnf(f_932_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2733,U_2734)
| sP313(U_2734,U_2733) ),
inference(clausify,[status(thm)],[f_932_3]) ).
cnf(f_932_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2733,U_2734)
| ~ sP313(U_2734,U_2733) ),
inference(clausify,[status(thm)],[f_932_3]) ).
cnf(f_932_6,plain,
( U_2733 != U_2734
| ~ sP313(U_2734,U_2733) ),
inference(clausify,[status(thm)],[f_932_3]) ).
fof(f_933_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_933_2,plain,
! [U_2735] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2735,U_2735),
inference(variable_rename,[status(thm)],[f_933_1]) ).
fof(f_933_3,plain,
! [U_2735] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2735,U_2735),
inference(definitional_conversion,[status(esa)],[f_933_2]) ).
cnf(f_933_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2735,U_2735),
inference(clausify,[status(thm)],[f_933_3]) ).
fof(f_934_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_934_2,plain,
! [U_2737,U_2736] :
( ( U_2736 != U_2737
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2737,U_2736)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2736,U_2737) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2737,U_2736)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2736,U_2737)
| U_2736 = U_2737 ) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
fof(f_934_3,plain,
( ! [U_2741,U_2739] :
( U_2739 != U_2741
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2741,U_2739)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2739,U_2741) ) )
& ! [U_2740,U_2738] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2740,U_2738)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2738,U_2740)
| U_2738 = U_2740 ) ),
inference(miniscope,[status(thm)],[f_934_2]) ).
fof(f_934_4,plain,
( ! [U_2739,U_2741] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2741,U_2739)
| ~ sP314(U_2739,U_2741) )
& ! [U_2739,U_2741] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2739,U_2741)
| ~ sP314(U_2739,U_2741) )
& ! [U_2739,U_2741] :
( U_2739 != U_2741
| sP314(U_2739,U_2741) )
& ! [U_2738,U_2740] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2740,U_2738)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2738,U_2740)
| U_2738 = U_2740 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP314])],[f_934_3]) ).
cnf(f_934_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2740,U_2738)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2738,U_2740)
| U_2738 = U_2740 ),
inference(clausify,[status(thm)],[f_934_4]) ).
cnf(f_934_6,plain,
( U_2739 != U_2741
| sP314(U_2739,U_2741) ),
inference(clausify,[status(thm)],[f_934_4]) ).
cnf(f_934_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2739,U_2741)
| ~ sP314(U_2739,U_2741) ),
inference(clausify,[status(thm)],[f_934_4]) ).
cnf(f_934_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2741,U_2739)
| ~ sP314(U_2739,U_2741) ),
inference(clausify,[status(thm)],[f_934_4]) ).
fof(f_935_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_935_2,plain,
! [U_2743,U_2742] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2743,U_2742)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2742,U_2743)
| U_2742 = U_2743 ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
fof(f_935_3,plain,
! [U_2743,U_2742] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2743,U_2742)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2742,U_2743)
| U_2742 = U_2743 ),
inference(definitional_conversion,[status(esa)],[f_935_2]) ).
cnf(f_935_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2743,U_2742)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2742,U_2743)
| U_2742 = U_2743 ),
inference(clausify,[status(thm)],[f_935_3]) ).
fof(f_936_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_936_2,plain,
! [U_2744] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2744,U_2744),
inference(variable_rename,[status(thm)],[f_936_1]) ).
fof(f_936_3,plain,
! [U_2744] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2744,U_2744),
inference(definitional_conversion,[status(esa)],[f_936_2]) ).
cnf(f_936_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2744,U_2744),
inference(clausify,[status(thm)],[f_936_3]) ).
fof(f_937_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_937_2,plain,
! [U_2746,U_2745] :
( U_2746 != U_2745
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2745,U_2746) ),
inference(variable_rename,[status(thm)],[f_937_1]) ).
fof(f_937_3,plain,
! [U_2745,U_2746] :
( U_2746 != U_2745
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2745,U_2746) ),
inference(definitional_conversion,[status(esa)],[f_937_2]) ).
cnf(f_937_4,plain,
( U_2746 != U_2745
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2745,U_2746) ),
inference(clausify,[status(thm)],[f_937_3]) ).
fof(f_938_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_938_2,plain,
! [U_2748,U_2747] :
( U_2747 != U_2748
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2747,U_2748) ),
inference(variable_rename,[status(thm)],[f_938_1]) ).
fof(f_938_3,plain,
! [U_2748,U_2747] :
( U_2747 != U_2748
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2747,U_2748) ),
inference(definitional_conversion,[status(esa)],[f_938_2]) ).
cnf(f_938_4,plain,
( U_2747 != U_2748
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2747,U_2748) ),
inference(clausify,[status(thm)],[f_938_3]) ).
fof(f_939_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_939_2,plain,
! [U_2751,U_2750,U_2749] :
( hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
| ( ~ hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2750,U_2749) )
| ( ~ hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
& U_2749 = U_2750 )
| ( ~ hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2749,U_2750) ) ),
inference(variable_rename,[status(thm)],[f_939_1]) ).
fof(f_939_3,plain,
( ! [U_2749,U_2750,U_2751] :
( ~ hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
| ~ sP317(U_2749,U_2750,U_2751) )
& ! [U_2749,U_2750,U_2751] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2750,U_2749)
| ~ sP317(U_2749,U_2750,U_2751) )
& ! [U_2749,U_2750,U_2751] :
( ~ hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
| ~ sP316(U_2749,U_2750,U_2751) )
& ! [U_2749,U_2750,U_2751] :
( U_2749 = U_2750
| ~ sP316(U_2749,U_2750,U_2751) )
& ! [U_2749,U_2750,U_2751] :
( ~ hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
| ~ sP315(U_2749,U_2750,U_2751) )
& ! [U_2749,U_2750,U_2751] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2749,U_2750)
| ~ sP315(U_2749,U_2750,U_2751) )
& ! [U_2749,U_2750,U_2751] :
( hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
| sP317(U_2749,U_2750,U_2751)
| sP316(U_2749,U_2750,U_2751)
| sP315(U_2749,U_2750,U_2751) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP315,sP316,sP317])],[f_939_2]) ).
cnf(f_939_4,plain,
( hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
| sP317(U_2749,U_2750,U_2751)
| sP316(U_2749,U_2750,U_2751)
| sP315(U_2749,U_2750,U_2751) ),
inference(clausify,[status(thm)],[f_939_3]) ).
cnf(f_939_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2749,U_2750)
| ~ sP315(U_2749,U_2750,U_2751) ),
inference(clausify,[status(thm)],[f_939_3]) ).
cnf(f_939_6,plain,
( ~ hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
| ~ sP315(U_2749,U_2750,U_2751) ),
inference(clausify,[status(thm)],[f_939_3]) ).
cnf(f_939_7,plain,
( U_2749 = U_2750
| ~ sP316(U_2749,U_2750,U_2751) ),
inference(clausify,[status(thm)],[f_939_3]) ).
cnf(f_939_8,plain,
( ~ hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
| ~ sP316(U_2749,U_2750,U_2751) ),
inference(clausify,[status(thm)],[f_939_3]) ).
cnf(f_939_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2750,U_2749)
| ~ sP317(U_2749,U_2750,U_2751) ),
inference(clausify,[status(thm)],[f_939_3]) ).
cnf(f_939_10,plain,
( ~ hBOOL(hAPP(hAPP(U_2751,U_2750),U_2749))
| ~ sP317(U_2749,U_2750,U_2751) ),
inference(clausify,[status(thm)],[f_939_3]) ).
fof(f_940_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_940_2,plain,
! [U_2753,U_2752] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2752,U_2753)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2752),c_Nat_OSuc(U_2753)) ),
inference(variable_rename,[status(thm)],[f_940_1]) ).
fof(f_940_3,plain,
! [U_2753,U_2752] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2752,U_2753)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2752),c_Nat_OSuc(U_2753)) ),
inference(definitional_conversion,[status(esa)],[f_940_2]) ).
cnf(f_940_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2752,U_2753)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2752),c_Nat_OSuc(U_2753)) ),
inference(clausify,[status(thm)],[f_940_3]) ).
fof(f_941_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_941_2,plain,
! [U_2755,U_2754] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2754,U_2755)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2754),U_2755) ),
inference(variable_rename,[status(thm)],[f_941_1]) ).
fof(f_941_3,plain,
! [U_2754,U_2755] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2754,U_2755)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2754),U_2755) ),
inference(definitional_conversion,[status(esa)],[f_941_2]) ).
cnf(f_941_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2754,U_2755)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2754),U_2755) ),
inference(clausify,[status(thm)],[f_941_3]) ).
fof(f_942_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_942_2,plain,
! [U_2757,U_2756] :
( U_2756 = U_2757
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2756,U_2757)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2756,c_Nat_OSuc(U_2757)) ),
inference(variable_rename,[status(thm)],[f_942_1]) ).
fof(f_942_3,plain,
! [U_2757,U_2756] :
( U_2756 = U_2757
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2756,U_2757)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2756,c_Nat_OSuc(U_2757)) ),
inference(definitional_conversion,[status(esa)],[f_942_2]) ).
cnf(f_942_4,plain,
( U_2756 = U_2757
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2756,U_2757)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2756,c_Nat_OSuc(U_2757)) ),
inference(clausify,[status(thm)],[f_942_3]) ).
fof(f_943_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_943_2,plain,
! [U_2760,U_2759,U_2758] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2758),U_2760)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2759,U_2760)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2758,U_2759) ),
inference(variable_rename,[status(thm)],[f_943_1]) ).
fof(f_943_3,plain,
! [U_2758,U_2759,U_2760] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2758),U_2760)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2759,U_2760)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2758,U_2759) ),
inference(definitional_conversion,[status(esa)],[f_943_2]) ).
cnf(f_943_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2758),U_2760)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2759,U_2760)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2758,U_2759) ),
inference(clausify,[status(thm)],[f_943_3]) ).
fof(f_944_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_944_2,plain,
! [U_2762,U_2761] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2761),U_2762)
| c_Nat_OSuc(U_2761) = U_2762
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2761,U_2762) ),
inference(variable_rename,[status(thm)],[f_944_1]) ).
fof(f_944_3,plain,
! [U_2762,U_2761] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2761),U_2762)
| c_Nat_OSuc(U_2761) = U_2762
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2761,U_2762) ),
inference(definitional_conversion,[status(esa)],[f_944_2]) ).
cnf(f_944_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2761),U_2762)
| c_Nat_OSuc(U_2761) = U_2762
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2761,U_2762) ),
inference(clausify,[status(thm)],[f_944_3]) ).
fof(f_945_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_945_2,plain,
! [U_2764,U_2763] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2763,c_Nat_OSuc(U_2764))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2763,U_2764) ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
fof(f_945_3,plain,
! [U_2764,U_2763] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2763,c_Nat_OSuc(U_2764))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2763,U_2764) ),
inference(definitional_conversion,[status(esa)],[f_945_2]) ).
cnf(f_945_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2763,c_Nat_OSuc(U_2764))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2763,U_2764) ),
inference(clausify,[status(thm)],[f_945_3]) ).
fof(f_946_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_946_2,plain,
! [U_2766,U_2765] :
( U_2766 = U_2765
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2765,c_Nat_OSuc(U_2766))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2765,U_2766) ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
fof(f_946_3,plain,
! [U_2766,U_2765] :
( U_2766 = U_2765
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2765,c_Nat_OSuc(U_2766))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2765,U_2766) ),
inference(definitional_conversion,[status(esa)],[f_946_2]) ).
cnf(f_946_4,plain,
( U_2766 = U_2765
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2765,c_Nat_OSuc(U_2766))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2765,U_2766) ),
inference(clausify,[status(thm)],[f_946_3]) ).
fof(f_947_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_947_2,plain,
! [U_2768,U_2767] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2767,c_Nat_OSuc(U_2768))
| U_2767 != U_2768 )
& ( U_2767 = U_2768
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2767,c_Nat_OSuc(U_2768)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2767,U_2768) ),
inference(variable_rename,[status(thm)],[f_947_1]) ).
fof(f_947_3,plain,
( ! [U_2768,U_2767] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2767,c_Nat_OSuc(U_2768))
| U_2767 != U_2768
| ~ sP318(U_2768,U_2767) )
& ! [U_2768,U_2767] :
( U_2767 = U_2768
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2767,c_Nat_OSuc(U_2768))
| ~ sP318(U_2768,U_2767) )
& ! [U_2768,U_2767] :
( sP318(U_2768,U_2767)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2767,U_2768) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP318])],[f_947_2]) ).
cnf(f_947_4,plain,
( sP318(U_2768,U_2767)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2767,U_2768) ),
inference(clausify,[status(thm)],[f_947_3]) ).
cnf(f_947_5,plain,
( U_2767 = U_2768
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2767,c_Nat_OSuc(U_2768))
| ~ sP318(U_2768,U_2767) ),
inference(clausify,[status(thm)],[f_947_3]) ).
cnf(f_947_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2767,c_Nat_OSuc(U_2768))
| U_2767 != U_2768
| ~ sP318(U_2768,U_2767) ),
inference(clausify,[status(thm)],[f_947_3]) ).
fof(f_948_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_948_2,plain,
! [U_2770,U_2769] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2769),c_Nat_OSuc(U_2770))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2769,U_2770) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2769,U_2770)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2769),c_Nat_OSuc(U_2770)) ) ),
inference(variable_rename,[status(thm)],[f_948_1]) ).
fof(f_948_3,plain,
( ! [U_2774,U_2772] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2772),c_Nat_OSuc(U_2774))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2772,U_2774) )
& ! [U_2773,U_2771] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2771,U_2773)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2771),c_Nat_OSuc(U_2773)) ) ),
inference(miniscope,[status(thm)],[f_948_2]) ).
fof(f_948_4,plain,
( ! [U_2772,U_2774] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2772),c_Nat_OSuc(U_2774))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2772,U_2774) )
& ! [U_2771,U_2773] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2771,U_2773)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2771),c_Nat_OSuc(U_2773)) ) ),
inference(definitional_conversion,[status(esa)],[f_948_3]) ).
cnf(f_948_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2771,U_2773)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2771),c_Nat_OSuc(U_2773)) ),
inference(clausify,[status(thm)],[f_948_4]) ).
cnf(f_948_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2772),c_Nat_OSuc(U_2774))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2772,U_2774) ),
inference(clausify,[status(thm)],[f_948_4]) ).
fof(f_949_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_949_2,plain,
! [U_2776,U_2775] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2775,c_Nat_OSuc(U_2776))
| ( U_2775 != U_2776
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2775,U_2776) ) )
& ( U_2775 = U_2776
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2775,U_2776)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2775,c_Nat_OSuc(U_2776)) ) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
fof(f_949_3,plain,
( ! [U_2780,U_2778] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,c_Nat_OSuc(U_2780))
| ( U_2778 != U_2780
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,U_2780) ) )
& ! [U_2779,U_2777] :
( U_2777 = U_2779
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,U_2779)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,c_Nat_OSuc(U_2779)) ) ),
inference(miniscope,[status(thm)],[f_949_2]) ).
fof(f_949_4,plain,
( ! [U_2780,U_2778] :
( U_2778 != U_2780
| ~ sP319(U_2780,U_2778) )
& ! [U_2780,U_2778] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,U_2780)
| ~ sP319(U_2780,U_2778) )
& ! [U_2780,U_2778] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,c_Nat_OSuc(U_2780))
| sP319(U_2780,U_2778) )
& ! [U_2777,U_2779] :
( U_2777 = U_2779
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,U_2779)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,c_Nat_OSuc(U_2779)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP319])],[f_949_3]) ).
cnf(f_949_5,plain,
( U_2777 = U_2779
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,U_2779)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2777,c_Nat_OSuc(U_2779)) ),
inference(clausify,[status(thm)],[f_949_4]) ).
cnf(f_949_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,c_Nat_OSuc(U_2780))
| sP319(U_2780,U_2778) ),
inference(clausify,[status(thm)],[f_949_4]) ).
cnf(f_949_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2778,U_2780)
| ~ sP319(U_2780,U_2778) ),
inference(clausify,[status(thm)],[f_949_4]) ).
cnf(f_949_8,plain,
( U_2778 != U_2780
| ~ sP319(U_2780,U_2778) ),
inference(clausify,[status(thm)],[f_949_4]) ).
fof(f_950_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_950_2,plain,
! [U_2782,U_2781] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2781,U_2782)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2782,c_Nat_OSuc(U_2781)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2782,c_Nat_OSuc(U_2781))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2781,U_2782) ) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
fof(f_950_3,plain,
( ! [U_2786,U_2784] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2784,U_2786)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2786,c_Nat_OSuc(U_2784)) )
& ! [U_2785,U_2783] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2785,c_Nat_OSuc(U_2783))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2783,U_2785) ) ),
inference(miniscope,[status(thm)],[f_950_2]) ).
fof(f_950_4,plain,
( ! [U_2784,U_2786] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2784,U_2786)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2786,c_Nat_OSuc(U_2784)) )
& ! [U_2785,U_2783] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2785,c_Nat_OSuc(U_2783))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2783,U_2785) ) ),
inference(definitional_conversion,[status(esa)],[f_950_3]) ).
cnf(f_950_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2785,c_Nat_OSuc(U_2783))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2783,U_2785) ),
inference(clausify,[status(thm)],[f_950_4]) ).
cnf(f_950_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2784,U_2786)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2786,c_Nat_OSuc(U_2784)) ),
inference(clausify,[status(thm)],[f_950_4]) ).
fof(f_951_1,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(fof_nnf,[status(thm)],[fact_rel__simps_I7_J]) ).
fof(f_951_2,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(definitional_conversion,[status(esa)],[f_951_1]) ).
cnf(f_951_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OMin,c_Int_OMin),
inference(clausify,[status(thm)],[f_951_2]) ).
fof(f_952_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_952_2,plain,
! [U_2788,U_2787] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2788,U_2787)
| U_2787 = U_2788
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2787,U_2788) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
fof(f_952_3,plain,
! [U_2788,U_2787] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2788,U_2787)
| U_2787 = U_2788
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2787,U_2788) ),
inference(definitional_conversion,[status(esa)],[f_952_2]) ).
cnf(f_952_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2788,U_2787)
| U_2787 = U_2788
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2787,U_2788) ),
inference(clausify,[status(thm)],[f_952_3]) ).
fof(f_953_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_953_2,plain,
! [U_2790,U_2789] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2789),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2790))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2789,U_2790) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2789,U_2790)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2789),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2790)) ) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
fof(f_953_3,plain,
( ! [U_2794,U_2792] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2792),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2794))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2792,U_2794) )
& ! [U_2793,U_2791] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2791,U_2793)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2791),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2793)) ) ),
inference(miniscope,[status(thm)],[f_953_2]) ).
fof(f_953_4,plain,
( ! [U_2792,U_2794] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2792),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2794))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2792,U_2794) )
& ! [U_2793,U_2791] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2791,U_2793)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2791),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2793)) ) ),
inference(definitional_conversion,[status(esa)],[f_953_3]) ).
cnf(f_953_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2791,U_2793)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2791),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2793)) ),
inference(clausify,[status(thm)],[f_953_4]) ).
cnf(f_953_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2792),c_Int_Onumber__class_Onumber__of(tc_Int_Oint,U_2794))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2792,U_2794) ),
inference(clausify,[status(thm)],[f_953_4]) ).
fof(f_954_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_954_2,plain,
! [U_2797,U_2796,U_2795] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2795,U_2797),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2796,U_2797))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2795,U_2796) ),
inference(variable_rename,[status(thm)],[f_954_1]) ).
fof(f_954_3,plain,
! [U_2796,U_2795,U_2797] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2795,U_2797),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2796,U_2797))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2795,U_2796) ),
inference(definitional_conversion,[status(esa)],[f_954_2]) ).
cnf(f_954_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2795,U_2797),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2796,U_2797))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2795,U_2796) ),
inference(clausify,[status(thm)],[f_954_3]) ).
fof(f_955_1,plain,
! [V_w_2,V_za_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_w_2)
| V_za_2 = V_w_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_w_2) )
& ( ( V_za_2 != V_w_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_za_2,V_w_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_za_2,V_w_2) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__le]) ).
fof(f_955_2,plain,
! [U_2799,U_2798] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2798,U_2799)
| U_2798 = U_2799
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2798,U_2799) )
& ( ( U_2798 != U_2799
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2798,U_2799) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2798,U_2799) ) ),
inference(variable_rename,[status(thm)],[f_955_1]) ).
fof(f_955_3,plain,
( ! [U_2803,U_2801] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2801,U_2803)
| U_2801 = U_2803
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2801,U_2803) )
& ! [U_2802,U_2800] :
( ( U_2800 != U_2802
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2800,U_2802) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2800,U_2802) ) ),
inference(miniscope,[status(thm)],[f_955_2]) ).
fof(f_955_4,plain,
( ! [U_2800,U_2802] :
( U_2800 != U_2802
| ~ sP320(U_2800,U_2802) )
& ! [U_2800,U_2802] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2800,U_2802)
| ~ sP320(U_2800,U_2802) )
& ! [U_2803,U_2801] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2801,U_2803)
| U_2801 = U_2803
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2801,U_2803) )
& ! [U_2800,U_2802] :
( sP320(U_2800,U_2802)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2800,U_2802) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP320])],[f_955_3]) ).
cnf(f_955_5,plain,
( sP320(U_2800,U_2802)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2800,U_2802) ),
inference(clausify,[status(thm)],[f_955_4]) ).
cnf(f_955_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2801,U_2803)
| U_2801 = U_2803
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2801,U_2803) ),
inference(clausify,[status(thm)],[f_955_4]) ).
cnf(f_955_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2800,U_2802)
| ~ sP320(U_2800,U_2802) ),
inference(clausify,[status(thm)],[f_955_4]) ).
cnf(f_955_8,plain,
( U_2800 != U_2802
| ~ sP320(U_2800,U_2802) ),
inference(clausify,[status(thm)],[f_955_4]) ).
fof(f_956_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_956_2,plain,
! [U_2805,U_2804] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2804),c_Int_OBit0(U_2805))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2804,U_2805) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2804,U_2805)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2804),c_Int_OBit0(U_2805)) ) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
fof(f_956_3,plain,
( ! [U_2809,U_2807] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2807),c_Int_OBit0(U_2809))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2807,U_2809) )
& ! [U_2808,U_2806] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2806,U_2808)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2806),c_Int_OBit0(U_2808)) ) ),
inference(miniscope,[status(thm)],[f_956_2]) ).
fof(f_956_4,plain,
( ! [U_2807,U_2809] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2807),c_Int_OBit0(U_2809))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2807,U_2809) )
& ! [U_2806,U_2808] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2806,U_2808)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2806),c_Int_OBit0(U_2808)) ) ),
inference(definitional_conversion,[status(esa)],[f_956_3]) ).
cnf(f_956_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2806,U_2808)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2806),c_Int_OBit0(U_2808)) ),
inference(clausify,[status(thm)],[f_956_4]) ).
cnf(f_956_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2807),c_Int_OBit0(U_2809))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2807,U_2809) ),
inference(clausify,[status(thm)],[f_956_4]) ).
fof(f_957_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_957_2,plain,
! [U_2811,U_2810] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2810),c_Int_OBit0(U_2811))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2810,U_2811) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2810,U_2811)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2810),c_Int_OBit0(U_2811)) ) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
fof(f_957_3,plain,
( ! [U_2815,U_2813] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2813),c_Int_OBit0(U_2815))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2813,U_2815) )
& ! [U_2814,U_2812] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2812,U_2814)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2812),c_Int_OBit0(U_2814)) ) ),
inference(miniscope,[status(thm)],[f_957_2]) ).
fof(f_957_4,plain,
( ! [U_2813,U_2815] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2813),c_Int_OBit0(U_2815))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2813,U_2815) )
& ! [U_2812,U_2814] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2812,U_2814)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2812),c_Int_OBit0(U_2814)) ) ),
inference(definitional_conversion,[status(esa)],[f_957_3]) ).
cnf(f_957_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2812,U_2814)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2812),c_Int_OBit0(U_2814)) ),
inference(clausify,[status(thm)],[f_957_4]) ).
cnf(f_957_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2813),c_Int_OBit0(U_2815))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2813,U_2815) ),
inference(clausify,[status(thm)],[f_957_4]) ).
fof(f_958_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]) ).
fof(f_958_2,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(definitional_conversion,[status(esa)],[f_958_1]) ).
cnf(f_958_3,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OPls),
inference(clausify,[status(thm)],[f_958_2]) ).
fof(f_959_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_959_2,plain,
! [U_2817,U_2816] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2816),c_Int_OBit1(U_2817))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2816,U_2817) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2816,U_2817)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2816),c_Int_OBit1(U_2817)) ) ),
inference(variable_rename,[status(thm)],[f_959_1]) ).
fof(f_959_3,plain,
( ! [U_2821,U_2819] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2819),c_Int_OBit1(U_2821))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2819,U_2821) )
& ! [U_2820,U_2818] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2818,U_2820)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2818),c_Int_OBit1(U_2820)) ) ),
inference(miniscope,[status(thm)],[f_959_2]) ).
fof(f_959_4,plain,
( ! [U_2819,U_2821] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2819),c_Int_OBit1(U_2821))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2819,U_2821) )
& ! [U_2820,U_2818] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2818,U_2820)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2818),c_Int_OBit1(U_2820)) ) ),
inference(definitional_conversion,[status(esa)],[f_959_3]) ).
cnf(f_959_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2818,U_2820)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2818),c_Int_OBit1(U_2820)) ),
inference(clausify,[status(thm)],[f_959_4]) ).
cnf(f_959_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2819),c_Int_OBit1(U_2821))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2819,U_2821) ),
inference(clausify,[status(thm)],[f_959_4]) ).
fof(f_960_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_960_2,plain,
! [U_2823,U_2822] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2822),c_Int_OBit1(U_2823))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2822,U_2823) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2822,U_2823)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2822),c_Int_OBit1(U_2823)) ) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
fof(f_960_3,plain,
( ! [U_2827,U_2825] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2825),c_Int_OBit1(U_2827))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2825,U_2827) )
& ! [U_2826,U_2824] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2824,U_2826)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2824),c_Int_OBit1(U_2826)) ) ),
inference(miniscope,[status(thm)],[f_960_2]) ).
fof(f_960_4,plain,
( ! [U_2825,U_2827] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2825),c_Int_OBit1(U_2827))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2825,U_2827) )
& ! [U_2826,U_2824] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2824,U_2826)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2824),c_Int_OBit1(U_2826)) ) ),
inference(definitional_conversion,[status(esa)],[f_960_3]) ).
cnf(f_960_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2824,U_2826)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2824),c_Int_OBit1(U_2826)) ),
inference(clausify,[status(thm)],[f_960_4]) ).
cnf(f_960_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2825),c_Int_OBit1(U_2827))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2825,U_2827) ),
inference(clausify,[status(thm)],[f_960_4]) ).
fof(f_961_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_961_2,plain,
! [U_2829,U_2828] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2828),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2829))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2828,U_2829)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2829)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2828,U_2829) ) )
& ( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2828,U_2829)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2829)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2828,U_2829) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2828),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2829)) ) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
fof(f_961_3,plain,
( ! [U_2833,U_2831] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2831),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2833))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2831,U_2833)
| ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2833)
& c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2831,U_2833) ) )
& ! [U_2832,U_2830] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2830,U_2832)
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2832)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2830,U_2832) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2830),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2832)) ) ),
inference(miniscope,[status(thm)],[f_961_2]) ).
fof(f_961_4,plain,
( ! [U_2831,U_2833] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2833)
| ~ sP322(U_2831,U_2833) )
& ! [U_2831,U_2833] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2831,U_2833)
| ~ sP322(U_2831,U_2833) )
& ! [U_2830,U_2832] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2830,U_2832)
| ~ sP321(U_2830,U_2832) )
& ! [U_2830,U_2832] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2832)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2830,U_2832)
| ~ sP321(U_2830,U_2832) )
& ! [U_2831,U_2833] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2831),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2833))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2831,U_2833)
| sP322(U_2831,U_2833) )
& ! [U_2830,U_2832] :
( sP321(U_2830,U_2832)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2830),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2832)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP321,sP322])],[f_961_3]) ).
cnf(f_961_5,plain,
( sP321(U_2830,U_2832)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2830),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2832)) ),
inference(clausify,[status(thm)],[f_961_4]) ).
cnf(f_961_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2831),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,U_2833))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2831,U_2833)
| sP322(U_2831,U_2833) ),
inference(clausify,[status(thm)],[f_961_4]) ).
cnf(f_961_7,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2832)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2830,U_2832)
| ~ sP321(U_2830,U_2832) ),
inference(clausify,[status(thm)],[f_961_4]) ).
cnf(f_961_8,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2830,U_2832)
| ~ sP321(U_2830,U_2832) ),
inference(clausify,[status(thm)],[f_961_4]) ).
cnf(f_961_9,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2831,U_2833)
| ~ sP322(U_2831,U_2833) ),
inference(clausify,[status(thm)],[f_961_4]) ).
cnf(f_961_10,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2833)
| ~ sP322(U_2831,U_2833) ),
inference(clausify,[status(thm)],[f_961_4]) ).
fof(f_962_1,plain,
! [V_g_2,V_f_2,T_a,T_b] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2)
| c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_g_2,V_f_2)
& c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b),V_f_2,V_g_2) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b),V_f_2,V_g_2) ) )
| ~ class_Orderings_Oord(T_b) ),
inference(fof_nnf,[status(thm)],[fact_less__fun__def]) ).
fof(f_962_2,plain,
! [U_2837,U_2836,U_2835,U_2834] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_2835,U_2834),U_2836,U_2837)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2837,U_2836)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2836,U_2837) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2837,U_2836)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2836,U_2837) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2835,U_2834),U_2836,U_2837) ) )
| ~ class_Orderings_Oord(U_2834) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
fof(f_962_3,plain,
( ! [U_2835,U_2836,U_2837,U_2834] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2837,U_2836)
| ~ sP323(U_2835,U_2836,U_2837,U_2834) )
& ! [U_2835,U_2836,U_2837,U_2834] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2836,U_2837)
| ~ sP323(U_2835,U_2836,U_2837,U_2834) )
& ! [U_2835,U_2836,U_2837,U_2834] :
( c_Orderings_Oord__class_Oless(tc_fun(U_2835,U_2834),U_2836,U_2837)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2837,U_2836)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2836,U_2837)
| ~ sP324(U_2835,U_2836,U_2837,U_2834) )
& ! [U_2835,U_2836,U_2837,U_2834] :
( sP323(U_2835,U_2836,U_2837,U_2834)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2835,U_2834),U_2836,U_2837)
| ~ sP324(U_2835,U_2836,U_2837,U_2834) )
& ! [U_2835,U_2836,U_2837,U_2834] :
( sP324(U_2835,U_2836,U_2837,U_2834)
| ~ class_Orderings_Oord(U_2834) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP323,sP324])],[f_962_2]) ).
cnf(f_962_4,plain,
( sP324(U_2835,U_2836,U_2837,U_2834)
| ~ class_Orderings_Oord(U_2834) ),
inference(clausify,[status(thm)],[f_962_3]) ).
cnf(f_962_5,plain,
( sP323(U_2835,U_2836,U_2837,U_2834)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_2835,U_2834),U_2836,U_2837)
| ~ sP324(U_2835,U_2836,U_2837,U_2834) ),
inference(clausify,[status(thm)],[f_962_3]) ).
cnf(f_962_6,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_2835,U_2834),U_2836,U_2837)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2837,U_2836)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2836,U_2837)
| ~ sP324(U_2835,U_2836,U_2837,U_2834) ),
inference(clausify,[status(thm)],[f_962_3]) ).
cnf(f_962_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2836,U_2837)
| ~ sP323(U_2835,U_2836,U_2837,U_2834) ),
inference(clausify,[status(thm)],[f_962_3]) ).
cnf(f_962_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_2835,U_2834),U_2837,U_2836)
| ~ sP323(U_2835,U_2836,U_2837,U_2834) ),
inference(clausify,[status(thm)],[f_962_3]) ).
fof(f_963_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_963_2,plain,
! [U_2838] :
( ( 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_2838))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2838) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2838)
| ~ 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_2838)) ) ),
inference(variable_rename,[status(thm)],[f_963_1]) ).
fof(f_963_3,plain,
( ! [U_2840] :
( 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_2840))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2840) )
& ! [U_2839] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2839)
| ~ 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_2839)) ) ),
inference(miniscope,[status(thm)],[f_963_2]) ).
fof(f_963_4,plain,
( ! [U_2840] :
( 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_2840))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2840) )
& ! [U_2839] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2839)
| ~ 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_2839)) ) ),
inference(definitional_conversion,[status(esa)],[f_963_3]) ).
cnf(f_963_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2839)
| ~ 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_2839)) ),
inference(clausify,[status(thm)],[f_963_4]) ).
cnf(f_963_6,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_2840))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2840) ),
inference(clausify,[status(thm)],[f_963_4]) ).
fof(f_964_1,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi),
inference(fof_nnf,[status(thm)],[fact_pi__ge__zero]) ).
fof(f_964_2,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi),
inference(definitional_conversion,[status(esa)],[f_964_1]) ).
cnf(f_964_3,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Transcendental_Opi),
inference(clausify,[status(thm)],[f_964_2]) ).
fof(f_965_1,plain,
c_Transcendental_Opi != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_pi__neq__zero]) ).
fof(f_965_2,plain,
c_Transcendental_Opi != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_965_1]) ).
cnf(f_965_3,plain,
c_Transcendental_Opi != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_965_2]) ).
fof(f_966_1,plain,
! [V_w_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I4_J]) ).
fof(f_966_2,plain,
! [U_2841] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2841),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2841,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2841,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2841),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
fof(f_966_3,plain,
( ! [U_2843] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2843),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2843,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2842] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2842,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2842),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_966_2]) ).
fof(f_966_4,plain,
( ! [U_2843] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2843),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2843,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2842] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2842,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2842),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa)],[f_966_3]) ).
cnf(f_966_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2842,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2842),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_966_4]) ).
cnf(f_966_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2843),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2843,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_966_4]) ).
fof(f_967_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_967_2,plain,
! [U_2844] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2844),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2844,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2844,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2844),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
fof(f_967_3,plain,
( ! [U_2846] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2846),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2846,c_Int_OPls) )
& ! [U_2845] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2845,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2845),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_967_2]) ).
fof(f_967_4,plain,
( ! [U_2846] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2846),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2846,c_Int_OPls) )
& ! [U_2845] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2845,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2845),c_Int_OPls) ) ),
inference(definitional_conversion,[status(esa)],[f_967_3]) ).
cnf(f_967_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2845,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2845),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_967_4]) ).
cnf(f_967_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2846),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2846,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_967_4]) ).
fof(f_968_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]) ).
fof(f_968_2,plain,
~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
inference(definitional_conversion,[status(esa)],[f_968_1]) ).
cnf(f_968_3,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_968_2]) ).
fof(f_969_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_969_2,plain,
! [U_2848,U_2847] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2847),c_Int_OBit0(U_2848))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2847,U_2848) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2847,U_2848)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2847),c_Int_OBit0(U_2848)) ) ),
inference(variable_rename,[status(thm)],[f_969_1]) ).
fof(f_969_3,plain,
( ! [U_2852,U_2850] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2850),c_Int_OBit0(U_2852))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2850,U_2852) )
& ! [U_2851,U_2849] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2849,U_2851)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2849),c_Int_OBit0(U_2851)) ) ),
inference(miniscope,[status(thm)],[f_969_2]) ).
fof(f_969_4,plain,
( ! [U_2850,U_2852] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2850),c_Int_OBit0(U_2852))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2850,U_2852) )
& ! [U_2851,U_2849] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2849,U_2851)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2849),c_Int_OBit0(U_2851)) ) ),
inference(definitional_conversion,[status(esa)],[f_969_3]) ).
cnf(f_969_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2849,U_2851)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2849),c_Int_OBit0(U_2851)) ),
inference(clausify,[status(thm)],[f_969_4]) ).
cnf(f_969_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2850),c_Int_OBit0(U_2852))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2850,U_2852) ),
inference(clausify,[status(thm)],[f_969_4]) ).
fof(f_970_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_970_2,plain,
! [U_2854,U_2853] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2853),c_Int_OBit0(U_2854))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2853,U_2854) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2853,U_2854)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2853),c_Int_OBit0(U_2854)) ) ),
inference(variable_rename,[status(thm)],[f_970_1]) ).
fof(f_970_3,plain,
( ! [U_2858,U_2856] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2856),c_Int_OBit0(U_2858))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2856,U_2858) )
& ! [U_2857,U_2855] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2855,U_2857)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2855),c_Int_OBit0(U_2857)) ) ),
inference(miniscope,[status(thm)],[f_970_2]) ).
fof(f_970_4,plain,
( ! [U_2856,U_2858] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2856),c_Int_OBit0(U_2858))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2856,U_2858) )
& ! [U_2857,U_2855] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2855,U_2857)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2855),c_Int_OBit0(U_2857)) ) ),
inference(definitional_conversion,[status(esa)],[f_970_3]) ).
cnf(f_970_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2855,U_2857)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2855),c_Int_OBit0(U_2857)) ),
inference(clausify,[status(thm)],[f_970_4]) ).
cnf(f_970_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit1(U_2856),c_Int_OBit0(U_2858))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2856,U_2858) ),
inference(clausify,[status(thm)],[f_970_4]) ).
fof(f_971_1,plain,
! [V_w_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_bin__less__0__simps_I3_J]) ).
fof(f_971_2,plain,
! [U_2859] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2859),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2859,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2859,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2859),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_971_1]) ).
fof(f_971_3,plain,
( ! [U_2861] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2861),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2861,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2860] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2860,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2860),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_971_2]) ).
fof(f_971_4,plain,
( ! [U_2861] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2861),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2861,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2860] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2860,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2860),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa)],[f_971_3]) ).
cnf(f_971_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2860,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2860),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_971_4]) ).
cnf(f_971_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2861),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2861,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_971_4]) ).
fof(f_972_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_972_2,plain,
! [U_2865,U_2864] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2864,c_Nat_OSuc(U_2865))
| ( ! [U_2863] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2863,U_2865)
| U_2864 != c_Nat_OSuc(U_2863) )
& U_2864 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_2862] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2862,U_2865)
& U_2864 = c_Nat_OSuc(U_2862) )
| U_2864 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2864,c_Nat_OSuc(U_2865)) ) ),
inference(variable_rename,[status(thm)],[f_972_1]) ).
fof(f_972_3,plain,
( ! [U_2869,U_2867] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2867,c_Nat_OSuc(U_2869))
| ( ! [U_2863] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2863,U_2869)
| U_2867 != c_Nat_OSuc(U_2863) )
& U_2867 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2868,U_2866] :
( ? [U_2862] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2862,U_2868)
& U_2866 = c_Nat_OSuc(U_2862) )
| U_2866 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2866,c_Nat_OSuc(U_2868)) ) ),
inference(miniscope,[status(thm)],[f_972_2]) ).
fof(f_972_4,plain,
( ! [U_2869,U_2867] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2867,c_Nat_OSuc(U_2869))
| ( ! [U_2863] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2863,U_2869)
| U_2867 != c_Nat_OSuc(U_2863) )
& U_2867 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2868,U_2866] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK7(U_2868,U_2866),U_2868)
& U_2866 = c_Nat_OSuc(sK7(U_2868,U_2866)) )
| U_2866 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2866,c_Nat_OSuc(U_2868)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_2862,sK7(U_2868,U_2866))],[f_972_3]) ).
fof(f_972_5,plain,
( ! [U_2863,U_2867,U_2869] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2863,U_2869)
| U_2867 != c_Nat_OSuc(U_2863)
| ~ sP326(U_2863,U_2867,U_2869) )
& ! [U_2863,U_2867,U_2869] :
( U_2867 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP326(U_2863,U_2867,U_2869) )
& ! [U_2866,U_2868] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK7(U_2868,U_2866),U_2868)
| ~ sP325(U_2866,U_2868) )
& ! [U_2866,U_2868] :
( U_2866 = c_Nat_OSuc(sK7(U_2868,U_2866))
| ~ sP325(U_2866,U_2868) )
& ! [U_2863,U_2867,U_2869] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2867,c_Nat_OSuc(U_2869))
| sP326(U_2863,U_2867,U_2869) )
& ! [U_2866,U_2868] :
( sP325(U_2866,U_2868)
| U_2866 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2866,c_Nat_OSuc(U_2868)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP325,sP326])],[f_972_4]) ).
cnf(f_972_6,plain,
( sP325(U_2866,U_2868)
| U_2866 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2866,c_Nat_OSuc(U_2868)) ),
inference(clausify,[status(thm)],[f_972_5]) ).
cnf(f_972_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2867,c_Nat_OSuc(U_2869))
| sP326(U_2863,U_2867,U_2869) ),
inference(clausify,[status(thm)],[f_972_5]) ).
cnf(f_972_8,plain,
( U_2866 = c_Nat_OSuc(sK7(U_2868,U_2866))
| ~ sP325(U_2866,U_2868) ),
inference(clausify,[status(thm)],[f_972_5]) ).
cnf(f_972_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK7(U_2868,U_2866),U_2868)
| ~ sP325(U_2866,U_2868) ),
inference(clausify,[status(thm)],[f_972_5]) ).
cnf(f_972_10,plain,
( U_2867 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP326(U_2863,U_2867,U_2869) ),
inference(clausify,[status(thm)],[f_972_5]) ).
cnf(f_972_11,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2863,U_2869)
| U_2867 != c_Nat_OSuc(U_2863)
| ~ sP326(U_2863,U_2867,U_2869) ),
inference(clausify,[status(thm)],[f_972_5]) ).
fof(f_973_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_973_2,plain,
! [U_2870] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2870,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2870 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2870 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2870,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
fof(f_973_3,plain,
( ! [U_2872] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2872,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2872 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2871] :
( U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2871,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_973_2]) ).
fof(f_973_4,plain,
( ! [U_2872] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2872,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2872 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2871] :
( U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2871,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa)],[f_973_3]) ).
cnf(f_973_5,plain,
( U_2871 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2871,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_973_4]) ).
cnf(f_973_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2872,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2872 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_973_4]) ).
fof(f_974_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_974_2,plain,
! [U_2875] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2875)
| ! [U_2874] : U_2875 != c_Nat_OSuc(U_2874) )
& ( ? [U_2873] : U_2875 = c_Nat_OSuc(U_2873)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2875) ) ),
inference(variable_rename,[status(thm)],[f_974_1]) ).
fof(f_974_3,plain,
( ! [U_2877] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2877)
| ! [U_2874] : U_2877 != c_Nat_OSuc(U_2874) )
& ! [U_2876] :
( ? [U_2873] : U_2876 = c_Nat_OSuc(U_2873)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2876) ) ),
inference(miniscope,[status(thm)],[f_974_2]) ).
fof(f_974_4,plain,
( ! [U_2877] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2877)
| ! [U_2874] : U_2877 != c_Nat_OSuc(U_2874) )
& ! [U_2876] :
( U_2876 = c_Nat_OSuc(sK8(U_2876))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2876) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_2873,sK8(U_2876))],[f_974_3]) ).
fof(f_974_5,plain,
( ! [U_2877,U_2874] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2877)
| U_2877 != c_Nat_OSuc(U_2874) )
& ! [U_2876] :
( U_2876 = c_Nat_OSuc(sK8(U_2876))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2876) ) ),
inference(definitional_conversion,[status(esa)],[f_974_4]) ).
cnf(f_974_6,plain,
( U_2876 = c_Nat_OSuc(sK8(U_2876))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2876) ),
inference(clausify,[status(thm)],[f_974_5]) ).
cnf(f_974_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2877)
| U_2877 != c_Nat_OSuc(U_2874) ),
inference(clausify,[status(thm)],[f_974_5]) ).
fof(f_975_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_975_2,plain,
! [U_2878] :
( U_2878 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2878,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[f_975_1]) ).
fof(f_975_3,plain,
! [U_2878] :
( U_2878 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2878,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(definitional_conversion,[status(esa)],[f_975_2]) ).
cnf(f_975_4,plain,
( U_2878 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2878 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2878,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_975_3]) ).
fof(f_976_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_976_2,plain,
! [U_2879] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2879),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2879,c_Int_OPls) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2879,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2879),c_Int_OPls) ) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
fof(f_976_3,plain,
( ! [U_2881] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2881),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2881,c_Int_OPls) )
& ! [U_2880] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2880,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2880),c_Int_OPls) ) ),
inference(miniscope,[status(thm)],[f_976_2]) ).
fof(f_976_4,plain,
( ! [U_2881] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2881),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2881,c_Int_OPls) )
& ! [U_2880] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2880,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2880),c_Int_OPls) ) ),
inference(definitional_conversion,[status(esa)],[f_976_3]) ).
cnf(f_976_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2880,c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2880),c_Int_OPls) ),
inference(clausify,[status(thm)],[f_976_4]) ).
cnf(f_976_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OBit0(U_2881),c_Int_OPls)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2881,c_Int_OPls) ),
inference(clausify,[status(thm)],[f_976_4]) ).
fof(f_977_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_977_2,plain,
! [U_2882] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2882))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2882) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2882)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2882)) ) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
fof(f_977_3,plain,
( ! [U_2884] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2884))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2884) )
& ! [U_2883] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2883)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2883)) ) ),
inference(miniscope,[status(thm)],[f_977_2]) ).
fof(f_977_4,plain,
( ! [U_2884] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2884))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2884) )
& ! [U_2883] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2883)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2883)) ) ),
inference(definitional_conversion,[status(esa)],[f_977_3]) ).
cnf(f_977_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2883)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2883)) ),
inference(clausify,[status(thm)],[f_977_4]) ).
cnf(f_977_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,c_Int_OBit0(U_2884))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Int_OPls,U_2884) ),
inference(clausify,[status(thm)],[f_977_4]) ).
fof(f_978_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_978_2,plain,
! [U_2886,U_2885] :
( ( 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_2885,U_2886))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2886)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2885) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2886)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2885)
| ~ 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_2885,U_2886)) ) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
fof(f_978_3,plain,
( ! [U_2890,U_2888] :
( 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_2888,U_2890))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2890)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2888) ) )
& ! [U_2889,U_2887] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2889)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2887)
| ~ 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_2887,U_2889)) ) ),
inference(miniscope,[status(thm)],[f_978_2]) ).
fof(f_978_4,plain,
( ! [U_2888,U_2890] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2890)
| ~ sP327(U_2888,U_2890) )
& ! [U_2888,U_2890] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2888)
| ~ sP327(U_2888,U_2890) )
& ! [U_2888,U_2890] :
( 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_2888,U_2890))
| sP327(U_2888,U_2890) )
& ! [U_2887,U_2889] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2889)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2887)
| ~ 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_2887,U_2889)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP327])],[f_978_3]) ).
cnf(f_978_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2889)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2887)
| ~ 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_2887,U_2889)) ),
inference(clausify,[status(thm)],[f_978_4]) ).
cnf(f_978_6,plain,
( 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_2888,U_2890))
| sP327(U_2888,U_2890) ),
inference(clausify,[status(thm)],[f_978_4]) ).
cnf(f_978_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2888)
| ~ sP327(U_2888,U_2890) ),
inference(clausify,[status(thm)],[f_978_4]) ).
cnf(f_978_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2890)
| ~ sP327(U_2888,U_2890) ),
inference(clausify,[status(thm)],[f_978_4]) ).
fof(f_979_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_979_2,plain,
! [U_2892,U_2891] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2891,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2891,U_2892))),
inference(variable_rename,[status(thm)],[f_979_1]) ).
fof(f_979_3,plain,
! [U_2891,U_2892] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2891,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2891,U_2892))),
inference(definitional_conversion,[status(esa)],[f_979_2]) ).
cnf(f_979_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2891,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2891,U_2892))),
inference(clausify,[status(thm)],[f_979_3]) ).
fof(f_980_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_980_2,plain,
! [U_2894,U_2893] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2893,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2894,U_2893))),
inference(variable_rename,[status(thm)],[f_980_1]) ).
fof(f_980_3,plain,
! [U_2893,U_2894] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2893,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2894,U_2893))),
inference(definitional_conversion,[status(esa)],[f_980_2]) ).
cnf(f_980_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2893,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2894,U_2893))),
inference(clausify,[status(thm)],[f_980_3]) ).
fof(f_981_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_981_2,plain,
! [U_2898,U_2897] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2897,U_2898)
| ! [U_2896] : U_2898 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2897,U_2896)) )
& ( ? [U_2895] : U_2898 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2897,U_2895))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2897,U_2898) ) ),
inference(variable_rename,[status(thm)],[f_981_1]) ).
fof(f_981_3,plain,
( ! [U_2902,U_2900] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2900,U_2902)
| ! [U_2896] : U_2902 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2900,U_2896)) )
& ! [U_2901,U_2899] :
( ? [U_2895] : U_2901 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2899,U_2895))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2899,U_2901) ) ),
inference(miniscope,[status(thm)],[f_981_2]) ).
fof(f_981_4,plain,
( ! [U_2902,U_2900] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2900,U_2902)
| ! [U_2896] : U_2902 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2900,U_2896)) )
& ! [U_2901,U_2899] :
( U_2901 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2899,sK9(U_2901,U_2899)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2899,U_2901) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_2895,sK9(U_2901,U_2899))],[f_981_3]) ).
fof(f_981_5,plain,
( ! [U_2896,U_2902,U_2900] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2900,U_2902)
| U_2902 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2900,U_2896)) )
& ! [U_2901,U_2899] :
( U_2901 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2899,sK9(U_2901,U_2899)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2899,U_2901) ) ),
inference(definitional_conversion,[status(esa)],[f_981_4]) ).
cnf(f_981_6,plain,
( U_2901 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2899,sK9(U_2901,U_2899)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2899,U_2901) ),
inference(clausify,[status(thm)],[f_981_5]) ).
cnf(f_981_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2900,U_2902)
| U_2902 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2900,U_2896)) ),
inference(clausify,[status(thm)],[f_981_5]) ).
fof(f_982_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_982_2,plain,
! [U_2904,U_2903] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2903,U_2904)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2903),U_2904) ),
inference(variable_rename,[status(thm)],[f_982_1]) ).
fof(f_982_3,plain,
! [U_2903,U_2904] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2903,U_2904)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2903),U_2904) ),
inference(definitional_conversion,[status(esa)],[f_982_2]) ).
cnf(f_982_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2903,U_2904)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2903),U_2904) ),
inference(clausify,[status(thm)],[f_982_3]) ).
fof(f_983_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_983_2,plain,
! [U_2906,U_2905] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2906,c_Nat_OSuc(U_2905))
| U_2906 != U_2905 )
& ( U_2906 = U_2905
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2906,c_Nat_OSuc(U_2905)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2905,U_2906) ),
inference(variable_rename,[status(thm)],[f_983_1]) ).
fof(f_983_3,plain,
( ! [U_2905,U_2906] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2906,c_Nat_OSuc(U_2905))
| U_2906 != U_2905
| ~ sP328(U_2905,U_2906) )
& ! [U_2905,U_2906] :
( U_2906 = U_2905
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2906,c_Nat_OSuc(U_2905))
| ~ sP328(U_2905,U_2906) )
& ! [U_2905,U_2906] :
( sP328(U_2905,U_2906)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2905,U_2906) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP328])],[f_983_2]) ).
cnf(f_983_4,plain,
( sP328(U_2905,U_2906)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2905,U_2906) ),
inference(clausify,[status(thm)],[f_983_3]) ).
cnf(f_983_5,plain,
( U_2906 = U_2905
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2906,c_Nat_OSuc(U_2905))
| ~ sP328(U_2905,U_2906) ),
inference(clausify,[status(thm)],[f_983_3]) ).
cnf(f_983_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2906,c_Nat_OSuc(U_2905))
| U_2906 != U_2905
| ~ sP328(U_2905,U_2906) ),
inference(clausify,[status(thm)],[f_983_3]) ).
fof(f_984_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_984_2,plain,
! [U_2908,U_2907] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2907),U_2908)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2907,U_2908) ),
inference(variable_rename,[status(thm)],[f_984_1]) ).
fof(f_984_3,plain,
! [U_2907,U_2908] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2907),U_2908)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2907,U_2908) ),
inference(definitional_conversion,[status(esa)],[f_984_2]) ).
cnf(f_984_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2907),U_2908)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2907,U_2908) ),
inference(clausify,[status(thm)],[f_984_3]) ).
fof(f_985_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_985_2,plain,
! [U_2910,U_2909] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2909,c_Nat_OSuc(U_2910))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2909,U_2910) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
fof(f_985_3,plain,
! [U_2909,U_2910] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2909,c_Nat_OSuc(U_2910))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2909,U_2910) ),
inference(definitional_conversion,[status(esa)],[f_985_2]) ).
cnf(f_985_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2909,c_Nat_OSuc(U_2910))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2909,U_2910) ),
inference(clausify,[status(thm)],[f_985_3]) ).
fof(f_986_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_986_2,plain,
! [U_2912,U_2911] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2911),U_2912)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2911,U_2912) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2911,U_2912)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2911),U_2912) ) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
fof(f_986_3,plain,
( ! [U_2916,U_2914] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2914),U_2916)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2914,U_2916) )
& ! [U_2915,U_2913] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2913,U_2915)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2913),U_2915) ) ),
inference(miniscope,[status(thm)],[f_986_2]) ).
fof(f_986_4,plain,
( ! [U_2914,U_2916] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2914),U_2916)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2914,U_2916) )
& ! [U_2915,U_2913] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2913,U_2915)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2913),U_2915) ) ),
inference(definitional_conversion,[status(esa)],[f_986_3]) ).
cnf(f_986_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2913,U_2915)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2913),U_2915) ),
inference(clausify,[status(thm)],[f_986_4]) ).
cnf(f_986_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2914),U_2916)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2914,U_2916) ),
inference(clausify,[status(thm)],[f_986_4]) ).
fof(f_987_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_987_2,plain,
! [U_2918,U_2917] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2917,c_Nat_OSuc(U_2918))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2917,U_2918) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2917,U_2918)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2917,c_Nat_OSuc(U_2918)) ) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
fof(f_987_3,plain,
( ! [U_2922,U_2920] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2920,c_Nat_OSuc(U_2922))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2920,U_2922) )
& ! [U_2921,U_2919] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2919,U_2921)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2919,c_Nat_OSuc(U_2921)) ) ),
inference(miniscope,[status(thm)],[f_987_2]) ).
fof(f_987_4,plain,
( ! [U_2922,U_2920] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2920,c_Nat_OSuc(U_2922))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2920,U_2922) )
& ! [U_2919,U_2921] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2919,U_2921)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2919,c_Nat_OSuc(U_2921)) ) ),
inference(definitional_conversion,[status(esa)],[f_987_3]) ).
cnf(f_987_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2919,U_2921)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2919,c_Nat_OSuc(U_2921)) ),
inference(clausify,[status(thm)],[f_987_4]) ).
cnf(f_987_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2920,c_Nat_OSuc(U_2922))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2920,U_2922) ),
inference(clausify,[status(thm)],[f_987_4]) ).
fof(f_988_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_988_2,plain,
! [U_2924,U_2923] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2923,U_2924)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2923),U_2924) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2923),U_2924)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2923,U_2924) ) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
fof(f_988_3,plain,
( ! [U_2928,U_2926] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2926,U_2928)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2926),U_2928) )
& ! [U_2927,U_2925] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2925),U_2927)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2925,U_2927) ) ),
inference(miniscope,[status(thm)],[f_988_2]) ).
fof(f_988_4,plain,
( ! [U_2926,U_2928] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2926,U_2928)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2926),U_2928) )
& ! [U_2925,U_2927] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2925),U_2927)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2925,U_2927) ) ),
inference(definitional_conversion,[status(esa)],[f_988_3]) ).
cnf(f_988_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2925),U_2927)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2925,U_2927) ),
inference(clausify,[status(thm)],[f_988_4]) ).
cnf(f_988_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2926,U_2928)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2926),U_2928) ),
inference(clausify,[status(thm)],[f_988_4]) ).
fof(f_989_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]) ).
fof(f_989_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(definitional_conversion,[status(esa)],[f_989_1]) ).
cnf(f_989_3,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_989_2]) ).
fof(f_990_1,plain,
! [V_n_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).
fof(f_990_2,plain,
! [U_2930,U_2929] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2929),U_2930))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2930)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2929) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2930)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2929) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2929),U_2930)) ) ),
inference(variable_rename,[status(thm)],[f_990_1]) ).
fof(f_990_3,plain,
( ! [U_2934,U_2932] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2932),U_2934))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2934)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2932) )
& ! [U_2933,U_2931] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2933)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2931) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2931),U_2933)) ) ),
inference(miniscope,[status(thm)],[f_990_2]) ).
fof(f_990_4,plain,
( ! [U_2933,U_2931] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2933)
| ~ sP329(U_2933,U_2931) )
& ! [U_2933,U_2931] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2931)
| ~ sP329(U_2933,U_2931) )
& ! [U_2932,U_2934] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2932),U_2934))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2934)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2932) )
& ! [U_2933,U_2931] :
( sP329(U_2933,U_2931)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2931),U_2933)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP329])],[f_990_3]) ).
cnf(f_990_5,plain,
( sP329(U_2933,U_2931)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2931),U_2933)) ),
inference(clausify,[status(thm)],[f_990_4]) ).
cnf(f_990_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2932),U_2934))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2934)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2932) ),
inference(clausify,[status(thm)],[f_990_4]) ).
cnf(f_990_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2931)
| ~ sP329(U_2933,U_2931) ),
inference(clausify,[status(thm)],[f_990_4]) ).
cnf(f_990_8,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2933)
| ~ sP329(U_2933,U_2931) ),
inference(clausify,[status(thm)],[f_990_4]) ).
fof(f_991_1,plain,
! [V_n_2,V_m_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel1]) ).
fof(f_991_2,plain,
! [U_2937,U_2936,U_2935] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2935),U_2936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2935),U_2937))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2936,U_2937)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2935) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2936,U_2937)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2935) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2935),U_2936),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2935),U_2937)) ) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
fof(f_991_3,plain,
( ! [U_2943,U_2941,U_2939] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2939),U_2941),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2939),U_2943))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2941,U_2943)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2939) )
& ! [U_2942,U_2940,U_2938] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2940,U_2942)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2938) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2938),U_2940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2938),U_2942)) ) ),
inference(miniscope,[status(thm)],[f_991_2]) ).
fof(f_991_4,plain,
( ! [U_2942,U_2940,U_2938] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2940,U_2942)
| ~ sP330(U_2942,U_2940,U_2938) )
& ! [U_2942,U_2940,U_2938] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2938)
| ~ sP330(U_2942,U_2940,U_2938) )
& ! [U_2943,U_2941,U_2939] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2939),U_2941),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2939),U_2943))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2941,U_2943)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2939) )
& ! [U_2942,U_2940,U_2938] :
( sP330(U_2942,U_2940,U_2938)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2938),U_2940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2938),U_2942)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP330])],[f_991_3]) ).
cnf(f_991_5,plain,
( sP330(U_2942,U_2940,U_2938)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2938),U_2940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2938),U_2942)) ),
inference(clausify,[status(thm)],[f_991_4]) ).
cnf(f_991_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2939),U_2941),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2939),U_2943))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2941,U_2943)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2939) ),
inference(clausify,[status(thm)],[f_991_4]) ).
cnf(f_991_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2938)
| ~ sP330(U_2942,U_2940,U_2938) ),
inference(clausify,[status(thm)],[f_991_4]) ).
cnf(f_991_8,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2940,U_2942)
| ~ sP330(U_2942,U_2940,U_2938) ),
inference(clausify,[status(thm)],[f_991_4]) ).
fof(f_992_1,plain,
! [V_n_2,V_k_2,V_m_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_k_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel2]) ).
fof(f_992_2,plain,
! [U_2946,U_2945,U_2944] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2944),U_2945),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2946),U_2945))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2944,U_2946)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2945) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2944,U_2946)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2945) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2944),U_2945),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2946),U_2945)) ) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
fof(f_992_3,plain,
( ! [U_2952,U_2950,U_2948] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2948),U_2950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2952),U_2950))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2948,U_2952)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2950) )
& ! [U_2951,U_2949,U_2947] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2947,U_2951)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2949) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2947),U_2949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2951),U_2949)) ) ),
inference(miniscope,[status(thm)],[f_992_2]) ).
fof(f_992_4,plain,
( ! [U_2949,U_2947,U_2951] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2947,U_2951)
| ~ sP331(U_2949,U_2947,U_2951) )
& ! [U_2949,U_2947,U_2951] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2949)
| ~ sP331(U_2949,U_2947,U_2951) )
& ! [U_2950,U_2948,U_2952] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2948),U_2950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2952),U_2950))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2948,U_2952)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2950) )
& ! [U_2949,U_2947,U_2951] :
( sP331(U_2949,U_2947,U_2951)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2947),U_2949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2951),U_2949)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP331])],[f_992_3]) ).
cnf(f_992_5,plain,
( sP331(U_2949,U_2947,U_2951)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2947),U_2949),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2951),U_2949)) ),
inference(clausify,[status(thm)],[f_992_4]) ).
cnf(f_992_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2948),U_2950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2952),U_2950))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2948,U_2952)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2950) ),
inference(clausify,[status(thm)],[f_992_4]) ).
cnf(f_992_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2949)
| ~ sP331(U_2949,U_2947,U_2951) ),
inference(clausify,[status(thm)],[f_992_4]) ).
cnf(f_992_8,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2947,U_2951)
| ~ sP331(U_2949,U_2947,U_2951) ),
inference(clausify,[status(thm)],[f_992_4]) ).
fof(f_993_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i),V_k),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j),V_k))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono1]) ).
fof(f_993_2,plain,
! [U_2955,U_2954,U_2953] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2953),U_2955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2954),U_2955))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2955)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2953,U_2954) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
fof(f_993_3,plain,
! [U_2953,U_2954,U_2955] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2953),U_2955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2954),U_2955))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2955)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2953,U_2954) ),
inference(definitional_conversion,[status(esa)],[f_993_2]) ).
cnf(f_993_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2953),U_2955),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2954),U_2955))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2955)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2953,U_2954) ),
inference(clausify,[status(thm)],[f_993_3]) ).
fof(f_994_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_j))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__mono2]) ).
fof(f_994_2,plain,
! [U_2958,U_2957,U_2956] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2958),U_2956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2958),U_2957))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2958)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2956,U_2957) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
fof(f_994_3,plain,
! [U_2958,U_2956,U_2957] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2958),U_2956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2958),U_2957))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2958)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2956,U_2957) ),
inference(definitional_conversion,[status(esa)],[f_994_2]) ).
cnf(f_994_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2958),U_2956),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2958),U_2957))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2958)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2956,U_2957) ),
inference(clausify,[status(thm)],[f_994_3]) ).
fof(f_995_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_995_2,plain,
! [U_2960,U_2959] :
( class_Orderings_Opreorder(tc_fun(U_2960,U_2959))
| ~ class_Orderings_Opreorder(U_2959) ),
inference(variable_rename,[status(thm)],[f_995_1]) ).
fof(f_995_3,plain,
! [U_2959,U_2960] :
( class_Orderings_Opreorder(tc_fun(U_2960,U_2959))
| ~ class_Orderings_Opreorder(U_2959) ),
inference(definitional_conversion,[status(esa)],[f_995_2]) ).
cnf(f_995_4,plain,
( class_Orderings_Opreorder(tc_fun(U_2960,U_2959))
| ~ class_Orderings_Opreorder(U_2959) ),
inference(clausify,[status(thm)],[f_995_3]) ).
fof(f_996_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_996_2,plain,
! [U_2962,U_2961] :
( class_Orderings_Oorder(tc_fun(U_2962,U_2961))
| ~ class_Orderings_Oorder(U_2961) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
fof(f_996_3,plain,
! [U_2962,U_2961] :
( class_Orderings_Oorder(tc_fun(U_2962,U_2961))
| ~ class_Orderings_Oorder(U_2961) ),
inference(definitional_conversion,[status(esa)],[f_996_2]) ).
cnf(f_996_4,plain,
( class_Orderings_Oorder(tc_fun(U_2962,U_2961))
| ~ class_Orderings_Oorder(U_2961) ),
inference(clausify,[status(thm)],[f_996_3]) ).
fof(f_997_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_997_2,plain,
! [U_2964,U_2963] :
( class_Orderings_Oord(tc_fun(U_2964,U_2963))
| ~ class_Orderings_Oord(U_2963) ),
inference(variable_rename,[status(thm)],[f_997_1]) ).
fof(f_997_3,plain,
! [U_2963,U_2964] :
( class_Orderings_Oord(tc_fun(U_2964,U_2963))
| ~ class_Orderings_Oord(U_2963) ),
inference(definitional_conversion,[status(esa)],[f_997_2]) ).
cnf(f_997_4,plain,
( class_Orderings_Oord(tc_fun(U_2964,U_2963))
| ~ class_Orderings_Oord(U_2963) ),
inference(clausify,[status(thm)],[f_997_3]) ).
fof(f_998_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]) ).
fof(f_998_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_998_1]) ).
cnf(f_998_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(clausify,[status(thm)],[f_998_2]) ).
fof(f_999_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]) ).
fof(f_999_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_999_1]) ).
cnf(f_999_3,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_999_2]) ).
fof(f_1000_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]) ).
fof(f_1000_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1000_1]) ).
cnf(f_1000_3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1000_2]) ).
fof(f_1001_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1001_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1001_1]) ).
cnf(f_1001_3,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1001_2]) ).
fof(f_1002_1,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1__strict]) ).
fof(f_1002_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1002_1]) ).
cnf(f_1002_3,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1002_2]) ).
fof(f_1003_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).
fof(f_1003_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1003_1]) ).
cnf(f_1003_3,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1003_2]) ).
fof(f_1004_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add]) ).
fof(f_1004_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1004_1]) ).
cnf(f_1004_3,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1004_2]) ).
fof(f_1005_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]) ).
fof(f_1005_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1005_1]) ).
cnf(f_1005_3,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1005_2]) ).
fof(f_1006_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__comm__monoid__add]) ).
fof(f_1006_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1006_1]) ).
cnf(f_1006_3,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1006_2]) ).
fof(f_1007_1,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Olinordered__ab__group__add]) ).
fof(f_1007_2,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1007_1]) ).
cnf(f_1007_3,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1007_2]) ).
fof(f_1008_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1008_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1008_1]) ).
cnf(f_1008_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1008_2]) ).
fof(f_1009_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]) ).
fof(f_1009_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1009_1]) ).
cnf(f_1009_3,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1009_2]) ).
fof(f_1010_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).
fof(f_1010_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1010_1]) ).
cnf(f_1010_3,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1010_2]) ).
fof(f_1011_1,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).
fof(f_1011_2,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1011_1]) ).
cnf(f_1011_3,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1011_2]) ).
fof(f_1012_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__no__zero__divisors]) ).
fof(f_1012_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1012_1]) ).
cnf(f_1012_3,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1012_2]) ).
fof(f_1013_1,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).
fof(f_1013_2,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1013_1]) ).
cnf(f_1013_3,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1013_2]) ).
fof(f_1014_1,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).
fof(f_1014_2,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1014_1]) ).
cnf(f_1014_3,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1014_2]) ).
fof(f_1015_1,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__group__add]) ).
fof(f_1015_2,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1015_1]) ).
cnf(f_1015_3,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1015_2]) ).
fof(f_1016_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).
fof(f_1016_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1016_1]) ).
cnf(f_1016_3,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1016_2]) ).
fof(f_1017_1,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).
fof(f_1017_2,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1017_1]) ).
cnf(f_1017_3,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1017_2]) ).
fof(f_1018_1,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).
fof(f_1018_2,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1018_1]) ).
cnf(f_1018_3,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1018_2]) ).
fof(f_1019_1,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).
fof(f_1019_2,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1019_1]) ).
cnf(f_1019_3,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1019_2]) ).
fof(f_1020_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).
fof(f_1020_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1020_1]) ).
cnf(f_1020_3,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1020_2]) ).
fof(f_1021_1,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).
fof(f_1021_2,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1021_1]) ).
cnf(f_1021_3,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1021_2]) ).
fof(f_1022_1,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).
fof(f_1022_2,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1022_1]) ).
cnf(f_1022_3,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1022_2]) ).
fof(f_1023_1,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).
fof(f_1023_2,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1023_1]) ).
cnf(f_1023_3,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1023_2]) ).
fof(f_1024_1,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).
fof(f_1024_2,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1024_1]) ).
cnf(f_1024_3,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1024_2]) ).
fof(f_1025_1,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).
fof(f_1025_2,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1025_1]) ).
cnf(f_1025_3,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1025_2]) ).
fof(f_1026_1,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).
fof(f_1026_2,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1026_1]) ).
cnf(f_1026_3,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1026_2]) ).
fof(f_1027_1,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).
fof(f_1027_2,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1027_1]) ).
cnf(f_1027_3,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1027_2]) ).
fof(f_1028_1,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).
fof(f_1028_2,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1028_1]) ).
cnf(f_1028_3,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1028_2]) ).
fof(f_1029_1,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).
fof(f_1029_2,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1029_1]) ).
cnf(f_1029_3,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1029_2]) ).
fof(f_1030_1,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).
fof(f_1030_2,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1030_1]) ).
cnf(f_1030_3,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1030_2]) ).
fof(f_1031_1,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).
fof(f_1031_2,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1031_1]) ).
cnf(f_1031_3,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1031_2]) ).
fof(f_1032_1,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).
fof(f_1032_2,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1032_1]) ).
cnf(f_1032_3,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1032_2]) ).
fof(f_1033_1,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).
fof(f_1033_2,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1033_1]) ).
cnf(f_1033_3,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1033_2]) ).
fof(f_1034_1,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).
fof(f_1034_2,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1034_1]) ).
cnf(f_1034_3,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1034_2]) ).
fof(f_1035_1,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).
fof(f_1035_2,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1035_1]) ).
cnf(f_1035_3,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1035_2]) ).
fof(f_1036_1,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).
fof(f_1036_2,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1036_1]) ).
cnf(f_1036_3,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1036_2]) ).
fof(f_1037_1,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).
fof(f_1037_2,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1037_1]) ).
cnf(f_1037_3,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1037_2]) ).
fof(f_1038_1,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__1]) ).
fof(f_1038_2,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1038_1]) ).
cnf(f_1038_3,plain,
class_Rings_Osemiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1038_2]) ).
fof(f_1039_1,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).
fof(f_1039_2,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1039_1]) ).
cnf(f_1039_3,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1039_2]) ).
fof(f_1040_1,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).
fof(f_1040_2,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1040_1]) ).
cnf(f_1040_3,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1040_2]) ).
fof(f_1041_1,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).
fof(f_1041_2,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1041_1]) ).
cnf(f_1041_3,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1041_2]) ).
fof(f_1042_1,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).
fof(f_1042_2,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1042_1]) ).
cnf(f_1042_3,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1042_2]) ).
fof(f_1043_1,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).
fof(f_1043_2,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1043_1]) ).
cnf(f_1043_3,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1043_2]) ).
fof(f_1044_1,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber__ring]) ).
fof(f_1044_2,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1044_1]) ).
cnf(f_1044_3,plain,
class_Int_Onumber__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1044_2]) ).
fof(f_1045_1,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).
fof(f_1045_2,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1045_1]) ).
cnf(f_1045_3,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1045_2]) ).
fof(f_1046_1,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).
fof(f_1046_2,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1046_1]) ).
cnf(f_1046_3,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1046_2]) ).
fof(f_1047_1,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).
fof(f_1047_2,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1047_1]) ).
cnf(f_1047_3,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1047_2]) ).
fof(f_1048_1,plain,
class_Power_Opower(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).
fof(f_1048_2,plain,
class_Power_Opower(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1048_1]) ).
cnf(f_1048_3,plain,
class_Power_Opower(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1048_2]) ).
fof(f_1049_1,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).
fof(f_1049_2,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1049_1]) ).
cnf(f_1049_3,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1049_2]) ).
fof(f_1050_1,plain,
class_Rings_Oring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).
fof(f_1050_2,plain,
class_Rings_Oring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1050_1]) ).
cnf(f_1050_3,plain,
class_Rings_Oring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1050_2]) ).
fof(f_1051_1,plain,
class_Int_Onumber(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Onumber]) ).
fof(f_1051_2,plain,
class_Int_Onumber(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1051_1]) ).
cnf(f_1051_3,plain,
class_Int_Onumber(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1051_2]) ).
fof(f_1052_1,plain,
class_Groups_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).
fof(f_1052_2,plain,
class_Groups_Oone(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1052_1]) ).
cnf(f_1052_3,plain,
class_Groups_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1052_2]) ).
fof(f_1053_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]) ).
fof(f_1053_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1053_1]) ).
cnf(f_1053_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1053_2]) ).
fof(f_1054_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]) ).
fof(f_1054_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1054_1]) ).
cnf(f_1054_3,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1054_2]) ).
fof(f_1055_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]) ).
fof(f_1055_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1055_1]) ).
cnf(f_1055_3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1055_2]) ).
fof(f_1056_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1056_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1056_1]) ).
cnf(f_1056_3,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1056_2]) ).
fof(f_1057_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).
fof(f_1057_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1057_1]) ).
cnf(f_1057_3,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1057_2]) ).
fof(f_1058_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__ab__semigroup__add]) ).
fof(f_1058_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1058_1]) ).
cnf(f_1058_3,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1058_2]) ).
fof(f_1059_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oordered__comm__monoid__add]) ).
fof(f_1059_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1059_1]) ).
cnf(f_1059_3,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1059_2]) ).
fof(f_1060_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1060_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1060_1]) ).
cnf(f_1060_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1060_2]) ).
fof(f_1061_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).
fof(f_1061_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1061_1]) ).
cnf(f_1061_3,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1061_2]) ).
fof(f_1062_1,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).
fof(f_1062_2,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1062_1]) ).
cnf(f_1062_3,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1062_2]) ).
fof(f_1063_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).
fof(f_1063_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1063_1]) ).
cnf(f_1063_3,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1063_2]) ).
fof(f_1064_1,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).
fof(f_1064_2,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1064_1]) ).
cnf(f_1064_3,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1064_2]) ).
fof(f_1065_1,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).
fof(f_1065_2,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1065_1]) ).
cnf(f_1065_3,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1065_2]) ).
fof(f_1066_1,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).
fof(f_1066_2,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1066_1]) ).
cnf(f_1066_3,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1066_2]) ).
fof(f_1067_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).
fof(f_1067_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1067_1]) ).
cnf(f_1067_3,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1067_2]) ).
fof(f_1068_1,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).
fof(f_1068_2,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1068_1]) ).
cnf(f_1068_3,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1068_2]) ).
fof(f_1069_1,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).
fof(f_1069_2,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1069_1]) ).
cnf(f_1069_3,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1069_2]) ).
fof(f_1070_1,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).
fof(f_1070_2,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1070_1]) ).
cnf(f_1070_3,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1070_2]) ).
fof(f_1071_1,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).
fof(f_1071_2,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1071_1]) ).
cnf(f_1071_3,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1071_2]) ).
fof(f_1072_1,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
fof(f_1072_2,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1072_1]) ).
cnf(f_1072_3,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1072_2]) ).
fof(f_1073_1,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).
fof(f_1073_2,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1073_1]) ).
cnf(f_1073_3,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1073_2]) ).
fof(f_1074_1,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).
fof(f_1074_2,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1074_1]) ).
cnf(f_1074_3,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1074_2]) ).
fof(f_1075_1,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
fof(f_1075_2,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1075_1]) ).
cnf(f_1075_3,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1075_2]) ).
fof(f_1076_1,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
fof(f_1076_2,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1076_1]) ).
cnf(f_1076_3,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1076_2]) ).
fof(f_1077_1,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).
fof(f_1077_2,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1077_1]) ).
cnf(f_1077_3,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1077_2]) ).
fof(f_1078_1,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).
fof(f_1078_2,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1078_1]) ).
cnf(f_1078_3,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1078_2]) ).
fof(f_1079_1,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__1]) ).
fof(f_1079_2,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1079_1]) ).
cnf(f_1079_3,plain,
class_Rings_Osemiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1079_2]) ).
fof(f_1080_1,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).
fof(f_1080_2,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1080_1]) ).
cnf(f_1080_3,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1080_2]) ).
fof(f_1081_1,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).
fof(f_1081_2,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1081_1]) ).
cnf(f_1081_3,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1081_2]) ).
fof(f_1082_1,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
fof(f_1082_2,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1082_1]) ).
cnf(f_1082_3,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1082_2]) ).
fof(f_1083_1,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).
fof(f_1083_2,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1083_1]) ).
cnf(f_1083_3,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1083_2]) ).
fof(f_1084_1,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
fof(f_1084_2,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1084_1]) ).
cnf(f_1084_3,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1084_2]) ).
fof(f_1085_1,plain,
class_Power_Opower(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).
fof(f_1085_2,plain,
class_Power_Opower(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1085_1]) ).
cnf(f_1085_3,plain,
class_Power_Opower(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1085_2]) ).
fof(f_1086_1,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).
fof(f_1086_2,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1086_1]) ).
cnf(f_1086_3,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1086_2]) ).
fof(f_1087_1,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Int_Onumber]) ).
fof(f_1087_2,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1087_1]) ).
cnf(f_1087_3,plain,
class_Int_Onumber(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1087_2]) ).
fof(f_1088_1,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).
fof(f_1088_2,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1088_1]) ).
cnf(f_1088_3,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1088_2]) ).
fof(f_1089_1,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).
fof(f_1089_2,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1089_1]) ).
cnf(f_1089_3,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1089_2]) ).
fof(f_1090_1,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).
fof(f_1090_2,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1090_1]) ).
cnf(f_1090_3,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1090_2]) ).
fof(f_1091_1,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).
fof(f_1091_2,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1091_1]) ).
cnf(f_1091_3,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1091_2]) ).
fof(f_1092_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]) ).
fof(f_1092_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1092_1]) ).
cnf(f_1092_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1092_2]) ).
fof(f_1093_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]) ).
fof(f_1093_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1093_1]) ).
cnf(f_1093_3,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1093_2]) ).
fof(f_1094_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]) ).
fof(f_1094_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1094_1]) ).
cnf(f_1094_3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1094_2]) ).
fof(f_1095_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1095_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1095_1]) ).
cnf(f_1095_3,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1095_2]) ).
fof(f_1096_1,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero]) ).
fof(f_1096_2,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1096_1]) ).
cnf(f_1096_3,plain,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1096_2]) ).
fof(f_1097_1,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict]) ).
fof(f_1097_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1097_1]) ).
cnf(f_1097_3,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1097_2]) ).
fof(f_1098_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra]) ).
fof(f_1098_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1098_1]) ).
cnf(f_1098_3,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1098_2]) ).
fof(f_1099_1,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]) ).
fof(f_1099_2,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1099_1]) ).
cnf(f_1099_3,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1099_2]) ).
fof(f_1100_1,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero]) ).
fof(f_1100_2,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1100_1]) ).
cnf(f_1100_3,plain,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1100_2]) ).
fof(f_1101_1,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1]) ).
fof(f_1101_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1101_1]) ).
cnf(f_1101_3,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1101_2]) ).
fof(f_1102_1,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add]) ).
fof(f_1102_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1102_1]) ).
cnf(f_1102_3,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1102_2]) ).
fof(f_1103_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]) ).
fof(f_1103_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1103_1]) ).
cnf(f_1103_3,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1103_2]) ).
fof(f_1104_1,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
fof(f_1104_2,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1104_1]) ).
cnf(f_1104_3,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1104_2]) ).
fof(f_1105_1,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add]) ).
fof(f_1105_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1105_1]) ).
cnf(f_1105_3,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1105_2]) ).
fof(f_1106_1,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Olinordered__ab__group__add]) ).
fof(f_1106_2,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1106_1]) ).
cnf(f_1106_3,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1106_2]) ).
fof(f_1107_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1107_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1107_1]) ).
cnf(f_1107_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1107_2]) ).
fof(f_1108_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]) ).
fof(f_1108_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1108_1]) ).
cnf(f_1108_3,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1108_2]) ).
fof(f_1109_1,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]) ).
fof(f_1109_2,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1109_1]) ).
cnf(f_1109_3,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1109_2]) ).
fof(f_1110_1,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
fof(f_1110_2,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1110_1]) ).
cnf(f_1110_3,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1110_2]) ).
fof(f_1111_1,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).
fof(f_1111_2,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1111_1]) ).
cnf(f_1111_3,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1111_2]) ).
fof(f_1112_1,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__field]) ).
fof(f_1112_2,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1112_1]) ).
cnf(f_1112_3,plain,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1112_2]) ).
fof(f_1113_1,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__no__zero__divisors]) ).
fof(f_1113_2,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1113_1]) ).
cnf(f_1113_3,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1113_2]) ).
fof(f_1114_1,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]) ).
fof(f_1114_2,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1114_1]) ).
cnf(f_1114_3,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1114_2]) ).
fof(f_1115_1,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]) ).
fof(f_1115_2,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1115_1]) ).
cnf(f_1115_3,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1115_2]) ).
fof(f_1116_1,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oordered__ab__group__add]) ).
fof(f_1116_2,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1116_1]) ).
cnf(f_1116_3,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1116_2]) ).
fof(f_1117_1,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).
fof(f_1117_2,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1117_1]) ).
cnf(f_1117_3,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1117_2]) ).
fof(f_1118_1,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]) ).
fof(f_1118_2,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1118_1]) ).
cnf(f_1118_3,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1118_2]) ).
fof(f_1119_1,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield__inverse__zero]) ).
fof(f_1119_2,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1119_1]) ).
cnf(f_1119_3,plain,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1119_2]) ).
fof(f_1120_1,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
fof(f_1120_2,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1120_1]) ).
cnf(f_1120_3,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1120_2]) ).
fof(f_1121_1,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]) ).
fof(f_1121_2,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1121_1]) ).
cnf(f_1121_3,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1121_2]) ).
fof(f_1122_1,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]) ).
fof(f_1122_2,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1122_1]) ).
cnf(f_1122_3,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1122_2]) ).
fof(f_1123_1,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).
fof(f_1123_2,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1123_1]) ).
cnf(f_1123_3,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1123_2]) ).
fof(f_1124_1,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Olinordered__field]) ).
fof(f_1124_2,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1124_1]) ).
cnf(f_1124_3,plain,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1124_2]) ).
fof(f_1125_1,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]) ).
fof(f_1125_2,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1125_1]) ).
cnf(f_1125_3,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1125_2]) ).
fof(f_1126_1,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]) ).
fof(f_1126_2,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1126_1]) ).
cnf(f_1126_3,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1126_2]) ).
fof(f_1127_1,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]) ).
fof(f_1127_2,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1127_1]) ).
cnf(f_1127_3,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1127_2]) ).
fof(f_1128_1,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
fof(f_1128_2,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1128_1]) ).
cnf(f_1128_3,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1128_2]) ).
fof(f_1129_1,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]) ).
fof(f_1129_2,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1129_1]) ).
cnf(f_1129_3,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1129_2]) ).
fof(f_1130_1,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
fof(f_1130_2,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1130_1]) ).
cnf(f_1130_3,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1130_2]) ).
fof(f_1131_1,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
fof(f_1131_2,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1131_1]) ).
cnf(f_1131_3,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1131_2]) ).
fof(f_1132_1,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__field]) ).
fof(f_1132_2,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1132_1]) ).
cnf(f_1132_3,plain,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1132_2]) ).
fof(f_1133_1,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odivision__ring]) ).
fof(f_1133_2,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1133_1]) ).
cnf(f_1133_3,plain,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1133_2]) ).
fof(f_1134_1,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]) ).
fof(f_1134_2,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1134_1]) ).
cnf(f_1134_3,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1134_2]) ).
fof(f_1135_1,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]) ).
fof(f_1135_2,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1135_1]) ).
cnf(f_1135_3,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1135_2]) ).
fof(f_1136_1,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]) ).
fof(f_1136_2,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1136_1]) ).
cnf(f_1136_3,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1136_2]) ).
fof(f_1137_1,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).
fof(f_1137_2,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1137_1]) ).
cnf(f_1137_3,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1137_2]) ).
fof(f_1138_1,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(f_1138_2,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1138_1]) ).
cnf(f_1138_3,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1138_2]) ).
fof(f_1139_1,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(f_1139_2,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1139_1]) ).
cnf(f_1139_3,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1139_2]) ).
fof(f_1140_1,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
fof(f_1140_2,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1140_1]) ).
cnf(f_1140_3,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1140_2]) ).
fof(f_1141_1,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]) ).
fof(f_1141_2,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1141_1]) ).
cnf(f_1141_3,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1141_2]) ).
fof(f_1142_1,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
fof(f_1142_2,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1142_1]) ).
cnf(f_1142_3,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1142_2]) ).
fof(f_1143_1,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__1]) ).
fof(f_1143_2,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1143_1]) ).
cnf(f_1143_3,plain,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1143_2]) ).
fof(f_1144_1,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]) ).
fof(f_1144_2,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1144_1]) ).
cnf(f_1144_3,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1144_2]) ).
fof(f_1145_1,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
fof(f_1145_2,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1145_1]) ).
cnf(f_1145_3,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1145_2]) ).
fof(f_1146_1,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]) ).
fof(f_1146_2,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1146_1]) ).
cnf(f_1146_3,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1146_2]) ).
fof(f_1147_1,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(f_1147_2,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1147_1]) ).
cnf(f_1147_3,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1147_2]) ).
fof(f_1148_1,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]) ).
fof(f_1148_2,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1148_1]) ).
cnf(f_1148_3,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1148_2]) ).
fof(f_1149_1,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Onumber__ring]) ).
fof(f_1149_2,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1149_1]) ).
cnf(f_1149_3,plain,
class_Int_Onumber__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1149_2]) ).
fof(f_1150_1,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]) ).
fof(f_1150_2,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1150_1]) ).
cnf(f_1150_3,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1150_2]) ).
fof(f_1151_1,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]) ).
fof(f_1151_2,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1151_1]) ).
cnf(f_1151_3,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1151_2]) ).
fof(f_1152_1,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]) ).
fof(f_1152_2,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1152_1]) ).
cnf(f_1152_3,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1152_2]) ).
fof(f_1153_1,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Fields_Ofield]) ).
fof(f_1153_2,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1153_1]) ).
cnf(f_1153_3,plain,
class_Fields_Ofield(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1153_2]) ).
fof(f_1154_1,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Power_Opower]) ).
fof(f_1154_2,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1154_1]) ).
cnf(f_1154_3,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1154_2]) ).
fof(f_1155_1,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]) ).
fof(f_1155_2,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1155_1]) ).
cnf(f_1155_3,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1155_2]) ).
fof(f_1156_1,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]) ).
fof(f_1156_2,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1156_1]) ).
cnf(f_1156_3,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1156_2]) ).
fof(f_1157_1,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Onumber]) ).
fof(f_1157_2,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1157_1]) ).
cnf(f_1157_3,plain,
class_Int_Onumber(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1157_2]) ).
fof(f_1158_1,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]) ).
fof(f_1158_2,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1158_1]) ).
cnf(f_1158_3,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1158_2]) ).
fof(f_1159_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]) ).
fof(f_1159_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1159_1]) ).
cnf(f_1159_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1159_2]) ).
fof(f_1160_1,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra]) ).
fof(f_1160_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1160_1]) ).
cnf(f_1160_3,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1160_2]) ).
fof(f_1161_1,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring__inverse__zero]) ).
fof(f_1161_2,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1161_1]) ).
cnf(f_1161_3,plain,
class_Rings_Odivision__ring__inverse__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1161_2]) ).
fof(f_1162_1,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1]) ).
fof(f_1162_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1162_1]) ).
cnf(f_1162_3,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1162_2]) ).
fof(f_1163_1,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
fof(f_1163_2,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1163_1]) ).
cnf(f_1163_3,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1163_2]) ).
fof(f_1164_1,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1164_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1164_1]) ).
cnf(f_1164_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1164_2]) ).
fof(f_1165_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]) ).
fof(f_1165_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1165_1]) ).
cnf(f_1165_3,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1165_2]) ).
fof(f_1166_1,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(f_1166_2,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1166_1]) ).
cnf(f_1166_3,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1166_2]) ).
fof(f_1167_1,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__field]) ).
fof(f_1167_2,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1167_1]) ).
cnf(f_1167_3,plain,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1167_2]) ).
fof(f_1168_1,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors]) ).
fof(f_1168_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1168_1]) ).
cnf(f_1168_3,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1168_2]) ).
fof(f_1169_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]) ).
fof(f_1169_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1169_1]) ).
cnf(f_1169_3,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1169_2]) ).
fof(f_1170_1,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield__inverse__zero]) ).
fof(f_1170_2,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1170_1]) ).
cnf(f_1170_3,plain,
class_Fields_Ofield__inverse__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1170_2]) ).
fof(f_1171_1,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]) ).
fof(f_1171_2,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1171_1]) ).
cnf(f_1171_3,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1171_2]) ).
fof(f_1172_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]) ).
fof(f_1172_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1172_1]) ).
cnf(f_1172_3,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1172_2]) ).
fof(f_1173_1,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]) ).
fof(f_1173_2,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1173_1]) ).
cnf(f_1173_3,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1173_2]) ).
fof(f_1174_1,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).
fof(f_1174_2,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1174_1]) ).
cnf(f_1174_3,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1174_2]) ).
fof(f_1175_1,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
fof(f_1175_2,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1175_1]) ).
cnf(f_1175_3,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1175_2]) ).
fof(f_1176_1,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(f_1176_2,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1176_1]) ).
cnf(f_1176_3,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1176_2]) ).
fof(f_1177_1,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__field]) ).
fof(f_1177_2,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1177_1]) ).
cnf(f_1177_3,plain,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1177_2]) ).
fof(f_1178_1,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odivision__ring]) ).
fof(f_1178_2,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1178_1]) ).
cnf(f_1178_3,plain,
class_Rings_Odivision__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1178_2]) ).
fof(f_1179_1,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]) ).
fof(f_1179_2,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1179_1]) ).
cnf(f_1179_3,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1179_2]) ).
fof(f_1180_1,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).
fof(f_1180_2,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1180_1]) ).
cnf(f_1180_3,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1180_2]) ).
fof(f_1181_1,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).
fof(f_1181_2,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1181_1]) ).
cnf(f_1181_3,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1181_2]) ).
fof(f_1182_1,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).
fof(f_1182_2,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1182_1]) ).
cnf(f_1182_3,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1182_2]) ).
fof(f_1183_1,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).
fof(f_1183_2,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1183_1]) ).
cnf(f_1183_3,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1183_2]) ).
fof(f_1184_1,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]) ).
fof(f_1184_2,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1184_1]) ).
cnf(f_1184_3,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1184_2]) ).
fof(f_1185_1,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__1]) ).
fof(f_1185_2,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1185_1]) ).
cnf(f_1185_3,plain,
class_Rings_Osemiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1185_2]) ).
fof(f_1186_1,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]) ).
fof(f_1186_2,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1186_1]) ).
cnf(f_1186_3,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1186_2]) ).
fof(f_1187_1,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
fof(f_1187_2,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1187_1]) ).
cnf(f_1187_3,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1187_2]) ).
fof(f_1188_1,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).
fof(f_1188_2,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1188_1]) ).
cnf(f_1188_3,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1188_2]) ).
fof(f_1189_1,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
fof(f_1189_2,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1189_1]) ).
cnf(f_1189_3,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1189_2]) ).
fof(f_1190_1,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber__ring]) ).
fof(f_1190_2,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1190_1]) ).
cnf(f_1190_3,plain,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1190_2]) ).
fof(f_1191_1,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]) ).
fof(f_1191_2,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1191_1]) ).
cnf(f_1191_3,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1191_2]) ).
fof(f_1192_1,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]) ).
fof(f_1192_2,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1192_1]) ).
cnf(f_1192_3,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1192_2]) ).
fof(f_1193_1,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Fields_Ofield]) ).
fof(f_1193_2,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1193_1]) ).
cnf(f_1193_3,plain,
class_Fields_Ofield(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1193_2]) ).
fof(f_1194_1,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
fof(f_1194_2,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1194_1]) ).
cnf(f_1194_3,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1194_2]) ).
fof(f_1195_1,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
fof(f_1195_2,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1195_1]) ).
cnf(f_1195_3,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1195_2]) ).
fof(f_1196_1,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]) ).
fof(f_1196_2,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1196_1]) ).
cnf(f_1196_3,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1196_2]) ).
fof(f_1197_1,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Onumber]) ).
fof(f_1197_2,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1197_1]) ).
cnf(f_1197_3,plain,
class_Int_Onumber(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1197_2]) ).
fof(f_1198_1,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]) ).
fof(f_1198_2,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1198_1]) ).
cnf(f_1198_3,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1198_2]) ).
fof(f_1199_1,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_1199_2,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(definitional_conversion,[status(esa)],[f_1199_1]) ).
cnf(f_1199_3,negated_conjecture,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
inference(clausify,[status(thm)],[f_1199_2]) ).
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_Otimes__class_Otimes(Eq_x_0) = c_Groups_Otimes__class_Otimes(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_6,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_7,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_8,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_9,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_10,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_11,axiom,
( c_Power_Opower__class_Opower(Eq_x_0) = c_Power_Opower__class_Opower(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_12,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_13,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_14,axiom,
( c_Complex_Ocomplex_OComplex(Eq_x_0,Eq_x_1) = c_Complex_Ocomplex_OComplex(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_15,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_16,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_17,axiom,
( c_Power_Opower_Opower(Eq_x_0,Eq_x_1,Eq_x_2) = c_Power_Opower_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_18,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_19,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_20,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_21,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_22,axiom,
( c_Complex_Ocomplex_Ocomplex__size(Eq_x_0) = c_Complex_Ocomplex_Ocomplex__size(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,axiom,
( c_Nat_Osize__class_Osize(Eq_x_0,Eq_x_1) = c_Nat_Osize__class_Osize(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_Complex_Ocomplex_Ocomplex__case(Eq_x_0,Eq_x_1,Eq_x_2) = c_Complex_Ocomplex_Ocomplex__case(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_Transcendental_Oarctan(Eq_x_0) = c_Transcendental_Oarctan(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_27,axiom,
( c_Complex_Ocomplex_Ocomplex__rec(Eq_x_0,Eq_x_1,Eq_x_2) = c_Complex_Ocomplex_Ocomplex__rec(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_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,
( 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_30,axiom,
( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK4(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_31,axiom,
( sK5(Eq_x_0,Eq_x_1) = sK5(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_32,axiom,
( sK6(Eq_x_0,Eq_x_1) = sK6(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_33,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_34,axiom,
( sK8(Eq_x_0) = sK8(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK9(Eq_x_0,Eq_x_1) = sK9(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,
( 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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,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_55,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_56,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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,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_67,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_68,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_69,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_70,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_71,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_72,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_73,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_74,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_75,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_76,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_77,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_78,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_79,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_80,axiom,
( class_Rings_Olinordered__semiring__1(Eq_y_0)
| ~ class_Rings_Olinordered__semiring__1(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_81,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_82,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_83,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_84,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_85,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_86,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_87,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_88,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_89,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_90,axiom,
( class_Rings_Oordered__ring__abs(Eq_y_0)
| ~ class_Rings_Oordered__ring__abs(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_91,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_92,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_93,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_94,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_95,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_96,axiom,
( class_RealVector_Oreal__field(Eq_y_0)
| ~ class_RealVector_Oreal__field(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_97,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_98,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_99,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_100,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_101,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_102,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_103,axiom,
( class_Rings_Olinordered__semiring(Eq_y_0)
| ~ class_Rings_Olinordered__semiring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_104,axiom,
( class_Rings_Olinordered__semiring__1__strict(Eq_y_0)
| ~ class_Rings_Olinordered__semiring__1__strict(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_105,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_106,axiom,
( sP0(Eq_y_0,Eq_y_1)
| ~ sP0(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_107,axiom,
( sP1(Eq_y_0,Eq_y_1)
| ~ sP1(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_108,axiom,
( sP2(Eq_y_0,Eq_y_1)
| ~ sP2(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_109,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_110,axiom,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_111,axiom,
( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_112,axiom,
( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_113,axiom,
( sP7(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP7(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_114,axiom,
( sP8(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP8(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_115,axiom,
( sP9(Eq_y_0,Eq_y_1)
| ~ sP9(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_116,axiom,
( sP10(Eq_y_0,Eq_y_1)
| ~ sP10(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_117,axiom,
( sP11(Eq_y_0,Eq_y_1)
| ~ sP11(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_118,axiom,
( sP12(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP12(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_119,axiom,
( sP13(Eq_y_0,Eq_y_1)
| ~ sP13(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_120,axiom,
( sP14(Eq_y_0,Eq_y_1)
| ~ sP14(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_121,axiom,
( sP15(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP15(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_122,axiom,
( sP16(Eq_y_0,Eq_y_1)
| ~ sP16(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_123,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP17(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_124,axiom,
( sP18(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP18(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_125,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP19(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_126,axiom,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_127,axiom,
( sP21(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP21(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_128,axiom,
( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP22(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_129,axiom,
( sP23(Eq_y_0,Eq_y_1)
| ~ sP23(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_130,axiom,
( sP24(Eq_y_0,Eq_y_1)
| ~ sP24(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_131,axiom,
( sP25(Eq_y_0,Eq_y_1)
| ~ sP25(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_132,axiom,
( sP26(Eq_y_0,Eq_y_1)
| ~ sP26(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_133,axiom,
( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP27(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_134,axiom,
( sP28(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP28(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_135,axiom,
( sP29(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP29(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_136,axiom,
( sP30(Eq_y_0,Eq_y_1)
| ~ sP30(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_137,axiom,
( sP31(Eq_y_0,Eq_y_1)
| ~ sP31(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_138,axiom,
( sP32(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP32(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_139,axiom,
( sP33(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP33(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_140,axiom,
( sP34(Eq_y_0,Eq_y_1)
| ~ sP34(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_141,axiom,
( sP35(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP35(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_142,axiom,
( sP36(Eq_y_0,Eq_y_1)
| ~ sP36(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_143,axiom,
( sP37(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP37(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_144,axiom,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP38(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_145,axiom,
( sP39(Eq_y_0,Eq_y_1)
| ~ sP39(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_146,axiom,
( sP40(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP40(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_147,axiom,
( sP41(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP41(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_148,axiom,
( sP42(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP42(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_149,axiom,
( sP43(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP43(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_150,axiom,
( sP44(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP44(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_151,axiom,
( sP45(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP45(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_152,axiom,
( sP46(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_153,axiom,
( sP47(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_154,axiom,
( sP48(Eq_y_0,Eq_y_1)
| ~ sP48(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_155,axiom,
( sP49(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_156,axiom,
( sP50(Eq_y_0,Eq_y_1)
| ~ sP50(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_157,axiom,
( sP51(Eq_y_0,Eq_y_1)
| ~ sP51(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_158,axiom,
( sP52(Eq_y_0,Eq_y_1)
| ~ sP52(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_159,axiom,
( sP53(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP53(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_160,axiom,
( sP54(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP54(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_161,axiom,
( sP55(Eq_y_0,Eq_y_1)
| ~ sP55(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_162,axiom,
( sP56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_163,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_164,axiom,
( sP58(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP58(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_165,axiom,
( sP59(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP59(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_166,axiom,
( sP60(Eq_y_0,Eq_y_1)
| ~ sP60(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_167,axiom,
( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP61(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_168,axiom,
( sP62(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP62(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_169,axiom,
( sP63(Eq_y_0,Eq_y_1)
| ~ sP63(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_170,axiom,
( sP64(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP64(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_171,axiom,
( sP65(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP65(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_172,axiom,
( sP66(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP66(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_173,axiom,
( sP67(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP67(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_174,axiom,
( sP68(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP68(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_175,axiom,
( sP69(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP69(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_176,axiom,
( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP70(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_177,axiom,
( sP71(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP71(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_178,axiom,
( sP72(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP72(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_179,axiom,
( sP73(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP73(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_180,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP74(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_181,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP75(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_182,axiom,
( sP76(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP76(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_183,axiom,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP77(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_184,axiom,
( sP78(Eq_y_0,Eq_y_1)
| ~ sP78(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_185,axiom,
( sP79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_186,axiom,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_187,axiom,
( sP81(Eq_y_0,Eq_y_1)
| ~ sP81(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_188,axiom,
( sP82(Eq_y_0,Eq_y_1)
| ~ sP82(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_189,axiom,
( sP83(Eq_y_0,Eq_y_1)
| ~ sP83(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_190,axiom,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP84(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_191,axiom,
( sP85(Eq_y_0)
| ~ sP85(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_192,axiom,
( sP86(Eq_y_0,Eq_y_1)
| ~ sP86(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_193,axiom,
( sP87(Eq_y_0,Eq_y_1)
| ~ sP87(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_194,axiom,
( sP88(Eq_y_0,Eq_y_1)
| ~ sP88(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_195,axiom,
( sP89(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP89(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_196,axiom,
( sP90(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP90(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_197,axiom,
( sP91(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP91(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_198,axiom,
( sP92(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP92(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_199,axiom,
( sP93(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP93(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_200,axiom,
( sP94(Eq_y_0,Eq_y_1)
| ~ sP94(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_201,axiom,
( sP95(Eq_y_0,Eq_y_1)
| ~ sP95(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_202,axiom,
( sP96(Eq_y_0,Eq_y_1)
| ~ sP96(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_203,axiom,
( sP97(Eq_y_0,Eq_y_1)
| ~ sP97(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_204,axiom,
( sP98(Eq_y_0,Eq_y_1)
| ~ sP98(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_205,axiom,
( sP99(Eq_y_0,Eq_y_1)
| ~ sP99(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_206,axiom,
( sP100(Eq_y_0,Eq_y_1)
| ~ sP100(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_207,axiom,
( sP101(Eq_y_0,Eq_y_1)
| ~ sP101(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_208,axiom,
( sP102(Eq_y_0,Eq_y_1)
| ~ sP102(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_209,axiom,
( sP103(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP103(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_210,axiom,
( sP104(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP104(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_211,axiom,
( sP105(Eq_y_0,Eq_y_1)
| ~ sP105(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_212,axiom,
( sP106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP106(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_213,axiom,
( sP107(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP107(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_214,axiom,
( sP108(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP108(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_215,axiom,
( sP109(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP109(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_216,axiom,
( sP110(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP110(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_217,axiom,
( sP111(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP111(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_218,axiom,
( sP112(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP112(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_219,axiom,
( sP113(Eq_y_0,Eq_y_1)
| ~ sP113(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_220,axiom,
( sP114(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP114(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_221,axiom,
( sP115(Eq_y_0,Eq_y_1)
| ~ sP115(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_222,axiom,
( sP116(Eq_y_0,Eq_y_1)
| ~ sP116(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_223,axiom,
( sP117(Eq_y_0,Eq_y_1)
| ~ sP117(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_224,axiom,
( sP118(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_225,axiom,
( sP119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_226,axiom,
( sP120(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP120(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_227,axiom,
( sP121(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP121(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_228,axiom,
( sP122(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP122(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_229,axiom,
( sP123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_230,axiom,
( sP124(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP124(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_231,axiom,
( sP125(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP125(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_232,axiom,
( sP126(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP126(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_233,axiom,
( sP127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP127(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_234,axiom,
( sP128(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP128(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_235,axiom,
( sP129(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_236,axiom,
( sP130(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP130(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_237,axiom,
( sP131(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP131(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_238,axiom,
( sP132(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP132(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_239,axiom,
( sP133(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_240,axiom,
( sP134(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP134(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_241,axiom,
( sP135(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP135(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_242,axiom,
( sP136(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP136(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_243,axiom,
( sP137(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP137(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_244,axiom,
( sP138(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP138(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_245,axiom,
( sP139(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP139(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_246,axiom,
( sP140(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP140(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_247,axiom,
( sP141(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP141(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_248,axiom,
( sP142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_249,axiom,
( sP143(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP143(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_250,axiom,
( sP144(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP144(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_251,axiom,
( sP145(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_252,axiom,
( sP146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_253,axiom,
( sP147(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP147(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_254,axiom,
( sP148(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP148(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_255,axiom,
( sP149(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP149(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_256,axiom,
( sP150(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP150(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_257,axiom,
( sP151(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP151(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_258,axiom,
( sP152(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP152(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_259,axiom,
( sP153(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP153(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_260,axiom,
( sP154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP154(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_261,axiom,
( sP155(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP155(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_262,axiom,
( sP156(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP156(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_263,axiom,
( sP157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_264,axiom,
( sP158(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP158(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_265,axiom,
( sP159(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP159(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_266,axiom,
( sP160(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP160(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_267,axiom,
( sP161(Eq_y_0,Eq_y_1)
| ~ sP161(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_268,axiom,
( sP162(Eq_y_0,Eq_y_1)
| ~ sP162(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_269,axiom,
( sP163(Eq_y_0,Eq_y_1)
| ~ sP163(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_270,axiom,
( sP164(Eq_y_0,Eq_y_1)
| ~ sP164(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_271,axiom,
( sP165(Eq_y_0,Eq_y_1)
| ~ sP165(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_272,axiom,
( sP166(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP166(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_273,axiom,
( sP167(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP167(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_274,axiom,
( sP168(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP168(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_275,axiom,
( sP169(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP169(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_276,axiom,
( sP170(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP170(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_277,axiom,
( sP171(Eq_y_0,Eq_y_1)
| ~ sP171(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_278,axiom,
( sP172(Eq_y_0,Eq_y_1)
| ~ sP172(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_279,axiom,
( sP173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_280,axiom,
( sP174(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_281,axiom,
( sP175(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP175(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_282,axiom,
( sP176(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP176(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_283,axiom,
( sP177(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP177(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_284,axiom,
( sP178(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP178(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_285,axiom,
( sP179(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP179(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_286,axiom,
( sP180(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP180(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_287,axiom,
( sP181(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP181(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_288,axiom,
( sP182(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP182(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_289,axiom,
( sP183(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP183(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_290,axiom,
( sP184(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP184(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_291,axiom,
( sP185(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP185(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_292,axiom,
( sP186(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP186(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_293,axiom,
( sP187(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP187(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_294,axiom,
( sP188(Eq_y_0,Eq_y_1)
| ~ sP188(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_295,axiom,
( sP189(Eq_y_0,Eq_y_1)
| ~ sP189(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_296,axiom,
( sP190(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP190(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_297,axiom,
( sP191(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP191(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_298,axiom,
( sP192(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP192(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_299,axiom,
( sP193(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP193(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_300,axiom,
( sP194(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP194(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_301,axiom,
( sP195(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP195(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_302,axiom,
( sP196(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP196(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_303,axiom,
( sP197(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP197(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_304,axiom,
( sP198(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP198(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_305,axiom,
( sP199(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP199(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_306,axiom,
( sP200(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP200(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_307,axiom,
( sP201(Eq_y_0,Eq_y_1)
| ~ sP201(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_308,axiom,
( sP202(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP202(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_309,axiom,
( sP203(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP203(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_310,axiom,
( sP204(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP204(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_311,axiom,
( sP205(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP205(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_312,axiom,
( sP206(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP206(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_313,axiom,
( sP207(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP207(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_314,axiom,
( sP208(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP208(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
| Eq_x_5 != Eq_y_5
| Eq_x_4 != Eq_y_4
| 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_predicates]) ).
cnf(equality_315,axiom,
( sP209(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP209(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_316,axiom,
( sP210(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP210(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_317,axiom,
( sP211(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP211(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_318,axiom,
( sP212(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP212(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_319,axiom,
( sP213(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP213(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_320,axiom,
( sP214(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP214(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_321,axiom,
( sP215(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_322,axiom,
( sP216(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_323,axiom,
( sP217(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP217(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_324,axiom,
( sP218(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP218(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_325,axiom,
( sP219(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_326,axiom,
( sP220(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP220(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_327,axiom,
( sP221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_328,axiom,
( sP222(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_329,axiom,
( sP223(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP223(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_330,axiom,
( sP224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_331,axiom,
( sP225(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_332,axiom,
( sP226(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP226(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_333,axiom,
( sP227(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP227(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_334,axiom,
( sP228(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_335,axiom,
( sP229(Eq_y_0,Eq_y_1)
| ~ sP229(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_336,axiom,
( sP230(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP230(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_337,axiom,
( sP231(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP231(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_338,axiom,
( sP232(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP232(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_339,axiom,
( sP233(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP233(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_340,axiom,
( sP234(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP234(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_341,axiom,
( sP235(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_342,axiom,
( sP236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_343,axiom,
( sP237(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_344,axiom,
( sP238(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_345,axiom,
( sP239(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP239(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_346,axiom,
( sP240(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP240(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_347,axiom,
( sP241(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP241(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_348,axiom,
( sP242(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP242(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_349,axiom,
( sP243(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP243(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_350,axiom,
( sP244(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP244(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_351,axiom,
( sP245(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP245(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_352,axiom,
( sP246(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP246(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_353,axiom,
( sP247(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP247(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_354,axiom,
( sP248(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP248(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_355,axiom,
( sP249(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP249(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_356,axiom,
( sP250(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP250(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_357,axiom,
( sP251(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP251(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_358,axiom,
( sP252(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP252(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_359,axiom,
( sP253(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP253(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_360,axiom,
( sP254(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP254(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_361,axiom,
( sP255(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP255(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_362,axiom,
( sP256(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP256(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_363,axiom,
( sP257(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP257(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_364,axiom,
( sP258(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP258(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_365,axiom,
( sP259(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP259(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_366,axiom,
( sP260(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP260(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_367,axiom,
( sP261(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP261(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_368,axiom,
( sP262(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP262(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_369,axiom,
( sP263(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP263(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_370,axiom,
( sP264(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP264(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_371,axiom,
( sP265(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP265(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_372,axiom,
( sP266(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP266(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_373,axiom,
( sP267(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP267(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_374,axiom,
( sP268(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP268(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_375,axiom,
( sP269(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP269(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_376,axiom,
( sP270(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP270(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_377,axiom,
( sP271(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP271(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_378,axiom,
( sP272(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP272(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_379,axiom,
( sP273(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_380,axiom,
( sP274(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP274(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_381,axiom,
( sP275(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP275(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_382,axiom,
( sP276(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP276(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_383,axiom,
( sP277(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP277(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_384,axiom,
( sP278(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP278(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_385,axiom,
( sP279(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP279(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_386,axiom,
( sP280(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP280(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_387,axiom,
( sP281(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP281(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_388,axiom,
( sP282(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP282(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_389,axiom,
( sP283(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP283(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_390,axiom,
( sP284(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP284(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_391,axiom,
( sP285(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_392,axiom,
( sP286(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP286(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_393,axiom,
( sP287(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP287(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_394,axiom,
( sP288(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP288(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_395,axiom,
( sP289(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP289(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_396,axiom,
( sP290(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP290(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_397,axiom,
( sP291(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP291(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_398,axiom,
( sP292(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP292(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_399,axiom,
( sP293(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP293(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_400,axiom,
( sP294(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP294(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_401,axiom,
( sP295(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP295(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_402,axiom,
( sP296(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP296(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_403,axiom,
( sP297(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP297(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_404,axiom,
( sP298(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP298(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_405,axiom,
( sP299(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP299(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_406,axiom,
( sP300(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP300(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_407,axiom,
( sP301(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP301(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_408,axiom,
( sP302(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP302(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_409,axiom,
( sP303(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP303(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_410,axiom,
( sP304(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP304(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_411,axiom,
( sP305(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP305(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_412,axiom,
( sP306(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP306(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_413,axiom,
( sP307(Eq_y_0,Eq_y_1)
| ~ sP307(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_414,axiom,
( sP308(Eq_y_0,Eq_y_1)
| ~ sP308(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_415,axiom,
( sP309(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP309(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_416,axiom,
( sP310(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP310(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_417,axiom,
( sP311(Eq_y_0,Eq_y_1)
| ~ sP311(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_418,axiom,
( sP312(Eq_y_0,Eq_y_1)
| ~ sP312(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_419,axiom,
( sP313(Eq_y_0,Eq_y_1)
| ~ sP313(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_420,axiom,
( sP314(Eq_y_0,Eq_y_1)
| ~ sP314(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_421,axiom,
( sP315(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP315(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_422,axiom,
( sP316(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP316(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_423,axiom,
( sP317(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP317(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_424,axiom,
( sP318(Eq_y_0,Eq_y_1)
| ~ sP318(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_425,axiom,
( sP319(Eq_y_0,Eq_y_1)
| ~ sP319(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_426,axiom,
( sP320(Eq_y_0,Eq_y_1)
| ~ sP320(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_427,axiom,
( sP321(Eq_y_0,Eq_y_1)
| ~ sP321(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_428,axiom,
( sP322(Eq_y_0,Eq_y_1)
| ~ sP322(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_429,axiom,
( sP323(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP323(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_430,axiom,
( sP324(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP324(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_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_predicates]) ).
cnf(equality_431,axiom,
( sP325(Eq_y_0,Eq_y_1)
| ~ sP325(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_432,axiom,
( sP326(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP326(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_433,axiom,
( sP327(Eq_y_0,Eq_y_1)
| ~ sP327(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_434,axiom,
( sP328(Eq_y_0,Eq_y_1)
| ~ sP328(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_435,axiom,
( sP329(Eq_y_0,Eq_y_1)
| ~ sP329(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_436,axiom,
( sP330(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP330(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_437,axiom,
( sP331(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP331(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(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW194+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
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 20 05:12:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 55.88/56.17 % SZS status Theorem for theBenchmark
% 55.88/56.17 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------