%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW181+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 : n020.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 09:04:45 AM UTC 2026
% Result : Theorem 240.36s 240.61s
% Output : Proof 240.49s
% 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_m,axiom,
! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),v_m____) ),
file('theBenchmark.p',fact_m) ).
fof(fact_pCons,axiom,
? [B_m] :
( ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
file('theBenchmark.p',fact_pCons) ).
fof(fact_zero__less__norm__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
<=> V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__less__norm__iff) ).
fof(fact_norm__le__zero__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_norm__le__zero__iff) ).
fof(fact_norm__not__less__zero,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_norm__not__less__zero) ).
fof(fact_norm__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_norm__zero,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_norm__zero) ).
fof(fact_norm__eq__zero,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_norm__eq__zero) ).
fof(fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096,axiom,
~ ! [B_m] :
~ ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m) ),
file('theBenchmark.p',fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096) ).
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_poly__0,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_poly__0) ).
fof(fact_pCons__0__0,axiom,
! [T_a] :
( class_Groups_Ozero(T_a)
=> c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_pCons__0__0) ).
fof(fact_pCons__eq__0__iff,axiom,
! [V_pa_2,V_a_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_OpCons(T_a,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
<=> ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_pCons__eq__0__iff) ).
fof(fact_real__less__def,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__less__def) ).
fof(fact_poly__zero,axiom,
! [V_pa_2,T_a] :
( ( class_Rings_Oidom(T_a)
& class_Int_Oring__char__0(T_a) )
=> ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
<=> V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_poly__zero) ).
fof(fact_linorder__le__cases,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__le__cases) ).
fof(fact_le__funE,axiom,
! [V_x_2,V_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_x_2),hAPP(V_g_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funE) ).
fof(fact_xt1_I6_J,axiom,
! [V_z,V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_z,V_x) ) ) ),
file('theBenchmark.p',fact_xt1_I6_J) ).
fof(fact_xt1_I5_J,axiom,
! [V_x,V_y,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_xt1_I5_J) ).
fof(fact_order__trans,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_z)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_order__trans) ).
fof(fact_order__antisym,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
=> V_x = V_y ) ) ),
file('theBenchmark.p',fact_order__antisym) ).
fof(fact_xt1_I4_J,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_a)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I4_J) ).
fof(fact_ord__le__eq__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( V_b = V_c
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__le__eq__trans) ).
fof(fact_xt1_I3_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_c,V_a) ) ) ),
file('theBenchmark.p',fact_xt1_I3_J) ).
fof(fact_ord__eq__le__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Orderings_Oord(T_a)
=> ( V_a = V_b
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_ord__eq__le__trans) ).
fof(fact_order__antisym__conv,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_order__antisym__conv) ).
fof(fact_le__funD,axiom,
! [V_x_2,V_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_x_2),hAPP(V_g_2,V_x_2)) ) ),
file('theBenchmark.p',fact_le__funD) ).
fof(fact_order__eq__refl,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( V_x = V_y
=> c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_order__eq__refl) ).
fof(fact_order__eq__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( V_x_2 = V_y_2
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__eq__iff) ).
fof(fact_linorder__linear,axiom,
! [V_y,V_x,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_y,V_x)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y) ) ),
file('theBenchmark.p',fact_linorder__linear) ).
fof(fact_le__fun__def,axiom,
! [V_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_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_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_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__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_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_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_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__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_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_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_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__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__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__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_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_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_linorder__antisym__conv3,axiom,
! [V_x_2,V_y_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv3) ).
fof(fact_linorder__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_not__less__iff__gr__or__eq,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ) ),
file('theBenchmark.p',fact_not__less__iff__gr__or__eq) ).
fof(fact_linorder__neq__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( V_x_2 != V_y_2
<=> ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_linorder__neq__iff) ).
fof(fact_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_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_pCons__eq__iff,axiom,
! [V_q_2,V_b_2,V_pa_2,V_a_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Polynomial_OpCons(T_a,V_a_2,V_pa_2) = c_Polynomial_OpCons(T_a,V_b_2,V_q_2)
<=> ( V_pa_2 = V_q_2
& V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_pCons__eq__iff) ).
fof(fact_poly__eq__iff,axiom,
! [V_q_2,V_pa_2,T_a] :
( ( class_Rings_Oidom(T_a)
& class_Int_Oring__char__0(T_a) )
=> ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
<=> V_pa_2 = V_q_2 ) ),
file('theBenchmark.p',fact_poly__eq__iff) ).
fof(fact_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_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv2) ).
fof(fact_order__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_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_linorder__antisym__conv1) ).
fof(fact_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_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__le__less) ).
fof(fact_less__le__not__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Opreorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_less__le__not__le) ).
fof(fact_order__less__le,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_order__less__le) ).
fof(fact_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_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__le) ).
fof(fact_linorder__not__less,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Orderings_Olinorder(T_a)
=> ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_linorder__not__less) ).
fof(fact_less__eq__real__def,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_less__eq__real__def) ).
fof(fact__096_B_Bz_O_Acmod_Az_A_060_061_Ar_A_061_061_062_Acmod_A_Ipoly_A_IpCons_Ac_Acs_J_Az_J_A_060_061_A1_A_L_Acmod_Ac_A_L_Aabs_A_Ir_A_K_Am_J_096,axiom,
! [V_z_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z_2),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),V_z_2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))) ),
file('theBenchmark.p',fact__096_B_Bz_O_Acmod_Az_A_060_061_Ar_A_061_061_062_Acmod_A_Ipoly_A_IpCons_Ac_Acs_J_Az_J_A_060_061_A1_A_L_Acmod_Ac_A_L_Aabs_A_Ir_A_K_Am_J_096) ).
fof(fact_pos__poly__pCons,axiom,
! [V_pa_2,V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_a_2,V_pa_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
& V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_Polynomial_Opos__poly(T_a,V_pa_2) ) ) ),
file('theBenchmark.p',fact_pos__poly__pCons) ).
fof(fact_order__root,axiom,
! [V_a_2,V_pa_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_order__root) ).
fof(fact_poly__rec__pCons,axiom,
! [V_pa_2,V_a_2,T_a,V_z_2,V_f_2,T_b] :
( class_Groups_Ozero(T_b)
=> ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
=> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)) ) ),
file('theBenchmark.p',fact_poly__rec__pCons) ).
fof(fact_poly__rec_Osimps,axiom,
! [V_pa_2,V_a_2,V_f_2,V_z_2,T_a,T_b] :
( class_Groups_Ozero(T_b)
=> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_If(T_a,c_fequal(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2))) ),
file('theBenchmark.p',fact_poly__rec_Osimps) ).
fof(fact_kp,axiom,
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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
file('theBenchmark.p',fact_kp) ).
fof(fact_synthetic__div__pCons,axiom,
! [V_c,V_p,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)) ),
file('theBenchmark.p',fact_synthetic__div__pCons) ).
fof(fact_poly__rec__0,axiom,
! [T_a,V_z_2,V_f_2,T_b] :
( class_Groups_Ozero(T_b)
=> ( hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) = V_z_2
=> c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2 ) ),
file('theBenchmark.p',fact_poly__rec__0) ).
fof(fact_Bseq__def,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) ),
file('theBenchmark.p',fact_Bseq__def) ).
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_zero__reorient,axiom,
! [V_x_2,T_a] :
( class_Groups_Ozero(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_zero__reorient) ).
fof(fact_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_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_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_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_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_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_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_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_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_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_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_add__right__imp__eq,axiom,
! [V_c,V_a,V_b,T_a] :
( class_Groups_Ocancel__semigroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_b,V_a) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a)
=> V_b = V_c ) ),
file('theBenchmark.p',fact_add__right__imp__eq) ).
fof(fact_add__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__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_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_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_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_add__right__cancel,axiom,
! [V_ca_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_ca_2,V_a_2)
<=> V_b_2 = V_ca_2 ) ),
file('theBenchmark.p',fact_add__right__cancel) ).
fof(fact_add__left__cancel,axiom,
! [V_ca_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_ca_2)
<=> V_b_2 = V_ca_2 ) ),
file('theBenchmark.p',fact_add__left__cancel) ).
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_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_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_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_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_one__reorient,axiom,
! [V_x_2,T_a] :
( class_Groups_Oone(T_a)
=> ( c_Groups_Oone__class_Oone(T_a) = V_x_2
<=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_one__reorient) ).
fof(fact_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__add__abs,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b)) ),
file('theBenchmark.p',fact_abs__add__abs) ).
fof(fact_abs__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__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_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_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_abs__zero,axiom,
! [T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_abs__zero) ).
fof(fact_abs__eq__0,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_abs__eq__0) ).
fof(fact_real__two__squares__add__zero__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_real__two__squares__add__zero__iff) ).
fof(fact_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__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_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_add__pCons,axiom,
! [V_q,V_b,V_p,V_a,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ),
file('theBenchmark.p',fact_add__pCons) ).
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_add__le__cancel__right,axiom,
! [V_b_2,V_ca_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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_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_add__le__cancel__left,axiom,
! [V_b_2,V_a_2,V_ca_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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_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__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__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__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__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__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__less__cancel__right,axiom,
! [V_b_2,V_ca_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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_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_ca_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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_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_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__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__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_poly__add,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__add) ).
fof(fact_poly__mult,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__mult) ).
fof(fact_poly__1,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_poly__1) ).
fof(fact_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_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_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_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_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_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_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_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_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_one__poly__def,axiom,
! [T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
file('theBenchmark.p',fact_one__poly__def) ).
fof(fact_poly__pCons,axiom,
! [V_x,V_p,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))) ),
file('theBenchmark.p',fact_poly__pCons) ).
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_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_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_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_abs__ge__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
file('theBenchmark.p',fact_abs__ge__zero) ).
fof(fact_abs__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__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__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_real__mult__right__cancel,axiom,
! [V_b_2,V_a_2,V_ca_2] :
( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_real__mult__right__cancel) ).
fof(fact_real__mult__left__cancel,axiom,
! [V_b_2,V_a_2,V_ca_2] :
( V_ca_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_real__mult__left__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_y_2,V_x_2,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ),
file('theBenchmark.p',fact_add__nonneg__eq__0__iff) ).
fof(fact_add__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_zero__less__double__add__iff__zero__less__single__add,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_zero__less__double__add__iff__zero__less__single__add) ).
fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_double__add__less__zero__iff__single__add__less__zero) ).
fof(fact_add__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__pos) ).
fof(fact_pos__add__strict,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_pos__add__strict) ).
fof(fact_add__neg__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__neg) ).
fof(fact_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_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_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__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_mult__less__cancel__right__disj,axiom,
! [V_b_2,V_ca_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_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
<=> ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__right__disj) ).
fof(fact_mult__less__cancel__left__disj,axiom,
! [V_b_2,V_a_2,V_ca_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_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_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_ca_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_ca_2) ) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__disj) ).
fof(fact_mult__less__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_ca_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_ca_2)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__pos) ).
fof(fact_mult__pos__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ) ) ),
file('theBenchmark.p',fact_mult__pos__pos) ).
fof(fact_mult__pos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,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__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_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_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_mult__less__cancel__left__neg,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2) ) ) ),
file('theBenchmark.p',fact_mult__less__cancel__left__neg) ).
fof(fact_mult__neg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__semiring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,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__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__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__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_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__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_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_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_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_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_add__pos__nonneg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__pos__nonneg) ).
fof(fact_add__nonneg__pos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) ) ) ),
file('theBenchmark.p',fact_add__nonneg__pos) ).
fof(fact_add__strict__increasing,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing) ).
fof(fact_add__strict__increasing2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,V_c)
=> c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c)) ) ) ),
file('theBenchmark.p',fact_add__strict__increasing2) ).
fof(fact_add__neg__nonpos,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__neg__nonpos) ).
fof(fact_add__nonpos__neg,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__comm__monoid__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> ( c_Orderings_Oord__class_Oless(T_a,V_b,c_Groups_Ozero__class_Ozero(T_a))
=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Ozero__class_Ozero(T_a)) ) ) ),
file('theBenchmark.p',fact_add__nonpos__neg) ).
fof(fact_mult__le__cancel__left__pos,axiom,
! [V_b_2,V_a_2,V_ca_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_ca_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_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_ca_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_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_not__pos__poly__0,axiom,
! [T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ),
file('theBenchmark.p',fact_not__pos__poly__0) ).
fof(fact_real__mult__less__iff1,axiom,
! [V_y_2,V_x_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__mult__less__iff1) ).
fof(fact_real__mult__order,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_y)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),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__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_synthetic__div__0,axiom,
! [V_c,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_synthetic__div__0) ).
fof(fact_real__mult__le__cancel__iff1,axiom,
! [V_y_2,V_x_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__mult__le__cancel__iff1) ).
fof(fact_real__mult__le__cancel__iff2,axiom,
! [V_y_2,V_x_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_real__mult__le__cancel__iff2) ).
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_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_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_y_2,V_x_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_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
<=> ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__gt__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_sum__squares__le__zero__iff,axiom,
! [V_y_2,V_x_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_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__le__zero__iff) ).
fof(fact_not__real__square__gt__zero,axiom,
! [V_x_2] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2))
<=> V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_not__real__square__gt__zero) ).
fof(fact_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_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_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_mult__poly__add__left,axiom,
! [V_r,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r)) ),
file('theBenchmark.p',fact_mult__poly__add__left) ).
fof(fact_add__poly__code_I1_J,axiom,
! [V_q,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q ),
file('theBenchmark.p',fact_add__poly__code_I1_J) ).
fof(fact_add__poly__code_I2_J,axiom,
! [V_p,T_a] :
( class_Groups_Ocomm__monoid__add(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
file('theBenchmark.p',fact_add__poly__code_I2_J) ).
fof(fact_mult__poly__0__left,axiom,
! [V_q,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_mult__poly__0__left) ).
fof(fact_mult__poly__0__right,axiom,
! [V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_mult__poly__0__right) ).
fof(fact_pos__poly__add,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,V_p)
=> ( c_Polynomial_Opos__poly(T_a,V_q)
=> c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ) ) ),
file('theBenchmark.p',fact_pos__poly__add) ).
fof(fact_pos__poly__mult,axiom,
! [V_q,V_p,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,V_p)
=> ( c_Polynomial_Opos__poly(T_a,V_q)
=> c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)) ) ) ),
file('theBenchmark.p',fact_pos__poly__mult) ).
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_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_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_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_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_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_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_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
! [V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,V_c) = c_Groups_Oplus__class_Oplus(T_a,V_c,V_a) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,V_c,c_Groups_Oplus__class_Oplus(T_a,V_a,V_d)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
! [V_d,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_d) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),V_c) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),V_b) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(T_a,V_c,V_d)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_c),c_Groups_Oplus__class_Oplus(T_a,V_b,V_d)) ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) ).
fof(fact_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_add__0__iff,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( V_b_2 = c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_add__0__iff) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = V_a ),
file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) ).
fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_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_ca_2,V_b_2,V_a_2,T_a] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
=> ( ( V_ca_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_ca_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_ca_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_z_2,V_x_2,V_y_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_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
<=> ( V_y_2 = V_z_2
| V_w_2 = V_x_2 ) ) ),
file('theBenchmark.p',fact_crossproduct__eq) ).
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_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_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_sum__squares__eq__zero__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__ring__strict(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
<=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sum__squares__eq__zero__iff) ).
fof(fact_pcompose__pCons,axiom,
! [V_q,V_p,V_a,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q))) ),
file('theBenchmark.p',fact_pcompose__pCons) ).
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_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_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_synthetic__div__correct_H,axiom,
! [V_p,V_c,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p ),
file('theBenchmark.p',fact_synthetic__div__correct_H) ).
fof(fact_mult__left_Opos__bounded,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : 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),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult__left_Opos__bounded) ).
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__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__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_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_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k) ),
file('theBenchmark.p',fact_le__iff__add) ).
fof(fact_nat__less__le,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ( V_ma_2 != V_n_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__less__le) ).
fof(fact_le__eq__less__or__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ( V_ma_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_le__eq__less__or__eq) ).
fof(fact_nat__add__left__cancel__le,axiom,
! [V_n_2,V_ma_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_ma_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_ma_2,V_n_2) ),
file('theBenchmark.p',fact_nat__add__left__cancel__le) ).
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_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_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_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_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_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_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_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_nat__less__cases,axiom,
! [V_P_2,V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
=> ( ( V_ma_2 = V_n_2
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
=> ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) )
=> hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2)) ) ) ),
file('theBenchmark.p',fact_nat__less__cases) ).
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_less__not__refl3,axiom,
! [V_t,V_s] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_s,V_t)
=> V_s != V_t ),
file('theBenchmark.p',fact_less__not__refl3) ).
fof(fact_less__not__refl2,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
=> V_m != V_n ),
file('theBenchmark.p',fact_less__not__refl2) ).
fof(fact_less__irrefl__nat,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__irrefl__nat) ).
fof(fact_linorder__neqE__nat,axiom,
! [V_y,V_x] :
( V_x != V_y
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_y,V_x) ) ),
file('theBenchmark.p',fact_linorder__neqE__nat) ).
fof(fact_nat__add__left__cancel__less,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_nat__add__left__cancel__less) ).
fof(fact_nat__neq__iff,axiom,
! [V_n_2,V_ma_2] :
( V_ma_2 != V_n_2
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__neq__iff) ).
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_less__not__refl,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_n),
file('theBenchmark.p',fact_less__not__refl) ).
fof(fact_poly__minus,axiom,
! [V_x,V_p,T_a] :
( class_Rings_Ocomm__ring(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)) ),
file('theBenchmark.p',fact_poly__minus) ).
fof(fact_minus__pCons,axiom,
! [V_p,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)) ),
file('theBenchmark.p',fact_minus__pCons) ).
fof(fact_minus__poly__code_I2_J,axiom,
! [V_p,V_a,T_b] :
( class_Groups_Oab__group__add(T_b)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p)) ),
file('theBenchmark.p',fact_minus__poly__code_I2_J) ).
fof(fact_minus__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a ),
file('theBenchmark.p',fact_minus__minus) ).
fof(fact_equation__minus__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) ),
file('theBenchmark.p',fact_equation__minus__iff) ).
fof(fact_minus__equation__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
<=> c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2 ) ),
file('theBenchmark.p',fact_minus__equation__iff) ).
fof(fact_neg__equal__iff__equal,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> V_a_2 = V_b_2 ) ),
file('theBenchmark.p',fact_neg__equal__iff__equal) ).
fof(fact_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_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_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_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_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_minus__zero,axiom,
! [T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_minus__zero) ).
fof(fact_neg__0__equal__iff__equal,axiom,
! [V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
<=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ),
file('theBenchmark.p',fact_neg__0__equal__iff__equal) ).
fof(fact_equal__neg__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_equal__neg__zero) ).
fof(fact_neg__equal__0__iff__equal,axiom,
! [V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_neg__equal__0__iff__equal) ).
fof(fact_neg__equal__zero,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
<=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_neg__equal__zero) ).
fof(fact_le__minus__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ),
file('theBenchmark.p',fact_le__minus__iff) ).
fof(fact_minus__le__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ),
file('theBenchmark.p',fact_minus__le__iff) ).
fof(fact_neg__le__iff__le,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_neg__le__iff__le) ).
fof(fact_le__imp__neg__le,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ) ),
file('theBenchmark.p',fact_le__imp__neg__le) ).
fof(fact_less__minus__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) ),
file('theBenchmark.p',fact_less__minus__iff) ).
fof(fact_minus__less__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) ) ),
file('theBenchmark.p',fact_minus__less__iff) ).
fof(fact_neg__less__iff__less,axiom,
! [V_a_2,V_b_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_neg__less__iff__less) ).
fof(fact_mult_Ominus__right,axiom,
! [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_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__right) ).
fof(fact_mult__right_Ominus,axiom,
! [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_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x)) ),
file('theBenchmark.p',fact_mult__right_Ominus) ).
fof(fact_mult_Ominus__left,axiom,
! [V_b,V_a,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
file('theBenchmark.p',fact_mult_Ominus__left) ).
fof(fact_mult__left_Ominus,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) ),
file('theBenchmark.p',fact_mult__left_Ominus) ).
fof(fact_square__eq__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
<=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_a_2 = V_b_2 ) ) ),
file('theBenchmark.p',fact_square__eq__iff) ).
fof(fact_minus__mult__minus,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) ),
file('theBenchmark.p',fact_minus__mult__minus) ).
fof(fact_minus__mult__commute,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__mult__commute) ).
fof(fact_minus__mult__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) ),
file('theBenchmark.p',fact_minus__mult__left) ).
fof(fact_minus__mult__right,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Oring(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__mult__right) ).
fof(fact_minus__add__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b ),
file('theBenchmark.p',fact_minus__add__cancel) ).
fof(fact_add__minus__cancel,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b ),
file('theBenchmark.p',fact_add__minus__cancel) ).
fof(fact_minus__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a)) ),
file('theBenchmark.p',fact_minus__add) ).
fof(fact_minus__add__distrib,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_minus__add__distrib) ).
fof(fact_abs__minus__cancel,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a) ),
file('theBenchmark.p',fact_abs__minus__cancel) ).
fof(fact_norm__minus__cancel,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x) ),
file('theBenchmark.p',fact_norm__minus__cancel) ).
fof(fact_minus__poly__code_I1_J,axiom,
! [T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_minus__poly__code_I1_J) ).
fof(fact_abs__poly__def,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
=> c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x) ) ) ),
file('theBenchmark.p',fact_abs__poly__def) ).
fof(fact_neg__0__le__iff__le,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_neg__0__le__iff__le) ).
fof(fact_le__minus__self__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_le__minus__self__iff) ).
fof(fact_neg__le__0__iff__le,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__le__0__iff__le) ).
fof(fact_minus__le__self__iff,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_minus__le__self__iff) ).
fof(fact_neg__0__less__iff__less,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_neg__0__less__iff__less) ).
fof(fact_less__minus__self__iff,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_less__minus__self__iff) ).
fof(fact_neg__less__0__iff__less,axiom,
! [V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__less__0__iff__less) ).
fof(fact_neg__less__nonneg,axiom,
! [V_a_2,T_a] :
( class_Groups_Olinordered__ab__group__add(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_neg__less__nonneg) ).
fof(fact_right__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_right__minus) ).
fof(fact_eq__neg__iff__add__eq__0,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
<=> c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_eq__neg__iff__add__eq__0) ).
fof(fact_left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_left__minus) ).
fof(fact_ab__left__minus,axiom,
! [V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_ab__left__minus) ).
fof(fact_minus__unique,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) = c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b ) ),
file('theBenchmark.p',fact_minus__unique) ).
fof(fact_add__eq__0__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Groups_Ogroup__add(T_a)
=> ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) ) ),
file('theBenchmark.p',fact_add__eq__0__iff) ).
fof(fact_square__eq__1__iff,axiom,
! [V_x_2,T_a] :
( class_Rings_Oring__1__no__zero__divisors(T_a)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
<=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ),
file('theBenchmark.p',fact_square__eq__1__iff) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
! [V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x) ),
file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J) ).
fof(fact_abs__ge__minus__self,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a)) ),
file('theBenchmark.p',fact_abs__ge__minus__self) ).
fof(fact_abs__le__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
<=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_abs__le__iff) ).
fof(fact_abs__leI,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b) ) ) ),
file('theBenchmark.p',fact_abs__leI) ).
fof(fact_abs__le__D2,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b) ) ),
file('theBenchmark.p',fact_abs__le__D2) ).
fof(fact_abs__less__iff,axiom,
! [V_b_2,V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
<=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_abs__less__iff) ).
fof(fact_real__minus__mult__self__le,axiom,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)),
file('theBenchmark.p',fact_real__minus__mult__self__le) ).
fof(fact_real__add__minus__iff,axiom,
! [V_a_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_x_2 = V_a_2 ),
file('theBenchmark.p',fact_real__add__minus__iff) ).
fof(fact_real__add__eq__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) ),
file('theBenchmark.p',fact_real__add__eq__0__iff) ).
fof(fact_abs__le__interval__iff,axiom,
! [V_ra_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)
<=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) ) ),
file('theBenchmark.p',fact_abs__le__interval__iff) ).
fof(fact_abs__minus__add__cancel,axiom,
! [V_y,V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))),
file('theBenchmark.p',fact_abs__minus__add__cancel) ).
fof(fact_pos__poly__total,axiom,
! [V_p,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
| c_Polynomial_Opos__poly(T_a,V_p)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ),
file('theBenchmark.p',fact_pos__poly__total) ).
fof(fact_pcompose__0,axiom,
! [V_q,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ),
file('theBenchmark.p',fact_pcompose__0) ).
fof(fact_abs__minus__le__zero,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_abs__minus__le__zero) ).
fof(fact_abs__of__nonpos,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ),
file('theBenchmark.p',fact_abs__of__nonpos) ).
fof(fact_abs__if,axiom,
! [V_a,T_a] :
( class_Groups_Oabs__if(T_a)
=> ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a )
& ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ) ),
file('theBenchmark.p',fact_abs__if) ).
fof(fact_abs__of__neg,axiom,
! [V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
=> c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ) ),
file('theBenchmark.p',fact_abs__of__neg) ).
fof(fact_poly__pcompose,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__semiring__0(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__pcompose) ).
fof(fact_real__0__le__add__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ),
file('theBenchmark.p',fact_real__0__le__add__iff) ).
fof(fact_real__add__le__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ),
file('theBenchmark.p',fact_real__add__le__0__iff) ).
fof(fact_real__0__less__add__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) ),
file('theBenchmark.p',fact_real__0__less__add__iff) ).
fof(fact_real__add__less__0__iff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) ),
file('theBenchmark.p',fact_real__add__less__0__iff) ).
fof(fact_abs__real__def,axiom,
! [V_a] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a) ) ),
file('theBenchmark.p',fact_abs__real__def) ).
fof(fact_real__abs__def,axiom,
! [V_r] :
( ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r) ) ),
file('theBenchmark.p',fact_real__abs__def) ).
fof(fact_abs__sum__triangle__ineq,axiom,
! [V_m,V_l,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))),
file('theBenchmark.p',fact_abs__sum__triangle__ineq) ).
fof(fact_not__less0,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_not__less0) ).
fof(fact_neq0__conv,axiom,
! [V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ),
file('theBenchmark.p',fact_neq0__conv) ).
fof(fact_less__eq__nat_Osimps_I1_J,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n),
file('theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
fof(fact_less__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_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_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_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_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_nat__0__less__mult__iff,axiom,
! [V_n_2,V_ma_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_ma_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_ma_2) ) ),
file('theBenchmark.p',fact_nat__0__less__mult__iff) ).
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_ma_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_mult__is__0) ).
fof(fact_mult__less__cancel1,axiom,
! [V_n_2,V_ma_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_ma_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_ma_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_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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_ma_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__le__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_mult__le__cancel1) ).
fof(fact_mult__le__cancel2,axiom,
! [V_n_2,V_k_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_mult__le__cancel2) ).
fof(fact_mult__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_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_ma_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__cancel1) ).
fof(fact_mult__cancel2,axiom,
! [V_n_2,V_k_2,V_ma_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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_ma_2 = V_n_2 ) ),
file('theBenchmark.p',fact_mult__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(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_add__gr__0,axiom,
! [V_n_2,V_ma_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_ma_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_ma_2) ) ),
file('theBenchmark.p',fact_add__gr__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_ma_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_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_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_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_nat__mult__le__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_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__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__mult__le__cancel1) ).
fof(fact_Bseq__iff2,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_k] :
( ? [B_x] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,B_x))),B_k)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) ) ) ),
file('theBenchmark.p',fact_Bseq__iff2) ).
fof(fact_Bseq__iff3,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_k] :
( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,B_N)))),B_k)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) ) ) ),
file('theBenchmark.p',fact_Bseq__iff3) ).
fof(fact_complex__mod__minus__le__complex__mod,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),
file('theBenchmark.p',fact_complex__mod__minus__le__complex__mod) ).
fof(fact_mult_Opos__bounded,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_a,B_b] : 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),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult_Opos__bounded) ).
fof(fact_mult__right_Opos__bounded,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : 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),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult__right_Opos__bounded) ).
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__add__right__cancel,axiom,
! [V_n_2,V_k_2,V_ma_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
<=> V_ma_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__right__cancel) ).
fof(fact_nat__add__left__cancel,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
<=> V_ma_2 = V_n_2 ),
file('theBenchmark.p',fact_nat__add__left__cancel) ).
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_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_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__mult__eq__1__iff,axiom,
! [V_n_2,V_ma_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__eq__1__iff) ).
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_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__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__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__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__1__eq__mult__iff,axiom,
! [V_n_2,V_ma_2] :
( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__1__eq__mult__iff) ).
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__mult__eq__cancel__disj,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> ( V_ma_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_nat__mult__less__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_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_ma_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_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__mult__less__cancel1) ).
fof(fact_nat__mult__eq__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
<=> V_ma_2 = V_n_2 ) ),
file('theBenchmark.p',fact_nat__mult__eq__cancel1) ).
fof(fact_termination__basic__simps_I4_J,axiom,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I4_J) ).
fof(fact_termination__basic__simps_I3_J,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I3_J) ).
fof(fact_termination__basic__simps_I5_J,axiom,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
file('theBenchmark.p',fact_termination__basic__simps_I5_J) ).
fof(fact_termination__basic__simps_I1_J,axiom,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I1_J) ).
fof(fact_termination__basic__simps_I2_J,axiom,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z)) ),
file('theBenchmark.p',fact_termination__basic__simps_I2_J) ).
fof(fact_decseq__def,axiom,
! [V_X_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_SEQ_Odecseq(T_a,V_X_2)
<=> ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m)) ) ) ),
file('theBenchmark.p',fact_decseq__def) ).
fof(fact_compl__mono,axiom,
! [V_y,V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) ) ),
file('theBenchmark.p',fact_compl__mono) ).
fof(fact_compl__le__compl__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) ) ),
file('theBenchmark.p',fact_compl__le__compl__iff) ).
fof(fact_sgn__poly__def,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( ( V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))) )
& ( c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x)
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) ) ) )
& ( V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) ) ),
file('theBenchmark.p',fact_sgn__poly__def) ).
fof(fact_sgn__sgn,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a) ),
file('theBenchmark.p',fact_sgn__sgn) ).
fof(fact_sgn__minus,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) ),
file('theBenchmark.p',fact_sgn__minus) ).
fof(fact_sgn__one,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra__1(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ),
file('theBenchmark.p',fact_sgn__one) ).
fof(fact_sgn__mult,axiom,
! [V_y,V_x,T_a] :
( class_RealVector_Oreal__normed__div__algebra(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y)) ),
file('theBenchmark.p',fact_sgn__mult) ).
fof(fact_sgn__times,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Osgn__class_Osgn(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_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b)) ),
file('theBenchmark.p',fact_sgn__times) ).
fof(fact_sgn0,axiom,
! [T_a] :
( class_Groups_Osgn__if(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_sgn0) ).
fof(fact_sgn__0__0,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(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_sgn__0__0) ).
fof(fact_sgn__zero,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
file('theBenchmark.p',fact_sgn__zero) ).
fof(fact_sgn__zero__iff,axiom,
! [V_x_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_sgn__zero__iff) ).
fof(fact_sgn__less,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(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)) ) ),
file('theBenchmark.p',fact_sgn__less) ).
fof(fact_sgn__greater,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2))
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_sgn__greater) ).
fof(fact_abs__sgn,axiom,
! [V_k,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ),
file('theBenchmark.p',fact_abs__sgn) ).
fof(fact_mult__sgn__abs,axiom,
! [V_x,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x ),
file('theBenchmark.p',fact_mult__sgn__abs) ).
fof(fact_times_Oidem,axiom,
! [V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ),
file('theBenchmark.p',fact_times_Oidem) ).
fof(fact_mult__idem,axiom,
! [V_x,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ),
file('theBenchmark.p',fact_mult__idem) ).
fof(fact_mult__left__idem,axiom,
! [V_b,V_a,T_a] :
( class_Lattices_Oab__semigroup__idem__mult(T_a)
=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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) ),
file('theBenchmark.p',fact_mult__left__idem) ).
fof(fact_double__compl,axiom,
! [V_x,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x ),
file('theBenchmark.p',fact_double__compl) ).
fof(fact_uminus__apply,axiom,
! [V_x_2,V_A_2,T_b,T_a] :
( class_Groups_Ouminus(T_a)
=> hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2)) ),
file('theBenchmark.p',fact_uminus__apply) ).
fof(fact_compl__eq__compl__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Lattices_Oboolean__algebra(T_a)
=> ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_compl__eq__compl__iff) ).
fof(fact_sgn__pos,axiom,
! [V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
file('theBenchmark.p',fact_sgn__pos) ).
fof(fact_sgn__1__pos,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
<=> c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) ) ),
file('theBenchmark.p',fact_sgn__1__pos) ).
fof(fact_sgn__neg,axiom,
! [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_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) ),
file('theBenchmark.p',fact_sgn__neg) ).
fof(fact_sgn__1__neg,axiom,
! [V_a_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
<=> c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) ) ),
file('theBenchmark.p',fact_sgn__1__neg) ).
fof(fact_sgn__if,axiom,
! [V_x,T_a] :
( class_Groups_Osgn__if(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_x)
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x)
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) ) )
& ( V_x = c_Groups_Ozero__class_Ozero(T_a)
=> c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_sgn__if) ).
fof(fact_norm__sgn,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( ( V_x != c_Groups_Ozero__class_Ozero(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) )
& ( V_x = c_Groups_Ozero__class_Ozero(T_a)
=> c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ) ),
file('theBenchmark.p',fact_norm__sgn) ).
fof(fact_BseqI,axiom,
! [V_X_2,V_K_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),V_K_2)
=> ( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)
=> c_SEQ_OBseq(T_a,V_X_2) ) ) ),
file('theBenchmark.p',fact_BseqI) ).
fof(fact_BseqD,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
=> ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) ),
file('theBenchmark.p',fact_BseqD) ).
fof(fact_ex__least__nat__less,axiom,
! [V_n_2,V_P_2] :
( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
=> ( hBOOL(hAPP(V_P_2,V_n_2))
=> ? [B_k] :
( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [B_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k)
=> ~ hBOOL(hAPP(V_P_2,B_i)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) ) ) ),
file('theBenchmark.p',fact_ex__least__nat__less) ).
fof(fact_mult__left_Ononneg__bounded,axiom,
! [V_y,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : 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),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult__left_Ononneg__bounded) ).
fof(fact_real__sgn__pos,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ),
file('theBenchmark.p',fact_real__sgn__pos) ).
fof(fact_sgn__real__def,axiom,
! [V_a] :
( ( V_a != 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_a)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) )
& ( V_a = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_sgn__real__def) ).
fof(fact_real__sgn__def,axiom,
! [V_x] :
( ( 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)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal) ) ) )
& ( V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
=> c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
file('theBenchmark.p',fact_real__sgn__def) ).
fof(fact_mult_Ononneg__bounded,axiom,
! [T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_a,B_b] : 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),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult_Ononneg__bounded) ).
fof(fact_mult__right_Ononneg__bounded,axiom,
! [V_x,T_a] :
( class_RealVector_Oreal__normed__algebra(T_a)
=> ? [B_K] :
( ! [B_x] : 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),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ),
file('theBenchmark.p',fact_mult__right_Ononneg__bounded) ).
fof(fact_poly__eq__0__iff__dvd,axiom,
! [V_ca_2,V_pa_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2) = c_Groups_Ozero__class_Ozero(T_a)
<=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2) ) ),
file('theBenchmark.p',fact_poly__eq__0__iff__dvd) ).
fof(fact_dvd__iff__poly__eq__0,axiom,
! [V_pa_2,V_ca_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)
<=> hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2)) = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_dvd__iff__poly__eq__0) ).
fof(fact_dvd__0__right,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ),
file('theBenchmark.p',fact_dvd__0__right) ).
fof(fact_minus__dvd__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)
<=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_minus__dvd__iff) ).
fof(fact_dvd__minus__iff,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
<=> c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_dvd__minus__iff) ).
fof(fact_dvd__0__left,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> V_a = c_Groups_Ozero__class_Ozero(T_a) ) ),
file('theBenchmark.p',fact_dvd__0__left) ).
fof(fact_dvd__trans,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
=> c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_dvd__trans) ).
fof(fact_dvd__refl,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Rings_Odvd__class_Odvd(T_a,V_a,V_a) ),
file('theBenchmark.p',fact_dvd__refl) ).
fof(fact_dvd__if__abs__eq,axiom,
! [V_k,V_l,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Groups_Oabs__class_Oabs(T_a,V_l) = c_Groups_Oabs__class_Oabs(T_a,V_k)
=> c_Rings_Odvd__class_Odvd(T_a,V_l,V_k) ) ),
file('theBenchmark.p',fact_dvd__if__abs__eq) ).
fof(fact_abs__dvd__iff,axiom,
! [V_k_2,V_ma_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oabs__class_Oabs(T_a,V_ma_2),V_k_2)
<=> c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2) ) ),
file('theBenchmark.p',fact_abs__dvd__iff) ).
fof(fact_dvd__abs__iff,axiom,
! [V_k_2,V_ma_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_ma_2,c_Groups_Oabs__class_Oabs(T_a,V_k_2))
<=> c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2) ) ),
file('theBenchmark.p',fact_dvd__abs__iff) ).
fof(fact_one__dvd,axiom,
! [V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a) ),
file('theBenchmark.p',fact_one__dvd) ).
fof(fact_dvd__add,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
=> c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c)) ) ) ),
file('theBenchmark.p',fact_dvd__add) ).
fof(fact_dvd__mult__right,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
=> c_Rings_Odvd__class_Odvd(T_a,V_b,V_c) ) ),
file('theBenchmark.p',fact_dvd__mult__right) ).
fof(fact_dvd__mult__left,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
=> c_Rings_Odvd__class_Odvd(T_a,V_a,V_c) ) ),
file('theBenchmark.p',fact_dvd__mult__left) ).
fof(fact_dvdI,axiom,
! [V_k,V_b,V_a,T_a] :
( class_Rings_Odvd(T_a)
=> ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
=> c_Rings_Odvd__class_Odvd(T_a,V_b,V_a) ) ),
file('theBenchmark.p',fact_dvdI) ).
fof(fact_mult__dvd__mono,axiom,
! [V_d,V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_c,V_d)
=> c_Rings_Odvd__class_Odvd(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__dvd__mono) ).
fof(fact_dvd__mult,axiom,
! [V_b,V_c,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
=> c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ),
file('theBenchmark.p',fact_dvd__mult) ).
fof(fact_dvd__mult2,axiom,
! [V_c,V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
=> c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) ) ),
file('theBenchmark.p',fact_dvd__mult2) ).
fof(fact_dvd__triv__right,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a)) ),
file('theBenchmark.p',fact_dvd__triv__right) ).
fof(fact_dvd__triv__left,axiom,
! [V_b,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)) ),
file('theBenchmark.p',fact_dvd__triv__left) ).
fof(fact_dvd__mult__cancel__left,axiom,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
<=> ( c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2)
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__left) ).
fof(fact_dvd__mult__cancel__right,axiom,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
<=> ( c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2)
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel__right) ).
fof(fact_unity__coeff__ex,axiom,
! [V_l_2,V_P_2,T_a] :
( ( class_Rings_Osemiring__0(T_a)
& class_Rings_Odvd(T_a) )
=> ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
<=> ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a))) ) ) ),
file('theBenchmark.p',fact_unity__coeff__ex) ).
fof(fact_order__1,axiom,
! [V_p,V_a,T_a] :
( class_Rings_Oidom(T_a)
=> c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p) ),
file('theBenchmark.p',fact_order__1) ).
fof(fact_incseq__def,axiom,
! [V_X_2,T_a] :
( class_Orderings_Oorder(T_a)
=> ( c_SEQ_Oincseq(T_a,V_X_2)
<=> ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n)
=> c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n)) ) ) ),
file('theBenchmark.p',fact_incseq__def) ).
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_nat__dvd__1__iff__1,axiom,
! [V_ma_2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
file('theBenchmark.p',fact_nat__dvd__1__iff__1) ).
fof(fact_dvd__reduce,axiom,
! [V_n_2,V_k_2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2) ),
file('theBenchmark.p',fact_dvd__reduce) ).
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_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_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_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_poly__power,axiom,
! [V_x,V_n,V_p,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n) ),
file('theBenchmark.p',fact_poly__power) ).
fof(fact_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_natceiling__zero,axiom,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_natceiling__zero) ).
fof(fact_zero__le__natceiling,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),
file('theBenchmark.p',fact_zero__le__natceiling) ).
fof(fact_natceiling__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_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y)) ),
file('theBenchmark.p',fact_natceiling__mono) ).
fof(fact_natceiling__one,axiom,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('theBenchmark.p',fact_natceiling__one) ).
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_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_nat__dvd__not__less,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m) ) ),
file('theBenchmark.p',fact_nat__dvd__not__less) ).
fof(fact_nat__mult__dvd__cancel__disj,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2)
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel__disj) ).
fof(fact_natceiling__neg,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_natceiling__neg) ).
fof(fact_dvd__imp__le,axiom,
! [V_n,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,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(tc_Nat_Onat,V_k,V_n) ) ),
file('theBenchmark.p',fact_dvd__imp__le) ).
fof(fact_dvd__mult__cancel,axiom,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(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))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel) ).
fof(fact_nat__mult__dvd__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_nat__mult__dvd__cancel1) ).
fof(fact_natceiling__le__eq__one,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_natceiling__le__eq__one) ).
fof(fact_dvd__mult__cancel1,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2),V_ma_2)
<=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel1) ).
fof(fact_dvd__mult__cancel2,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ma_2),V_ma_2)
<=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_dvd__mult__cancel2) ).
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_dvd__power,axiom,
! [V_x,V_n,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( ( V_x = c_Groups_Oone__class_Oone(T_a)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) )
=> c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ) ),
file('theBenchmark.p',fact_dvd__power) ).
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_dvd_Oorder__refl,axiom,
! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x),
file('theBenchmark.p',fact_dvd_Oorder__refl) ).
fof(fact_dvd_Oless__asym,axiom,
! [V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
=> ~ ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) ) ),
file('theBenchmark.p',fact_dvd_Oless__asym) ).
fof(fact_dvd_Oless__trans,axiom,
! [V_z,V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
=> ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) )
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_dvd_Oless__trans) ).
fof(fact_dvd_Oless__asym_H,axiom,
! [V_b,V_a] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) )
=> ~ ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a) ) ),
file('theBenchmark.p',fact_dvd_Oless__asym_H) ).
fof(fact_dvd_Oless__le__trans,axiom,
! [V_z,V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_dvd_Oless__le__trans) ).
fof(fact_dvd_Oord__less__eq__trans,axiom,
! [V_c,V_b,V_a] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) )
=> ( V_b = V_c
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_dvd_Oord__less__eq__trans) ).
fof(fact_dvd_Oless__imp__not__eq2,axiom,
! [V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
=> V_y != V_x ),
file('theBenchmark.p',fact_dvd_Oless__imp__not__eq2) ).
fof(fact_dvd_Oless__imp__not__eq,axiom,
! [V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
=> V_x != V_y ),
file('theBenchmark.p',fact_dvd_Oless__imp__not__eq) ).
fof(fact_dvd_Oless__imp__not__less,axiom,
! [V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
=> ~ ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) ) ),
file('theBenchmark.p',fact_dvd_Oless__imp__not__less) ).
fof(fact_dvd_Oless__imp__le,axiom,
! [V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
file('theBenchmark.p',fact_dvd_Oless__imp__le) ).
fof(fact_dvd_Oless__not__sym,axiom,
! [V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
=> ~ ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x) ) ),
file('theBenchmark.p',fact_dvd_Oless__not__sym) ).
fof(fact_dvd_Oless__imp__neq,axiom,
! [V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
=> V_x != V_y ),
file('theBenchmark.p',fact_dvd_Oless__imp__neq) ).
fof(fact_dvd_Ole__less__trans,axiom,
! [V_z,V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
=> ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z) )
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__less__trans) ).
fof(fact_dvd_Oord__eq__less__trans,axiom,
! [V_c,V_b,V_a] :
( V_a = V_b
=> ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c) )
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ) ),
file('theBenchmark.p',fact_dvd_Oord__eq__less__trans) ).
fof(fact_dvd_Oorder__trans,axiom,
! [V_z,V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) ) ),
file('theBenchmark.p',fact_dvd_Oorder__trans) ).
fof(fact_dvd_Oantisym,axiom,
! [V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
=> V_x = V_y ) ),
file('theBenchmark.p',fact_dvd_Oantisym) ).
fof(fact_dvd__antisym,axiom,
! [V_n,V_m] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_dvd__antisym) ).
fof(fact_dvd_Oord__le__eq__trans,axiom,
! [V_c,V_b,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
=> ( V_b = V_c
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ),
file('theBenchmark.p',fact_dvd_Oord__le__eq__trans) ).
fof(fact_dvd_Oord__eq__le__trans,axiom,
! [V_c,V_b,V_a] :
( V_a = V_b
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) ) ),
file('theBenchmark.p',fact_dvd_Oord__eq__le__trans) ).
fof(fact_dvd_Ole__neq__trans,axiom,
! [V_b,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
=> ( V_a != V_b
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__neq__trans) ).
fof(fact_dvd_Ole__imp__less__or__eq,axiom,
! [V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
=> ( V_x = V_y
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__imp__less__or__eq) ).
fof(fact_dvd_Oantisym__conv,axiom,
! [V_x_2,V_y_2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
<=> V_x_2 = V_y_2 ) ),
file('theBenchmark.p',fact_dvd_Oantisym__conv) ).
fof(fact_dvd_Oeq__refl,axiom,
! [V_y,V_x] :
( V_x = V_y
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
file('theBenchmark.p',fact_dvd_Oeq__refl) ).
fof(fact_dvd_Oneq__le__trans,axiom,
! [V_b,V_a] :
( V_a != V_b
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ) ),
file('theBenchmark.p',fact_dvd_Oneq__le__trans) ).
fof(fact_dvd_Oless__le,axiom,
! [V_y_2,V_x_2] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
<=> ( V_x_2 != V_y_2
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_dvd_Oless__le) ).
fof(fact_dvd_Ole__less,axiom,
! [V_y_2,V_x_2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
<=> ( V_x_2 = V_y_2
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_dvd_Ole__less) ).
fof(fact_dvd_Oeq__iff,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
<=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ),
file('theBenchmark.p',fact_dvd_Oeq__iff) ).
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_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_zero__less__zpower__abs__iff,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zero__less__zpower__abs__iff) ).
fof(fact_nat__zero__less__power__iff,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
<=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) ),
file('theBenchmark.p',fact_nat__zero__less__power__iff) ).
fof(fact_nat__power__less__imp__less,axiom,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_nat__power__less__imp__less) ).
fof(fact_power__dvd__imp__le,axiom,
! [V_n,V_m,V_i] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_power__dvd__imp__le) ).
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_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_dvd__power__same,axiom,
! [V_n,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
=> c_Rings_Odvd__class_Odvd(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_y),V_n)) ) ),
file('theBenchmark.p',fact_dvd__power__same) ).
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_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_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_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__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_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_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_power__inject__exp,axiom,
! [V_n_2,V_ma_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_ma_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
<=> V_ma_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_power__inject__exp) ).
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_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_le__imp__power__dvd,axiom,
! [V_a,V_n,V_m,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Rings_Odvd__class_Odvd(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_le__imp__power__dvd) ).
fof(fact_dvd__power__le,axiom,
! [V_m,V_n,V_y,V_x,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Rings_Odvd__class_Odvd(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_y),V_m)) ) ) ),
file('theBenchmark.p',fact_dvd__power__le) ).
fof(fact_power__le__dvd,axiom,
! [V_m,V_b,V_n,V_a,T_a] :
( class_Rings_Ocomm__semiring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b) ) ) ),
file('theBenchmark.p',fact_power__le__dvd) ).
fof(fact_abs__power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_abs__power__minus) ).
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_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_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_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_power__minus,axiom,
! [V_n,V_a,T_a] :
( class_Rings_Oring__1(T_a)
=> hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
file('theBenchmark.p',fact_power__minus) ).
fof(fact_power__strict__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
=> ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_power__strict__increasing__iff) ).
fof(fact_power__less__imp__less__exp,axiom,
! [V_n,V_m,V_a,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless(T_a,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,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__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_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_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_power__eq__imp__eq__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),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,c_Groups_Ozero__class_Ozero(T_a),V_b)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> V_a = V_b ) ) ) ) ),
file('theBenchmark.p',fact_power__eq__imp__eq__base) ).
fof(fact_power__decreasing,axiom,
! [V_a,V_N,V_n,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_N)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Oone__class_Oone(T_a))
=> c_Orderings_Oord__class_Oless__eq(T_a,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_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_power__increasing__iff,axiom,
! [V_y_2,V_x_2,V_b_2,T_a] :
( class_Rings_Olinordered__semidom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
=> ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) ) ) ),
file('theBenchmark.p',fact_power__increasing__iff) ).
fof(fact_dvd__pos__nat,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ) ),
file('theBenchmark.p',fact_dvd__pos__nat) ).
fof(fact_order,axiom,
! [V_a,V_p,T_a] :
( class_Rings_Oidom(T_a)
=> ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)
& c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p) ) ) ),
file('theBenchmark.p',fact_order) ).
fof(fact_order__2,axiom,
! [V_a,V_p,T_a] :
( class_Rings_Oidom(T_a)
=> ( V_p != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
=> ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p) ) ),
file('theBenchmark.p',fact_order__2) ).
fof(fact_lessI,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_lessI) ).
fof(fact_Suc__mono,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_Suc__mono) ).
fof(fact_zero__less__Suc,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(V_n)),
file('theBenchmark.p',fact_zero__less__Suc) ).
fof(fact_dvd__1__left,axiom,
! [V_k] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k),
file('theBenchmark.p',fact_dvd__1__left) ).
fof(fact_zdvd__antisym__nonneg,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
=> V_m = V_n ) ) ) ),
file('theBenchmark.p',fact_zdvd__antisym__nonneg) ).
fof(fact_zdvd__mono,axiom,
! [V_t_2,V_ma_2,V_k_2] :
( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ma_2,V_t_2)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)) ) ),
file('theBenchmark.p',fact_zdvd__mono) ).
fof(fact_zdvd1__eq,axiom,
! [V_x_2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
file('theBenchmark.p',fact_zdvd1__eq) ).
fof(fact_zdvd__reduce,axiom,
! [V_ma_2,V_n_2,V_k_2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2)))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2) ),
file('theBenchmark.p',fact_zdvd__reduce) ).
fof(fact_zdvd__period,axiom,
! [V_ca_2,V_t_2,V_x_2,V_d_2,V_a_2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2)) ) ),
file('theBenchmark.p',fact_zdvd__period) ).
fof(fact_zdvd__antisym__abs,axiom,
! [V_b,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_b,V_a)
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_a) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_b) ) ),
file('theBenchmark.p',fact_zdvd__antisym__abs) ).
fof(fact_zdvd__mult__cancel,axiom,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n))
=> ( V_k != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n) ) ),
file('theBenchmark.p',fact_zdvd__mult__cancel) ).
fof(fact_zdvd__imp__le,axiom,
! [V_n,V_z] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n) ) ),
file('theBenchmark.p',fact_zdvd__imp__le) ).
fof(fact_zdvd__not__zless,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
=> ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m) ) ),
file('theBenchmark.p',fact_zdvd__not__zless) ).
fof(fact_dvd__imp__le__int,axiom,
! [V_d,V_i] :
( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d,V_i)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_d),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i)) ) ),
file('theBenchmark.p',fact_dvd__imp__le__int) ).
fof(fact_zdvd__mult__cancel1,axiom,
! [V_n_2,V_ma_2] :
( V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2),V_ma_2)
<=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zdvd__mult__cancel1) ).
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_nat__power__eq__Suc__0__iff,axiom,
! [V_ma_2,V_x_2] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
<=> ( V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).
fof(fact_power__Suc__0,axiom,
! [V_n] : 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_zsgn__def,axiom,
! [V_i] :
( ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> ( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i)
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
& ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
=> c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
file('theBenchmark.p',fact_zsgn__def) ).
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_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_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_int__one__le__iff__zero__less,axiom,
! [V_z_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) ),
file('theBenchmark.p',fact_int__one__le__iff__zero__less) ).
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_zless__le,axiom,
! [V_w_2,V_z_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
<=> ( V_z_2 != V_w_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) ) ),
file('theBenchmark.p',fact_zless__le) ).
fof(fact_zle__add1__eq__le,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) ),
file('theBenchmark.p',fact_zle__add1__eq__le) ).
fof(fact_zabs__less__one__iff,axiom,
! [V_z_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
<=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
file('theBenchmark.p',fact_zabs__less__one__iff) ).
fof(fact_add1__zle__eq,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ),
file('theBenchmark.p',fact_add1__zle__eq) ).
fof(fact_odd__less__0,axiom,
! [V_z_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_odd__less__0) ).
fof(fact_le__imp__0__less,axiom,
! [V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z)) ),
file('theBenchmark.p',fact_le__imp__0__less) ).
fof(fact_pos__zmult__eq__1__iff,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2)
=> ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
<=> ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ),
file('theBenchmark.p',fact_pos__zmult__eq__1__iff) ).
fof(fact_zless__imp__add1__zle,axiom,
! [V_z,V_w] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) ),
file('theBenchmark.p',fact_zless__imp__add1__zle) ).
fof(fact_zmult__zless__mono2,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_Ozero__class_Ozero(tc_Int_Oint),V_k)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j)) ) ),
file('theBenchmark.p',fact_zmult__zless__mono2) ).
fof(fact_zadd__zless__mono,axiom,
! [V_z,V_z_H,V_w,V_w_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z)) ) ),
file('theBenchmark.p',fact_zadd__zless__mono) ).
fof(fact_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_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_Suc__mult__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
<=> V_ma_2 = V_n_2 ),
file('theBenchmark.p',fact_Suc__mult__cancel1) ).
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_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_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_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_zless__add1__eq,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> ( V_w_2 = V_z_2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) ),
file('theBenchmark.p',fact_zless__add1__eq) ).
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_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_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_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__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_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_not__less__eq,axiom,
! [V_n_2,V_ma_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2)) ),
file('theBenchmark.p',fact_not__less__eq) ).
fof(fact_less__Suc__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
<=> ( V_ma_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_less__Suc__eq) ).
fof(fact_Suc__less__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__less__eq) ).
fof(fact_not__less__less__Suc__eq,axiom,
! [V_ma_2,V_n_2] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
<=> V_n_2 = V_ma_2 ) ),
file('theBenchmark.p',fact_not__less__less__Suc__eq) ).
fof(fact_less__antisym,axiom,
! [V_m,V_n] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,V_m)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,c_Nat_OSuc(V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__antisym) ).
fof(fact_less__SucI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n)) ),
file('theBenchmark.p',fact_less__SucI) ).
fof(fact_Suc__lessI,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ( c_Nat_OSuc(V_m) != V_n
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n) ) ),
file('theBenchmark.p',fact_Suc__lessI) ).
fof(fact_less__trans__Suc,axiom,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,V_j)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_i),V_k) ) ),
file('theBenchmark.p',fact_less__trans__Suc) ).
fof(fact_less__SucE,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,c_Nat_OSuc(V_n))
=> ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> V_m = V_n ) ),
file('theBenchmark.p',fact_less__SucE) ).
fof(fact_Suc__lessD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__lessD) ).
fof(fact_Suc__less__SucD,axiom,
! [V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_m),c_Nat_OSuc(V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
file('theBenchmark.p',fact_Suc__less__SucD) ).
fof(fact_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_ma_2] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) ),
file('theBenchmark.p',fact_not__less__eq__eq) ).
fof(fact_le__Suc__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
<=> ( V_ma_2 = c_Nat_OSuc(V_n_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
file('theBenchmark.p',fact_le__Suc__eq) ).
fof(fact_Suc__le__mono,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_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_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_zminus__0,axiom,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zminus__0) ).
fof(fact_zmult__zminus,axiom,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
file('theBenchmark.p',fact_zmult__zminus) ).
fof(fact_zadd__zminus__inverse2,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_zadd__zminus__inverse2) ).
fof(fact_zabs__def,axiom,
! [V_i] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i) ) ),
file('theBenchmark.p',fact_zabs__def) ).
fof(fact_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_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_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_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_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_less__Suc__eq__0__disj,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
<=> ( ? [B_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
& V_ma_2 = c_Nat_OSuc(B_j) )
| V_ma_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_dvd__1__iff__1,axiom,
! [V_ma_2] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
<=> V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_dvd__1__iff__1) ).
fof(fact_one__is__add,axiom,
! [V_n_2,V_ma_2] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ( ( V_n_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_one__is__add) ).
fof(fact_add__is__1,axiom,
! [V_n_2,V_ma_2] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_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_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ),
file('theBenchmark.p',fact_add__is__1) ).
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_mult__eq__1__iff,axiom,
! [V_n_2,V_ma_2] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_mult__eq__1__iff) ).
fof(fact_less__iff__Suc__add,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
<=> ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)) ),
file('theBenchmark.p',fact_less__iff__Suc__add) ).
fof(fact_less__add__Suc2,axiom,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_i))),
file('theBenchmark.p',fact_less__add__Suc2) ).
fof(fact_less__add__Suc1,axiom,
! [V_m,V_i] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i,V_m))),
file('theBenchmark.p',fact_less__add__Suc1) ).
fof(fact_less__eq__Suc__le,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) ),
file('theBenchmark.p',fact_less__eq__Suc__le) ).
fof(fact_less__Suc__eq__le,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_less__Suc__eq__le) ).
fof(fact_Suc__le__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2)
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__le__eq) ).
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__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__less__Suc__eq,axiom,
! [V_n_2,V_ma_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
<=> V_n_2 = V_ma_2 ) ),
file('theBenchmark.p',fact_le__less__Suc__eq) ).
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_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_Suc__mult__less__cancel1,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_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(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__mult__less__cancel1) ).
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_ma_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_ma_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_ma_2,V_n_2) ),
file('theBenchmark.p',fact_Suc__mult__le__cancel1) ).
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_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_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_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__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_realpow__two__disj,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Oidom(T_a)
=> ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),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_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
<=> ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_realpow__two__disj) ).
fof(fact_n__less__m__mult__n,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) ) ),
file('theBenchmark.p',fact_n__less__m__mult__n) ).
fof(fact_n__less__n__mult__m,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)) ) ),
file('theBenchmark.p',fact_n__less__n__mult__m) ).
fof(fact_one__less__mult,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
=> c_Orderings_Oord__class_Oless(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),V_n)) ) ),
file('theBenchmark.p',fact_one__less__mult) ).
fof(fact_one__le__mult__iff,axiom,
! [V_n_2,V_ma_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_ma_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_ma_2) ) ),
file('theBenchmark.p',fact_one__le__mult__iff) ).
fof(fact_pow__divides__pow__int,axiom,
! [V_b,V_n,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n))
=> ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b) ) ),
file('theBenchmark.p',fact_pow__divides__pow__int) ).
fof(fact_pow__divides__eq__int,axiom,
! [V_b_2,V_a_2,V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_pow__divides__eq__int) ).
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_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_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
file('theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Otop__greatest) ).
fof(fact_pow__divides__pow__nat,axiom,
! [V_b,V_n,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n))
=> ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ) ),
file('theBenchmark.p',fact_pow__divides__pow__nat) ).
fof(fact_pow__divides__eq__nat,axiom,
! [V_b_2,V_a_2,V_n_2] :
( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))
<=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2) ) ),
file('theBenchmark.p',fact_pow__divides__eq__nat) ).
fof(fact_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x),
file('theBenchmark.p',fact_gcd__lcm__complete__lattice__nat_Obot__least) ).
fof(fact_zero__less__power__nat__eq,axiom,
! [V_n_2,V_x_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
<=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
file('theBenchmark.p',fact_zero__less__power__nat__eq) ).
fof(fact_self__quotient__aux2,axiom,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux2) ).
fof(fact_self__quotient__aux1,axiom,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a)
=> ( V_a = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q) ) ) ),
file('theBenchmark.p',fact_self__quotient__aux1) ).
fof(fact_zminus__zadd__distrib,axiom,
! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
file('theBenchmark.p',fact_zminus__zadd__distrib) ).
fof(fact_zminus__zminus,axiom,
! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
file('theBenchmark.p',fact_zminus__zminus) ).
fof(fact_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_zadd__commute,axiom,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
file('theBenchmark.p',fact_zadd__commute) ).
fof(fact_zadd__left__commute,axiom,
! [V_z,V_y,V_x] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,V_z)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_y,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,V_z)),
file('theBenchmark.p',fact_zadd__left__commute) ).
fof(fact_zadd__assoc,axiom,
! [V_z3,V_z2,V_z1] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,V_z2),V_z3) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z1,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z2,V_z3)),
file('theBenchmark.p',fact_zadd__assoc) ).
fof(fact_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_uminus__dvd__conv_I2_J,axiom,
! [V_t_2,V_d_2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)) ),
file('theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).
fof(fact_uminus__dvd__conv_I1_J,axiom,
! [V_t_2,V_d_2] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)
<=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2) ),
file('theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).
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_zdiv__mono2__neg__lemma,axiom,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__neg__lemma) ).
fof(fact_unique__quotient__lemma__neg,axiom,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ),
file('theBenchmark.p',fact_unique__quotient__lemma__neg) ).
fof(fact_zdiv__mono2__lemma,axiom,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)
=> ( 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H) ) ) ) ) ) ),
file('theBenchmark.p',fact_zdiv__mono2__lemma) ).
fof(fact_unique__quotient__lemma,axiom,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q) ) ) ) ),
file('theBenchmark.p',fact_unique__quotient__lemma) ).
fof(fact_q__neg__lemma,axiom,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ) ),
file('theBenchmark.p',fact_q__neg__lemma) ).
fof(fact_q__pos__lemma,axiom,
! [V_r_H,V_q_H,V_b_H] :
( 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
=> ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
=> c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H) ) ) ),
file('theBenchmark.p',fact_q__pos__lemma) ).
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_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_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_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_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_natfloor__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_Onatfloor(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_Onatfloor(V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
file('theBenchmark.p',fact_natfloor__add__one) ).
fof(fact_natfloor__one,axiom,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
file('theBenchmark.p',fact_natfloor__one) ).
fof(fact_natfloor__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_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y)) ),
file('theBenchmark.p',fact_natfloor__mono) ).
fof(fact_zero__le__natfloor,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),
file('theBenchmark.p',fact_zero__le__natfloor) ).
fof(fact_natfloor__zero,axiom,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_natfloor__zero) ).
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_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_natfloor__neg,axiom,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
=> c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_natfloor__neg) ).
fof(fact_le__natfloor__eq__one,axiom,
! [V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) ),
file('theBenchmark.p',fact_le__natfloor__eq__one) ).
fof(fact_le__mult__natfloor,axiom,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b))) ) ),
file('theBenchmark.p',fact_le__mult__natfloor) ).
fof(fact_natceiling__eq,axiom,
! [V_x,V_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
=> ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
file('theBenchmark.p',fact_natceiling__eq) ).
fof(fact_incr__mult__lemma,axiom,
! [V_k_2,V_P_2,V_d_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2)
=> ( ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2))) )
=> ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
=> ! [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
=> hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2)))) ) ) ) ),
file('theBenchmark.p',fact_incr__mult__lemma) ).
fof(fact_real__of__nat__ge__zero,axiom,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
file('theBenchmark.p',fact_real__of__nat__ge__zero) ).
fof(fact_natfloor__real__of__nat,axiom,
! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
file('theBenchmark.p',fact_natfloor__real__of__nat) ).
fof(fact_real__of__nat__le__iff,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ),
file('theBenchmark.p',fact_real__of__nat__le__iff) ).
fof(fact_real__of__nat__mult,axiom,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
file('theBenchmark.p',fact_real__of__nat__mult) ).
fof(fact_real__of__nat__add,axiom,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
file('theBenchmark.p',fact_real__of__nat__add) ).
fof(fact_real__of__nat__1,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__of__nat__1) ).
fof(fact_power__real__of__nat,axiom,
! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
file('theBenchmark.p',fact_power__real__of__nat) ).
fof(fact_real__of__nat__power,axiom,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n),
file('theBenchmark.p',fact_real__of__nat__power) ).
fof(fact_real__natceiling__ge,axiom,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))),
file('theBenchmark.p',fact_real__natceiling__ge) ).
fof(fact_real__of__nat__inject,axiom,
! [V_ma_2,V_n_2] :
( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)
<=> V_n_2 = V_ma_2 ),
file('theBenchmark.p',fact_real__of__nat__inject) ).
fof(fact_natceiling__real__of__nat,axiom,
! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
file('theBenchmark.p',fact_natceiling__real__of__nat) ).
fof(fact_real__of__nat__less__iff,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ),
file('theBenchmark.p',fact_real__of__nat__less__iff) ).
fof(fact_not__real__of__nat__less__zero,axiom,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_not__real__of__nat__less__zero) ).
fof(fact_real__of__nat__zero,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__of__nat__zero) ).
fof(fact_real__of__nat__zero__iff,axiom,
! [V_n_2] :
( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_real__of__nat__zero__iff) ).
fof(fact_abs__real__of__nat__cancel,axiom,
! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x),
file('theBenchmark.p',fact_abs__real__of__nat__cancel) ).
fof(fact_real__of__nat__le__zero__cancel__iff,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
<=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
file('theBenchmark.p',fact_real__of__nat__le__zero__cancel__iff) ).
fof(fact_real__of__nat__Suc__gt__zero,axiom,
! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),
file('theBenchmark.p',fact_real__of__nat__Suc__gt__zero) ).
fof(fact_real__of__nat__one,axiom,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',fact_real__of__nat__one) ).
fof(fact_real__of__nat__Suc,axiom,
! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('theBenchmark.p',fact_real__of__nat__Suc) ).
fof(fact_real__natfloor__le,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_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),V_x) ),
file('theBenchmark.p',fact_real__natfloor__le) ).
fof(fact_le__natfloor,axiom,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a)) ),
file('theBenchmark.p',fact_le__natfloor) ).
fof(fact_natceiling__le,axiom,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ),
file('theBenchmark.p',fact_natceiling__le) ).
fof(fact_natfloor__power,axiom,
! [V_n,V_x] :
( V_x = c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x))
=> c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n) ),
file('theBenchmark.p',fact_natfloor__power) ).
fof(fact_real__of__nat__gt__zero__cancel__iff,axiom,
! [V_n_2] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) ),
file('theBenchmark.p',fact_real__of__nat__gt__zero__cancel__iff) ).
fof(fact_nat__less__real__le,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) ),
file('theBenchmark.p',fact_nat__less__real__le) ).
fof(fact_nat__le__real__less,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
<=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
file('theBenchmark.p',fact_nat__le__real__less) ).
fof(fact_le__natfloor__eq,axiom,
! [V_a_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2) ) ),
file('theBenchmark.p',fact_le__natfloor__eq) ).
fof(fact_Bseq__iff,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_Bseq__iff) ).
fof(fact_Bseq__iff1a,axiom,
! [V_X_2,T_a] :
( class_RealVector_Oreal__normed__vector(T_a)
=> ( c_SEQ_OBseq(T_a,V_X_2)
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_Bseq__iff1a) ).
fof(fact_natceiling__le__eq,axiom,
! [V_a_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)) ) ),
file('theBenchmark.p',fact_natceiling__le__eq) ).
fof(fact_real__natfloor__add__one__gt,axiom,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
file('theBenchmark.p',fact_real__natfloor__add__one__gt) ).
fof(fact_lemma__NBseq__def2,axiom,
! [V_X_2,T_b] :
( class_RealVector_Oreal__normed__vector(T_b)
=> ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_lemma__NBseq__def2) ).
fof(fact_lemma__NBseq__def,axiom,
! [V_X_2,T_b] :
( class_RealVector_Oreal__normed__vector(T_b)
=> ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
<=> ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) ) ),
file('theBenchmark.p',fact_lemma__NBseq__def) ).
fof(fact_less__natfloor,axiom,
! [V_n,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(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n) ) ),
file('theBenchmark.p',fact_less__natfloor) ).
fof(fact_natfloor__add,axiom,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x)
=> c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ),
file('theBenchmark.p',fact_natfloor__add) ).
fof(fact_ge__natfloor__plus__one__imp__gt,axiom,
! [V_n,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n)) ),
file('theBenchmark.p',fact_ge__natfloor__plus__one__imp__gt) ).
fof(fact_natfloor__eq,axiom,
! [V_x,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x)
=> ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
=> c_RComplete_Onatfloor(V_x) = V_n ) ),
file('theBenchmark.p',fact_natfloor__eq) ).
fof(fact_natceiling__add,axiom,
! [V_a,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_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ),
file('theBenchmark.p',fact_natceiling__add) ).
fof(fact_LIMSEQ__inverse__realpow__zero__lemma,axiom,
! [V_n,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_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n)) ),
file('theBenchmark.p',fact_LIMSEQ__inverse__realpow__zero__lemma) ).
fof(fact_reals__Archimedean6a,axiom,
! [V_r] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r)
=> ? [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n),V_r) ) ),
file('theBenchmark.p',fact_reals__Archimedean6a) ).
fof(fact_realpow__pos__nth__unique,axiom,
! [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(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
=> ? [B_x] :
( ! [B_y] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y) )
=> B_y = B_x )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x) ) ) ),
file('theBenchmark.p',fact_realpow__pos__nth__unique) ).
fof(fact_realpow__pos__nth,axiom,
! [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(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
=> ? [B_r] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) ) ) ),
file('theBenchmark.p',fact_realpow__pos__nth) ).
fof(fact_incr__lemma,axiom,
! [V_x,V_z,V_d] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d))) ),
file('theBenchmark.p',fact_incr__lemma) ).
fof(fact_le__add__iff1,axiom,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_2),V_d_2) ) ),
file('theBenchmark.p',fact_le__add__iff1) ).
fof(fact_le__add__iff2,axiom,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_less__add__iff2,axiom,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_ca_2),V_d_2) ) ),
file('theBenchmark.p',fact_less__add__iff1) ).
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_inf__period_I3_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_a] :
( ( class_Rings_Odvd(T_a)
& class_Rings_Ocomm__ring(T_a) )
=> ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
=> ! [B_x,B_k] :
( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
<=> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) ) ) ),
file('theBenchmark.p',fact_inf__period_I3_J) ).
fof(fact_inf__period_I4_J,axiom,
! [V_t_2,V_D_2,V_d_2,T_a] :
( ( class_Rings_Odvd(T_a)
& class_Rings_Ocomm__ring(T_a) )
=> ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
=> ! [B_x,B_k] :
( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
<=> c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) ) ) ),
file('theBenchmark.p',fact_inf__period_I4_J) ).
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_abs__diff__less__iff,axiom,
! [V_ra_2,V_a_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
<=> ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) ) ) ),
file('theBenchmark.p',fact_abs__diff__less__iff) ).
fof(fact_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_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_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_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__iff1,axiom,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_2) = V_d_2 ) ),
file('theBenchmark.p',fact_eq__add__iff1) ).
fof(fact_eq__add__iff2,axiom,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_diff__0,axiom,
! [V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a) ),
file('theBenchmark.p',fact_diff__0) ).
fof(fact_diff__minus__eq__add,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) ),
file('theBenchmark.p',fact_diff__minus__eq__add) ).
fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
! [V_y,V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y)) ),
file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).
fof(fact_ab__diff__minus,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_ab__diff__minus) ).
fof(fact_diff__def,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Ogroup__add(T_a)
=> c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) ),
file('theBenchmark.p',fact_diff__def) ).
fof(fact_abs__triangle__ineq3,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oordered__ab__group__add__abs(T_a)
=> c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_b))),c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b))) ),
file('theBenchmark.p',fact_abs__triangle__ineq3) ).
fof(fact_abs__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__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_diff__int__def__symmetric,axiom,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
file('theBenchmark.p',fact_diff__int__def__symmetric) ).
fof(fact_diff__int__def,axiom,
! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
file('theBenchmark.p',fact_diff__int__def) ).
fof(fact_minus__diff__eq,axiom,
! [V_b,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a) ),
file('theBenchmark.p',fact_minus__diff__eq) ).
fof(fact_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_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_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_diff__eq__diff__less__eq,axiom,
! [V_d_2,V_ca_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_ca_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_ca_2,V_d_2) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less__eq) ).
fof(fact_dvd__diff,axiom,
! [V_z,V_y,V_x,T_a] :
( class_Rings_Ocomm__ring__1(T_a)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
=> ( c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
=> c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z)) ) ) ),
file('theBenchmark.p',fact_dvd__diff) ).
fof(fact_zdvd__zdiffD,axiom,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n))
=> ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)
=> c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m) ) ),
file('theBenchmark.p',fact_zdvd__zdiffD) ).
fof(fact_less__bin__lemma,axiom,
! [V_l_2,V_k_2] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
file('theBenchmark.p',fact_less__bin__lemma) ).
fof(fact_minus__apply,axiom,
! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
( class_Groups_Ominus(T_a)
=> hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2)) ),
file('theBenchmark.p',fact_minus__apply) ).
fof(fact_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_poly__diff,axiom,
! [V_x,V_q,V_p,T_a] :
( class_Rings_Ocomm__ring(T_a)
=> hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x)) ),
file('theBenchmark.p',fact_poly__diff) ).
fof(fact_diff__pCons,axiom,
! [V_q,V_b,V_p,V_a,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)) ),
file('theBenchmark.p',fact_diff__pCons) ).
fof(fact_diff__eq__diff__eq,axiom,
! [V_d_2,V_ca_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_ca_2,V_d_2)
=> ( V_a_2 = V_b_2
<=> V_ca_2 = V_d_2 ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__eq) ).
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_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_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_diff__eq__diff__less,axiom,
! [V_d_2,V_ca_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_ca_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_ca_2,V_d_2) ) ) ),
file('theBenchmark.p',fact_diff__eq__diff__less) ).
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_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_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_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_zle__diff1__eq,axiom,
! [V_z_2,V_w_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
<=> c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ),
file('theBenchmark.p',fact_zle__diff1__eq) ).
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_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_decr__lemma,axiom,
! [V_z,V_x,V_d] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d)
=> c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z) ),
file('theBenchmark.p',fact_decr__lemma) ).
fof(fact_lemmaCauchy,axiom,
! [V_X_2,V_M_2,T_a,T_b] :
( ( class_Orderings_Oord(T_a)
& class_RealVector_Oreal__normed__vector(T_b) )
=> ( ! [B_n] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
=> ! [B_n] :
( c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n)
=> c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2)))) ) ) ),
file('theBenchmark.p',fact_lemmaCauchy) ).
fof(fact_tsub__def,axiom,
! [V_x,V_y] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x)
=> c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y) ) ),
file('theBenchmark.p',fact_tsub__def) ).
fof(fact_complex__diff__def,axiom,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)),
file('theBenchmark.p',fact_complex__diff__def) ).
fof(fact_less__eq__poly__def,axiom,
! [V_y_2,V_x_2,T_a] :
( class_Rings_Olinordered__idom(T_a)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
<=> ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
| V_x_2 = V_y_2 ) ) ),
file('theBenchmark.p',fact_less__eq__poly__def) ).
fof(fact_le__diff__iff,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_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_ma_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_ma_2,V_n_2) ) ) ),
file('theBenchmark.p',fact_le__diff__iff) ).
fof(fact_Nat_Odiff__diff__eq,axiom,
! [V_n,V_m,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_m)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_k),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_k)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n) ) ),
file('theBenchmark.p',fact_Nat_Odiff__diff__eq) ).
fof(fact_eq__diff__iff,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_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_ma_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
<=> V_ma_2 = V_n_2 ) ) ),
file('theBenchmark.p',fact_eq__diff__iff) ).
fof(fact_diff__diff__cancel,axiom,
! [V_n,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i,V_n)
=> c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_i)) = V_i ),
file('theBenchmark.p',fact_diff__diff__cancel) ).
fof(fact_diff__le__mono,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_l),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,V_l)) ),
file('theBenchmark.p',fact_diff__le__mono) ).
fof(fact_diff__le__mono2,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ),
file('theBenchmark.p',fact_diff__le__mono2) ).
fof(fact_diff__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__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_dvd__diff__nat,axiom,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ) ),
file('theBenchmark.p',fact_dvd__diff__nat) ).
fof(fact_real__le__eq__diff,axiom,
! [V_y_2,V_x_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
<=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('theBenchmark.p',fact_real__le__eq__diff) ).
fof(fact_zero__less__diff,axiom,
! [V_ma_2,V_n_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_zero__less__diff) ).
fof(fact_diff__less,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m) ) ),
file('theBenchmark.p',fact_diff__less) ).
fof(fact_diff__less__Suc,axiom,
! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
file('theBenchmark.p',fact_diff__less__Suc) ).
fof(fact_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,axiom,
! [V_n_2,V_ma_2] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
<=> c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ),
file('theBenchmark.p',fact_diff__is__0__eq) ).
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_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_less__diff__conv,axiom,
! [V_k_2,V_j_2,V_i_2] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) ),
file('theBenchmark.p',fact_less__diff__conv) ).
fof(fact_add__diff__inverse,axiom,
! [V_n,V_m] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m ),
file('theBenchmark.p',fact_add__diff__inverse) ).
fof(fact_less__diff__iff,axiom,
! [V_n_2,V_ma_2,V_k_2] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_ma_2)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k_2,V_n_2)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
<=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ) ),
file('theBenchmark.p',fact_less__diff__iff) ).
fof(fact_diff__less__mono,axiom,
! [V_c,V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c)) ) ),
file('theBenchmark.p',fact_diff__less__mono) ).
fof(fact_dvd__diffD,axiom,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) ) ) ),
file('theBenchmark.p',fact_dvd__diffD) ).
fof(fact_dvd__diffD1,axiom,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
=> ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
=> ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) ) ) ),
file('theBenchmark.p',fact_dvd__diffD1) ).
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__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_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_minus__real__def,axiom,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)),
file('theBenchmark.p',fact_minus__real__def) ).
fof(fact_real__diff__def,axiom,
! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)),
file('theBenchmark.p',fact_real__diff__def) ).
fof(fact_diff__poly__code_I1_J,axiom,
! [V_q,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q) ),
file('theBenchmark.p',fact_diff__poly__code_I1_J) ).
fof(fact_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_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_diff__poly__code_I2_J,axiom,
! [V_p,T_a] :
( class_Groups_Oab__group__add(T_a)
=> c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p ),
file('theBenchmark.p',fact_diff__poly__code_I2_J) ).
fof(fact_diff__less__mono2,axiom,
! [V_l,V_n,V_m] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
=> ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_l)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_n),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_l,V_m)) ) ),
file('theBenchmark.p',fact_diff__less__mono2) ).
fof(fact_less__imp__diff__less,axiom,
! [V_n,V_k,V_j] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_j,V_k)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j,V_n),V_k) ),
file('theBenchmark.p',fact_less__imp__diff__less) ).
fof(fact_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_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_real__of__nat__diff,axiom,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
=> c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)) ),
file('theBenchmark.p',fact_real__of__nat__diff) ).
fof(fact_natceiling__subtract,axiom,
! [V_x,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
=> c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a) ),
file('theBenchmark.p',fact_natceiling__subtract) ).
fof(fact_natfloor__subtract,axiom,
! [V_x,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x)
=> c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a) ),
file('theBenchmark.p',fact_natfloor__subtract) ).
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_diff__Suc__less,axiom,
! [V_i,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n) ),
file('theBenchmark.p',fact_diff__Suc__less) ).
fof(fact_Suc__pred,axiom,
! [V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
=> c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n ),
file('theBenchmark.p',fact_Suc__pred) ).
fof(fact_nat__diff__split,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
<=> ( ! [B_d] :
( V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d)
=> hBOOL(hAPP(V_P_2,B_d)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2)
=> hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
file('theBenchmark.p',fact_nat__diff__split) ).
fof(fact_nat__diff__split__asm,axiom,
! [V_b_2,V_a_2,V_P_2] :
( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
<=> ~ ( ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) ) ),
file('theBenchmark.p',fact_nat__diff__split__asm) ).
fof(fact_diff__Suc__diff__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_nat__eq__add__iff2,axiom,
! [V_n_2,V_ma_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_ma_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_ma_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(arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add) ).
fof(arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Nat__Onat__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ocancel__comm__monoid__add) ).
fof(arity_Int__Oint__Groups_Ocancel__comm__monoid__add,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ocancel__comm__monoid__add) ).
fof(arity_fun__Lattices_Oboolean__algebra,axiom,
! [T_2,T_1] :
( class_Lattices_Oboolean__algebra(T_1)
=> class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Lattices_Oboolean__algebra) ).
fof(arity_fun__Orderings_Opreorder,axiom,
! [T_2,T_1] :
( class_Orderings_Opreorder(T_1)
=> class_Orderings_Opreorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Opreorder) ).
fof(arity_fun__Orderings_Oorder,axiom,
! [T_2,T_1] :
( class_Orderings_Oorder(T_1)
=> class_Orderings_Oorder(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oorder) ).
fof(arity_fun__Orderings_Oord,axiom,
! [T_2,T_1] :
( class_Orderings_Oord(T_1)
=> class_Orderings_Oord(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Orderings_Oord) ).
fof(arity_fun__Groups_Ouminus,axiom,
! [T_2,T_1] :
( class_Groups_Ouminus(T_1)
=> class_Groups_Ouminus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ouminus) ).
fof(arity_fun__Groups_Ominus,axiom,
! [T_2,T_1] :
( class_Groups_Ominus(T_1)
=> class_Groups_Ominus(tc_fun(T_2,T_1)) ),
file('theBenchmark.p',arity_fun__Groups_Ominus) ).
fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Int__Oint__Rings_Olinordered__semiring__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__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring__0) ).
fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__semiring) ).
fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
class_Groups_Oab__group__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oab__group__add) ).
fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ozero__neq__one) ).
fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
class_Rings_Oordered__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oordered__ring) ).
fof(arity_Int__Oint__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Opreorder) ).
fof(arity_Int__Oint__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Olinorder) ).
fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__mult) ).
fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring__1) ).
fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Omonoid__add) ).
fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring__0) ).
fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ogroup__add) ).
fof(arity_Int__Oint__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Omult__zero) ).
fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Ocomm__ring) ).
fof(arity_Int__Oint__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oorder) ).
fof(arity_Int__Oint__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Int_Oring__char__0) ).
fof(arity_Int__Oint__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Osemiring) ).
fof(arity_Int__Oint__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Orderings_Oord) ).
fof(arity_Int__Oint__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ouminus) ).
fof(arity_Int__Oint__Groups_Osgn__if,axiom,
class_Groups_Osgn__if(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Osgn__if) ).
fof(arity_Int__Oint__Groups_Oabs__if,axiom,
class_Groups_Oabs__if(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oabs__if) ).
fof(arity_Int__Oint__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring__1) ).
fof(arity_Int__Oint__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ominus) ).
fof(arity_Int__Oint__Power_Opower,axiom,
class_Power_Opower(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Power_Opower) ).
fof(arity_Int__Oint__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Ozero) ).
fof(arity_Int__Oint__Rings_Oring,axiom,
class_Rings_Oring(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oring) ).
fof(arity_Int__Oint__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Oidom) ).
fof(arity_Int__Oint__Groups_Oone,axiom,
class_Groups_Oone(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Groups_Oone) ).
fof(arity_Int__Oint__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Int_Oint),
file('theBenchmark.p',arity_Int__Oint__Rings_Odvd) ).
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__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring__0) ).
fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ocomm__semiring) ).
fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Ozero__neq__one) ).
fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Opreorder) ).
fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
class_Orderings_Olinorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
class_Groups_Omonoid__mult(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__mult) ).
fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
class_Groups_Omonoid__add(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Omonoid__add) ).
fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
class_Rings_Osemiring__0(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring__0) ).
fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Omult__zero) ).
fof(arity_Nat__Onat__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oorder) ).
fof(arity_Nat__Onat__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Osemiring) ).
fof(arity_Nat__Onat__Orderings_Oord,axiom,
class_Orderings_Oord(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
fof(arity_Nat__Onat__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
fof(arity_Nat__Onat__Power_Opower,axiom,
class_Power_Opower(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Power_Opower) ).
fof(arity_Nat__Onat__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Ozero) ).
fof(arity_Nat__Onat__Groups_Oone,axiom,
class_Groups_Oone(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Groups_Oone) ).
fof(arity_Nat__Onat__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Nat_Onat),
file('theBenchmark.p',arity_Nat__Onat__Rings_Odvd) ).
fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Lattices_Oboolean__algebra) ).
fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
class_Orderings_Opreorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Opreorder) ).
fof(arity_HOL__Obool__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oorder) ).
fof(arity_HOL__Obool__Orderings_Oord,axiom,
class_Orderings_Oord(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
fof(arity_HOL__Obool__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ouminus) ).
fof(arity_HOL__Obool__Groups_Ominus,axiom,
class_Groups_Ominus(tc_HOL_Obool),
file('theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
fof(arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_RealDef__Oreal__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__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__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__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__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__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__semiring__0) ).
fof(arity_RealDef__Oreal__Rings_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__0,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring__0) ).
fof(arity_RealDef__Oreal__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ogroup__add) ).
fof(arity_RealDef__Oreal__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Omult__zero) ).
fof(arity_RealDef__Oreal__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Ocomm__ring) ).
fof(arity_RealDef__Oreal__Orderings_Oorder,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oorder) ).
fof(arity_RealDef__Oreal__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Int_Oring__char__0) ).
fof(arity_RealDef__Oreal__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Osemiring) ).
fof(arity_RealDef__Oreal__Orderings_Oord,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Orderings_Oord) ).
fof(arity_RealDef__Oreal__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ouminus) ).
fof(arity_RealDef__Oreal__Groups_Osgn__if,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Osgn__if) ).
fof(arity_RealDef__Oreal__Groups_Oabs__if,axiom,
class_Groups_Oabs__if(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oabs__if) ).
fof(arity_RealDef__Oreal__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring__1) ).
fof(arity_RealDef__Oreal__Groups_Ominus,axiom,
class_Groups_Ominus(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ominus) ).
fof(arity_RealDef__Oreal__Power_Opower,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Power_Opower) ).
fof(arity_RealDef__Oreal__Groups_Ozero,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Ozero) ).
fof(arity_RealDef__Oreal__Rings_Oring,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oring) ).
fof(arity_RealDef__Oreal__Rings_Oidom,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Oidom) ).
fof(arity_RealDef__Oreal__Groups_Oone,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Groups_Oone) ).
fof(arity_RealDef__Oreal__Rings_Odvd,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('theBenchmark.p',arity_RealDef__Oreal__Rings_Odvd) ).
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__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__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__Groups_Oab__semigroup__mult,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__mult) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult) ).
fof(arity_Complex__Ocomplex__Groups_Oab__semigroup__add,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oab__semigroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Ono__zero__divisors,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ono__zero__divisors) ).
fof(arity_Complex__Ocomplex__Groups_Ocomm__monoid__add,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ocomm__monoid__add) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__1,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__1) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__semiring__0,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__semiring__0) ).
fof(arity_Complex__Ocomplex__Rings_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__0,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring__0) ).
fof(arity_Complex__Ocomplex__Groups_Ogroup__add,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ogroup__add) ).
fof(arity_Complex__Ocomplex__Rings_Omult__zero,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Omult__zero) ).
fof(arity_Complex__Ocomplex__Rings_Ocomm__ring,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Ocomm__ring) ).
fof(arity_Complex__Ocomplex__Int_Oring__char__0,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Int_Oring__char__0) ).
fof(arity_Complex__Ocomplex__Rings_Osemiring,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Osemiring) ).
fof(arity_Complex__Ocomplex__Groups_Ouminus,axiom,
class_Groups_Ouminus(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ouminus) ).
fof(arity_Complex__Ocomplex__Rings_Oring__1,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring__1) ).
fof(arity_Complex__Ocomplex__Groups_Ominus,axiom,
class_Groups_Ominus(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ominus) ).
fof(arity_Complex__Ocomplex__Power_Opower,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Power_Opower) ).
fof(arity_Complex__Ocomplex__Groups_Ozero,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Ozero) ).
fof(arity_Complex__Ocomplex__Rings_Oring,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oring) ).
fof(arity_Complex__Ocomplex__Rings_Oidom,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Oidom) ).
fof(arity_Complex__Ocomplex__Groups_Oone,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Groups_Oone) ).
fof(arity_Complex__Ocomplex__Rings_Odvd,axiom,
class_Rings_Odvd(tc_Complex_Ocomplex),
file('theBenchmark.p',arity_Complex__Ocomplex__Rings_Odvd) ).
fof(arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add) ).
fof(arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring__strict,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring__strict) ).
fof(arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__comm__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__comm__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring__1,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring__1) ).
fof(arity_Polynomial__Opoly__Groups_Oordered__ab__group__add,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oordered__ab__group__add) ).
fof(arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add,axiom,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(T_1)
=> class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__semidom,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__semidom) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__mult) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult) ).
fof(arity_Polynomial__Opoly__Groups_Oab__semigroup__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__semigroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__semiring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__semiring) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring__abs,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring__abs) ).
fof(arity_Polynomial__Opoly__Rings_Ono__zero__divisors,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ono__zero__divisors) ).
fof(arity_Polynomial__Opoly__Groups_Ocomm__monoid__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ocomm__monoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__ring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__ring) ).
fof(arity_Polynomial__Opoly__Rings_Olinordered__idom,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Olinordered__idom) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__1) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring__0,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring__0) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__semiring,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__semiring) ).
fof(arity_Polynomial__Opoly__Groups_Oab__group__add,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oab__group__add) ).
fof(arity_Polynomial__Opoly__Rings_Ozero__neq__one,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ozero__neq__one) ).
fof(arity_Polynomial__Opoly__Rings_Oordered__ring,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oordered__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Opreorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Opreorder) ).
fof(arity_Polynomial__Opoly__Orderings_Olinorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Olinorder) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__mult,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__mult) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring__1) ).
fof(arity_Polynomial__Opoly__Groups_Omonoid__add,axiom,
! [T_1] :
( class_Groups_Ocomm__monoid__add(T_1)
=> class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Omonoid__add) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring__0,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring__0) ).
fof(arity_Polynomial__Opoly__Groups_Ogroup__add,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ogroup__add) ).
fof(arity_Polynomial__Opoly__Rings_Omult__zero,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Omult__zero) ).
fof(arity_Polynomial__Opoly__Rings_Ocomm__ring,axiom,
! [T_1] :
( class_Rings_Ocomm__ring(T_1)
=> class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Ocomm__ring) ).
fof(arity_Polynomial__Opoly__Orderings_Oorder,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Oorder(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oorder) ).
fof(arity_Polynomial__Opoly__Int_Oring__char__0,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Int_Oring__char__0) ).
fof(arity_Polynomial__Opoly__Rings_Osemiring,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__0(T_1)
=> class_Rings_Osemiring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Osemiring) ).
fof(arity_Polynomial__Opoly__Orderings_Oord,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Orderings_Oord(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Orderings_Oord) ).
fof(arity_Polynomial__Opoly__Groups_Ouminus,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ouminus(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ouminus) ).
fof(arity_Polynomial__Opoly__Groups_Osgn__if,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Osgn__if) ).
fof(arity_Polynomial__Opoly__Groups_Oabs__if,axiom,
! [T_1] :
( class_Rings_Olinordered__idom(T_1)
=> class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oabs__if) ).
fof(arity_Polynomial__Opoly__Rings_Oring__1,axiom,
! [T_1] :
( class_Rings_Ocomm__ring__1(T_1)
=> class_Rings_Oring__1(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring__1) ).
fof(arity_Polynomial__Opoly__Groups_Ominus,axiom,
! [T_1] :
( class_Groups_Oab__group__add(T_1)
=> class_Groups_Ominus(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ominus) ).
fof(arity_Polynomial__Opoly__Power_Opower,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Power_Opower(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Power_Opower) ).
fof(arity_Polynomial__Opoly__Groups_Ozero,axiom,
! [T_1] :
( class_Groups_Ozero(T_1)
=> class_Groups_Ozero(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Ozero) ).
fof(arity_Polynomial__Opoly__Rings_Oring,axiom,
! [T_1] :
( class_Rings_Ocomm__ring(T_1)
=> class_Rings_Oring(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oring) ).
fof(arity_Polynomial__Opoly__Rings_Oidom,axiom,
! [T_1] :
( class_Rings_Oidom(T_1)
=> class_Rings_Oidom(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Oidom) ).
fof(arity_Polynomial__Opoly__Groups_Oone,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Groups_Oone(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Groups_Oone) ).
fof(arity_Polynomial__Opoly__Rings_Odvd,axiom,
! [T_1] :
( class_Rings_Ocomm__semiring__1(T_1)
=> class_Rings_Odvd(tc_Polynomial_Opoly(T_1)) ),
file('theBenchmark.p',arity_Polynomial__Opoly__Rings_Odvd) ).
fof(help_c__fequal__1,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(c_fequal(V_x_2,V_y_2)) ),
file('theBenchmark.p',help_c__fequal__1) ).
fof(help_c__fequal__2,axiom,
! [V_y_2,V_x_2] :
( hBOOL(c_fequal(V_x_2,V_y_2))
| V_x_2 != V_y_2 ),
file('theBenchmark.p',help_c__fequal__2) ).
fof(conj_0,conjecture,
? [B_m] :
( ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),B_z)),B_m) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
file('theBenchmark.p',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,
! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
inference(fof_nnf,[status(thm)],[fact_m]) ).
fof(f_2_2,plain,
! [U_3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_3)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3),v_r) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_3)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3),v_r) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_3)),v_m____)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3),v_r) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
? [B_m] :
( ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
inference(fof_nnf,[status(thm)],[fact_pCons]) ).
fof(f_3_2,plain,
? [U_5] :
( ! [U_4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_4)),U_5)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_4),v_r) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_5) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_4)),sK2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_4),v_r) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_5,sK2)],[f_3_2]) ).
fof(f_3_4,plain,
( ! [U_4] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_4)),sK2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_4),v_r) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK2) ),
inference(definitional_conversion,[status(esa)],[f_3_3]) ).
cnf(f_3_5,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK2),
inference(clausify,[status(thm)],[f_3_4]) ).
cnf(f_3_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_4)),sK2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_4),v_r) ),
inference(clausify,[status(thm)],[f_3_4]) ).
fof(f_4_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2))
| V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,V_x_2)) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__norm__iff]) ).
fof(f_4_2,plain,
! [U_7,U_6] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_6,U_7))
| U_7 = c_Groups_Ozero__class_Ozero(U_6) )
& ( U_7 != c_Groups_Ozero__class_Ozero(U_6)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_6,U_7)) ) )
| ~ class_RealVector_Oreal__normed__vector(U_6) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_6,U_7] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_6,U_7))
| U_7 = c_Groups_Ozero__class_Ozero(U_6)
| ~ sP0(U_6,U_7) )
& ! [U_6,U_7] :
( U_7 != c_Groups_Ozero__class_Ozero(U_6)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_6,U_7))
| ~ sP0(U_6,U_7) )
& ! [U_6,U_7] :
( sP0(U_6,U_7)
| ~ class_RealVector_Oreal__normed__vector(U_6) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_4_2]) ).
cnf(f_4_4,plain,
( sP0(U_6,U_7)
| ~ class_RealVector_Oreal__normed__vector(U_6) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( U_7 != c_Groups_Ozero__class_Ozero(U_6)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_6,U_7))
| ~ sP0(U_6,U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_6,U_7))
| U_7 = c_Groups_Ozero__class_Ozero(U_6)
| ~ sP0(U_6,U_7) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,V_x_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__le__zero__iff]) ).
fof(f_5_2,plain,
! [U_9,U_8] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_8,U_9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_9 != c_Groups_Ozero__class_Ozero(U_8) )
& ( U_9 = c_Groups_Ozero__class_Ozero(U_8)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_8,U_9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) )
| ~ class_RealVector_Oreal__normed__vector(U_8) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_9,U_8] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_8,U_9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_9 != c_Groups_Ozero__class_Ozero(U_8)
| ~ sP1(U_9,U_8) )
& ! [U_9,U_8] :
( U_9 = c_Groups_Ozero__class_Ozero(U_8)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_8,U_9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP1(U_9,U_8) )
& ! [U_9,U_8] :
( sP1(U_9,U_8)
| ~ class_RealVector_Oreal__normed__vector(U_8) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1])],[f_5_2]) ).
cnf(f_5_4,plain,
( sP1(U_9,U_8)
| ~ class_RealVector_Oreal__normed__vector(U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( U_9 = c_Groups_Ozero__class_Ozero(U_8)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_8,U_9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ sP1(U_9,U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_8,U_9),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_9 != c_Groups_Ozero__class_Ozero(U_8)
| ~ sP1(U_9,U_8) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_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_6_2,plain,
! [U_11,U_10] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,U_11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_10) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_10,U_11] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,U_11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_10) ),
inference(definitional_conversion,[status(esa)],[f_6_2]) ).
cnf(f_6_4,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_10,U_11),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_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_7_2,plain,
! [U_13,U_12] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_12,U_13))
| ~ class_RealVector_Oreal__normed__vector(U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_12,U_13] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_12,U_13))
| ~ class_RealVector_Oreal__normed__vector(U_12) ),
inference(definitional_conversion,[status(esa)],[f_7_2]) ).
cnf(f_7_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_12,U_13))
| ~ class_RealVector_Oreal__normed__vector(U_12) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_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_8_2,plain,
! [U_14] :
( c_RealVector_Onorm__class_Onorm(U_14,c_Groups_Ozero__class_Ozero(U_14)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_14] :
( c_RealVector_Onorm__class_Onorm(U_14,c_Groups_Ozero__class_Ozero(U_14)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_14) ),
inference(definitional_conversion,[status(esa)],[f_8_2]) ).
cnf(f_8_4,plain,
( c_RealVector_Onorm__class_Onorm(U_14,c_Groups_Ozero__class_Ozero(U_14)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__vector(U_14) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [V_x_2,T_a] :
( ( ( c_RealVector_Onorm__class_Onorm(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_RealVector_Onorm__class_Onorm(T_a,V_x_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__eq__zero]) ).
fof(f_9_2,plain,
! [U_16,U_15] :
( ( ( c_RealVector_Onorm__class_Onorm(U_15,U_16) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_16 != c_Groups_Ozero__class_Ozero(U_15) )
& ( U_16 = c_Groups_Ozero__class_Ozero(U_15)
| c_RealVector_Onorm__class_Onorm(U_15,U_16) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) )
| ~ class_RealVector_Oreal__normed__vector(U_15) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_15,U_16] :
( c_RealVector_Onorm__class_Onorm(U_15,U_16) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_16 != c_Groups_Ozero__class_Ozero(U_15)
| ~ sP2(U_15,U_16) )
& ! [U_15,U_16] :
( U_16 = c_Groups_Ozero__class_Ozero(U_15)
| c_RealVector_Onorm__class_Onorm(U_15,U_16) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP2(U_15,U_16) )
& ! [U_15,U_16] :
( sP2(U_15,U_16)
| ~ class_RealVector_Oreal__normed__vector(U_15) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP2])],[f_9_2]) ).
cnf(f_9_4,plain,
( sP2(U_15,U_16)
| ~ class_RealVector_Oreal__normed__vector(U_15) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( U_16 = c_Groups_Ozero__class_Ozero(U_15)
| c_RealVector_Onorm__class_Onorm(U_15,U_16) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP2(U_15,U_16) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( c_RealVector_Onorm__class_Onorm(U_15,U_16) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_16 != c_Groups_Ozero__class_Ozero(U_15)
| ~ sP2(U_15,U_16) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
? [B_m] :
! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),B_z)),B_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) ),
inference(fof_nnf,[status(thm)],[fact__096_B_Bthesis_O_A_I_B_Bm_O_AALL_Az_O_Acmod_Az_A_060_061_Ar_A_N_N_062_Acmod_A_Ipoly_Acs_Az_J_A_060_061_Am_A_061_061_062_Athesis_J_A_061_061_062_Athesis_096]) ).
fof(f_10_2,plain,
? [U_18] :
! [U_17] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_17)),U_18)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_17),v_r) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_17] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_17)),sK3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_17),v_r) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_18,sK3)],[f_10_2]) ).
fof(f_10_4,plain,
! [U_17] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_17)),sK3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_17),v_r) ),
inference(definitional_conversion,[status(esa)],[f_10_3]) ).
cnf(f_10_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,v_cs____),U_17)),sK3)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_17),v_r) ),
inference(clausify,[status(thm)],[f_10_4]) ).
fof(f_11_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_11_2,plain,
! [U_20,U_19] :
( c_Orderings_Oord__class_Oless__eq(U_19,U_20,U_20)
| ~ class_Orderings_Opreorder(U_19) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_20,U_19] :
( c_Orderings_Oord__class_Oless__eq(U_19,U_20,U_20)
| ~ class_Orderings_Opreorder(U_19) ),
inference(definitional_conversion,[status(esa)],[f_11_2]) ).
cnf(f_11_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_19,U_20,U_20)
| ~ class_Orderings_Opreorder(U_19) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [V_x,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__0]) ).
fof(f_12_2,plain,
! [U_22,U_21] :
( hAPP(c_Polynomial_Opoly(U_21,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_21))),U_22) = c_Groups_Ozero__class_Ozero(U_21)
| ~ class_Rings_Ocomm__semiring__0(U_21) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_21,U_22] :
( hAPP(c_Polynomial_Opoly(U_21,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_21))),U_22) = c_Groups_Ozero__class_Ozero(U_21)
| ~ class_Rings_Ocomm__semiring__0(U_21) ),
inference(definitional_conversion,[status(esa)],[f_12_2]) ).
cnf(f_12_4,plain,
( hAPP(c_Polynomial_Opoly(U_21,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_21))),U_22) = c_Groups_Ozero__class_Ozero(U_21)
| ~ class_Rings_Ocomm__semiring__0(U_21) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [T_a] :
( c_Polynomial_OpCons(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pCons__0__0]) ).
fof(f_13_2,plain,
! [U_23] :
( c_Polynomial_OpCons(U_23,c_Groups_Ozero__class_Ozero(U_23),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_23))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_23))
| ~ class_Groups_Ozero(U_23) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_23] :
( c_Polynomial_OpCons(U_23,c_Groups_Ozero__class_Ozero(U_23),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_23))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_23))
| ~ class_Groups_Ozero(U_23) ),
inference(definitional_conversion,[status(esa)],[f_13_2]) ).
cnf(f_13_4,plain,
( c_Polynomial_OpCons(U_23,c_Groups_Ozero__class_Ozero(U_23),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_23))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_23))
| ~ class_Groups_Ozero(U_23) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [V_pa_2,V_a_2,T_a] :
( ( ( c_Polynomial_OpCons(T_a,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
& V_a_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Polynomial_OpCons(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pCons__eq__0__iff]) ).
fof(f_14_2,plain,
! [U_26,U_25,U_24] :
( ( ( c_Polynomial_OpCons(U_24,U_25,U_26) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| U_26 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| U_25 != c_Groups_Ozero__class_Ozero(U_24) )
& ( ( U_26 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
& U_25 = c_Groups_Ozero__class_Ozero(U_24) )
| c_Polynomial_OpCons(U_24,U_25,U_26) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24)) ) )
| ~ class_Groups_Ozero(U_24) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
( ! [U_24,U_25,U_26] :
( U_26 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| ~ sP3(U_24,U_25,U_26) )
& ! [U_24,U_25,U_26] :
( U_25 = c_Groups_Ozero__class_Ozero(U_24)
| ~ sP3(U_24,U_25,U_26) )
& ! [U_24,U_25,U_26] :
( c_Polynomial_OpCons(U_24,U_25,U_26) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| U_26 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| U_25 != c_Groups_Ozero__class_Ozero(U_24)
| ~ sP4(U_24,U_25,U_26) )
& ! [U_24,U_25,U_26] :
( sP3(U_24,U_25,U_26)
| c_Polynomial_OpCons(U_24,U_25,U_26) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| ~ sP4(U_24,U_25,U_26) )
& ! [U_24,U_25,U_26] :
( sP4(U_24,U_25,U_26)
| ~ class_Groups_Ozero(U_24) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3,sP4])],[f_14_2]) ).
cnf(f_14_4,plain,
( sP4(U_24,U_25,U_26)
| ~ class_Groups_Ozero(U_24) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_5,plain,
( sP3(U_24,U_25,U_26)
| c_Polynomial_OpCons(U_24,U_25,U_26) != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| ~ sP4(U_24,U_25,U_26) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_6,plain,
( c_Polynomial_OpCons(U_24,U_25,U_26) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| U_26 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| U_25 != c_Groups_Ozero__class_Ozero(U_24)
| ~ sP4(U_24,U_25,U_26) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_7,plain,
( U_25 = c_Groups_Ozero__class_Ozero(U_24)
| ~ sP3(U_24,U_25,U_26) ),
inference(clausify,[status(thm)],[f_14_3]) ).
cnf(f_14_8,plain,
( U_26 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_24))
| ~ sP3(U_24,U_25,U_26) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__less__def]) ).
fof(f_15_2,plain,
! [U_28,U_27] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_27,U_28)
| U_27 = U_28
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_27,U_28) )
& ( ( U_27 != U_28
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_27,U_28) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_27,U_28) ) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_32,U_30] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_30,U_32)
| U_30 = U_32
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_30,U_32) )
& ! [U_31,U_29] :
( ( U_29 != U_31
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_29,U_31) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_29,U_31) ) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
fof(f_15_4,plain,
( ! [U_29,U_31] :
( U_29 != U_31
| ~ sP5(U_29,U_31) )
& ! [U_29,U_31] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_29,U_31)
| ~ sP5(U_29,U_31) )
& ! [U_30,U_32] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_30,U_32)
| U_30 = U_32
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_30,U_32) )
& ! [U_29,U_31] :
( sP5(U_29,U_31)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_29,U_31) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_15_3]) ).
cnf(f_15_5,plain,
( sP5(U_29,U_31)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_29,U_31) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_30,U_32)
| U_30 = U_32
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_30,U_32) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_29,U_31)
| ~ sP5(U_29,U_31) ),
inference(clausify,[status(thm)],[f_15_4]) ).
cnf(f_15_8,plain,
( U_29 != U_31
| ~ sP5(U_29,U_31) ),
inference(clausify,[status(thm)],[f_15_4]) ).
fof(f_16_1,plain,
! [V_pa_2,T_a] :
( ( ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__zero]) ).
fof(f_16_2,plain,
! [U_34,U_33] :
( ( ( c_Polynomial_Opoly(U_33,U_34) = c_Polynomial_Opoly(U_33,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33)))
| U_34 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33)) )
& ( U_34 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33))
| c_Polynomial_Opoly(U_33,U_34) != c_Polynomial_Opoly(U_33,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33))) ) )
| ~ class_Rings_Oidom(U_33)
| ~ class_Int_Oring__char__0(U_33) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_33,U_34] :
( c_Polynomial_Opoly(U_33,U_34) = c_Polynomial_Opoly(U_33,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33)))
| U_34 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33))
| ~ sP6(U_33,U_34) )
& ! [U_33,U_34] :
( U_34 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33))
| c_Polynomial_Opoly(U_33,U_34) != c_Polynomial_Opoly(U_33,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33)))
| ~ sP6(U_33,U_34) )
& ! [U_33,U_34] :
( sP6(U_33,U_34)
| ~ class_Rings_Oidom(U_33)
| ~ class_Int_Oring__char__0(U_33) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_16_2]) ).
cnf(f_16_4,plain,
( sP6(U_33,U_34)
| ~ class_Rings_Oidom(U_33)
| ~ class_Int_Oring__char__0(U_33) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_5,plain,
( U_34 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33))
| c_Polynomial_Opoly(U_33,U_34) != c_Polynomial_Opoly(U_33,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33)))
| ~ sP6(U_33,U_34) ),
inference(clausify,[status(thm)],[f_16_3]) ).
cnf(f_16_6,plain,
( c_Polynomial_Opoly(U_33,U_34) = c_Polynomial_Opoly(U_33,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33)))
| U_34 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_33))
| ~ sP6(U_33,U_34) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_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_17_2,plain,
! [U_37,U_36,U_35] :
( c_Orderings_Oord__class_Oless__eq(U_35,U_37,U_36)
| c_Orderings_Oord__class_Oless__eq(U_35,U_36,U_37)
| ~ class_Orderings_Olinorder(U_35) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_37,U_36,U_35] :
( c_Orderings_Oord__class_Oless__eq(U_35,U_37,U_36)
| c_Orderings_Oord__class_Oless__eq(U_35,U_36,U_37)
| ~ class_Orderings_Olinorder(U_35) ),
inference(definitional_conversion,[status(esa)],[f_17_2]) ).
cnf(f_17_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_35,U_37,U_36)
| c_Orderings_Oord__class_Oless__eq(U_35,U_36,U_37)
| ~ class_Orderings_Olinorder(U_35) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_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_18_2,plain,
! [U_42,U_41,U_40,U_39,U_38] :
( c_Orderings_Oord__class_Oless__eq(U_38,hAPP(U_40,U_42),hAPP(U_41,U_42))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_39,U_38),U_40,U_41)
| ~ class_Orderings_Oord(U_38) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
fof(f_18_3,plain,
! [U_38,U_39,U_41,U_42,U_40] :
( c_Orderings_Oord__class_Oless__eq(U_38,hAPP(U_40,U_42),hAPP(U_41,U_42))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_39,U_38),U_40,U_41)
| ~ class_Orderings_Oord(U_38) ),
inference(definitional_conversion,[status(esa)],[f_18_2]) ).
cnf(f_18_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_38,hAPP(U_40,U_42),hAPP(U_41,U_42))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_39,U_38),U_40,U_41)
| ~ class_Orderings_Oord(U_38) ),
inference(clausify,[status(thm)],[f_18_3]) ).
fof(f_19_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_19_2,plain,
! [U_46,U_45,U_44,U_43] :
( c_Orderings_Oord__class_Oless__eq(U_43,U_46,U_45)
| ~ c_Orderings_Oord__class_Oless__eq(U_43,U_46,U_44)
| ~ c_Orderings_Oord__class_Oless__eq(U_43,U_44,U_45)
| ~ class_Orderings_Oorder(U_43) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
fof(f_19_3,plain,
! [U_43,U_45,U_46,U_44] :
( c_Orderings_Oord__class_Oless__eq(U_43,U_46,U_45)
| ~ c_Orderings_Oord__class_Oless__eq(U_43,U_46,U_44)
| ~ c_Orderings_Oord__class_Oless__eq(U_43,U_44,U_45)
| ~ class_Orderings_Oorder(U_43) ),
inference(definitional_conversion,[status(esa)],[f_19_2]) ).
cnf(f_19_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_43,U_46,U_45)
| ~ c_Orderings_Oord__class_Oless__eq(U_43,U_46,U_44)
| ~ c_Orderings_Oord__class_Oless__eq(U_43,U_44,U_45)
| ~ class_Orderings_Oorder(U_43) ),
inference(clausify,[status(thm)],[f_19_3]) ).
fof(f_20_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_20_2,plain,
! [U_49,U_48,U_47] :
( U_49 = U_48
| ~ c_Orderings_Oord__class_Oless__eq(U_47,U_49,U_48)
| ~ c_Orderings_Oord__class_Oless__eq(U_47,U_48,U_49)
| ~ class_Orderings_Oorder(U_47) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_49,U_47,U_48] :
( U_49 = U_48
| ~ c_Orderings_Oord__class_Oless__eq(U_47,U_49,U_48)
| ~ c_Orderings_Oord__class_Oless__eq(U_47,U_48,U_49)
| ~ class_Orderings_Oorder(U_47) ),
inference(definitional_conversion,[status(esa)],[f_20_2]) ).
cnf(f_20_4,plain,
( U_49 = U_48
| ~ c_Orderings_Oord__class_Oless__eq(U_47,U_49,U_48)
| ~ c_Orderings_Oord__class_Oless__eq(U_47,U_48,U_49)
| ~ class_Orderings_Oorder(U_47) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_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_21_2,plain,
! [U_53,U_52,U_51,U_50] :
( c_Orderings_Oord__class_Oless__eq(U_50,U_51,U_53)
| ~ c_Orderings_Oord__class_Oless__eq(U_50,U_52,U_53)
| ~ c_Orderings_Oord__class_Oless__eq(U_50,U_51,U_52)
| ~ class_Orderings_Opreorder(U_50) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
! [U_51,U_50,U_52,U_53] :
( c_Orderings_Oord__class_Oless__eq(U_50,U_51,U_53)
| ~ c_Orderings_Oord__class_Oless__eq(U_50,U_52,U_53)
| ~ c_Orderings_Oord__class_Oless__eq(U_50,U_51,U_52)
| ~ class_Orderings_Opreorder(U_50) ),
inference(definitional_conversion,[status(esa)],[f_21_2]) ).
cnf(f_21_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_50,U_51,U_53)
| ~ c_Orderings_Oord__class_Oless__eq(U_50,U_52,U_53)
| ~ c_Orderings_Oord__class_Oless__eq(U_50,U_51,U_52)
| ~ class_Orderings_Opreorder(U_50) ),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_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_22_2,plain,
! [U_56,U_55,U_54] :
( U_55 = U_56
| ~ c_Orderings_Oord__class_Oless__eq(U_54,U_56,U_55)
| ~ c_Orderings_Oord__class_Oless__eq(U_54,U_55,U_56)
| ~ class_Orderings_Oorder(U_54) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_55,U_54,U_56] :
( U_55 = U_56
| ~ c_Orderings_Oord__class_Oless__eq(U_54,U_56,U_55)
| ~ c_Orderings_Oord__class_Oless__eq(U_54,U_55,U_56)
| ~ class_Orderings_Oorder(U_54) ),
inference(definitional_conversion,[status(esa)],[f_22_2]) ).
cnf(f_22_4,plain,
( U_55 = U_56
| ~ c_Orderings_Oord__class_Oless__eq(U_54,U_56,U_55)
| ~ c_Orderings_Oord__class_Oless__eq(U_54,U_55,U_56)
| ~ class_Orderings_Oorder(U_54) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_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_23_2,plain,
! [U_60,U_59,U_58,U_57] :
( c_Orderings_Oord__class_Oless__eq(U_57,U_60,U_59)
| U_58 != U_60
| ~ c_Orderings_Oord__class_Oless__eq(U_57,U_58,U_59)
| ~ class_Orderings_Oorder(U_57) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_57,U_58,U_59,U_60] :
( c_Orderings_Oord__class_Oless__eq(U_57,U_60,U_59)
| U_58 != U_60
| ~ c_Orderings_Oord__class_Oless__eq(U_57,U_58,U_59)
| ~ class_Orderings_Oorder(U_57) ),
inference(definitional_conversion,[status(esa)],[f_23_2]) ).
cnf(f_23_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_57,U_60,U_59)
| U_58 != U_60
| ~ c_Orderings_Oord__class_Oless__eq(U_57,U_58,U_59)
| ~ class_Orderings_Oorder(U_57) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_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_24_2,plain,
! [U_64,U_63,U_62,U_61] :
( c_Orderings_Oord__class_Oless__eq(U_61,U_62,U_64)
| U_63 != U_64
| ~ c_Orderings_Oord__class_Oless__eq(U_61,U_62,U_63)
| ~ class_Orderings_Oord(U_61) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
fof(f_24_3,plain,
! [U_63,U_61,U_64,U_62] :
( c_Orderings_Oord__class_Oless__eq(U_61,U_62,U_64)
| U_63 != U_64
| ~ c_Orderings_Oord__class_Oless__eq(U_61,U_62,U_63)
| ~ class_Orderings_Oord(U_61) ),
inference(definitional_conversion,[status(esa)],[f_24_2]) ).
cnf(f_24_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_61,U_62,U_64)
| U_63 != U_64
| ~ c_Orderings_Oord__class_Oless__eq(U_61,U_62,U_63)
| ~ class_Orderings_Oord(U_61) ),
inference(clausify,[status(thm)],[f_24_3]) ).
fof(f_25_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_25_2,plain,
! [U_68,U_67,U_66,U_65] :
( c_Orderings_Oord__class_Oless__eq(U_65,U_68,U_66)
| ~ c_Orderings_Oord__class_Oless__eq(U_65,U_68,U_67)
| U_66 != U_67
| ~ class_Orderings_Oorder(U_65) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
fof(f_25_3,plain,
! [U_65,U_66,U_67,U_68] :
( c_Orderings_Oord__class_Oless__eq(U_65,U_68,U_66)
| ~ c_Orderings_Oord__class_Oless__eq(U_65,U_68,U_67)
| U_66 != U_67
| ~ class_Orderings_Oorder(U_65) ),
inference(definitional_conversion,[status(esa)],[f_25_2]) ).
cnf(f_25_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_65,U_68,U_66)
| ~ c_Orderings_Oord__class_Oless__eq(U_65,U_68,U_67)
| U_66 != U_67
| ~ class_Orderings_Oorder(U_65) ),
inference(clausify,[status(thm)],[f_25_3]) ).
fof(f_26_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_26_2,plain,
! [U_72,U_71,U_70,U_69] :
( c_Orderings_Oord__class_Oless__eq(U_69,U_70,U_72)
| ~ c_Orderings_Oord__class_Oless__eq(U_69,U_71,U_72)
| U_70 != U_71
| ~ class_Orderings_Oord(U_69) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
fof(f_26_3,plain,
! [U_69,U_70,U_71,U_72] :
( c_Orderings_Oord__class_Oless__eq(U_69,U_70,U_72)
| ~ c_Orderings_Oord__class_Oless__eq(U_69,U_71,U_72)
| U_70 != U_71
| ~ class_Orderings_Oord(U_69) ),
inference(definitional_conversion,[status(esa)],[f_26_2]) ).
cnf(f_26_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_69,U_70,U_72)
| ~ c_Orderings_Oord__class_Oless__eq(U_69,U_71,U_72)
| U_70 != U_71
| ~ class_Orderings_Oord(U_69) ),
inference(clausify,[status(thm)],[f_26_3]) ).
fof(f_27_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__antisym__conv]) ).
fof(f_27_2,plain,
! [U_75,U_74,U_73] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_73,U_75,U_74)
| U_75 != U_74 )
& ( U_75 = U_74
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_75,U_74) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_74,U_75)
| ~ class_Orderings_Oorder(U_73) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
fof(f_27_3,plain,
( ! [U_74,U_73,U_75] :
( c_Orderings_Oord__class_Oless__eq(U_73,U_75,U_74)
| U_75 != U_74
| ~ sP7(U_74,U_73,U_75) )
& ! [U_74,U_73,U_75] :
( U_75 = U_74
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_75,U_74)
| ~ sP7(U_74,U_73,U_75) )
& ! [U_74,U_73,U_75] :
( sP7(U_74,U_73,U_75)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_74,U_75)
| ~ class_Orderings_Oorder(U_73) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_27_2]) ).
cnf(f_27_4,plain,
( sP7(U_74,U_73,U_75)
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_74,U_75)
| ~ class_Orderings_Oorder(U_73) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_5,plain,
( U_75 = U_74
| ~ c_Orderings_Oord__class_Oless__eq(U_73,U_75,U_74)
| ~ sP7(U_74,U_73,U_75) ),
inference(clausify,[status(thm)],[f_27_3]) ).
cnf(f_27_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_73,U_75,U_74)
| U_75 != U_74
| ~ sP7(U_74,U_73,U_75) ),
inference(clausify,[status(thm)],[f_27_3]) ).
fof(f_28_1,plain,
! [V_x_2,V_g_2,V_f_2,T_a,T_b] :
( c_Orderings_Oord__class_Oless__eq(T_b,hAPP(V_f_2,V_x_2),hAPP(V_g_2,V_x_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_28_2,plain,
! [U_80,U_79,U_78,U_77,U_76] :
( c_Orderings_Oord__class_Oless__eq(U_76,hAPP(U_78,U_80),hAPP(U_79,U_80))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_77,U_76),U_78,U_79)
| ~ class_Orderings_Oord(U_76) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
fof(f_28_3,plain,
! [U_76,U_79,U_78,U_77,U_80] :
( c_Orderings_Oord__class_Oless__eq(U_76,hAPP(U_78,U_80),hAPP(U_79,U_80))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_77,U_76),U_78,U_79)
| ~ class_Orderings_Oord(U_76) ),
inference(definitional_conversion,[status(esa)],[f_28_2]) ).
cnf(f_28_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_76,hAPP(U_78,U_80),hAPP(U_79,U_80))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_77,U_76),U_78,U_79)
| ~ class_Orderings_Oord(U_76) ),
inference(clausify,[status(thm)],[f_28_3]) ).
fof(f_29_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_29_2,plain,
! [U_83,U_82,U_81] :
( c_Orderings_Oord__class_Oless__eq(U_81,U_82,U_83)
| U_82 != U_83
| ~ class_Orderings_Opreorder(U_81) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
fof(f_29_3,plain,
! [U_83,U_82,U_81] :
( c_Orderings_Oord__class_Oless__eq(U_81,U_82,U_83)
| U_82 != U_83
| ~ class_Orderings_Opreorder(U_81) ),
inference(definitional_conversion,[status(esa)],[f_29_2]) ).
cnf(f_29_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_81,U_82,U_83)
| U_82 != U_83
| ~ class_Orderings_Opreorder(U_81) ),
inference(clausify,[status(thm)],[f_29_3]) ).
fof(f_30_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| V_x_2 != V_y_2 ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__eq__iff]) ).
fof(f_30_2,plain,
! [U_86,U_85,U_84] :
( ( ( U_85 = U_86
| ~ c_Orderings_Oord__class_Oless__eq(U_84,U_86,U_85)
| ~ c_Orderings_Oord__class_Oless__eq(U_84,U_85,U_86) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_84,U_86,U_85)
& c_Orderings_Oord__class_Oless__eq(U_84,U_85,U_86) )
| U_85 != U_86 ) )
| ~ class_Orderings_Oorder(U_84) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
fof(f_30_3,plain,
( ! [U_85,U_84,U_86] :
( c_Orderings_Oord__class_Oless__eq(U_84,U_86,U_85)
| ~ sP8(U_85,U_84,U_86) )
& ! [U_85,U_84,U_86] :
( c_Orderings_Oord__class_Oless__eq(U_84,U_85,U_86)
| ~ sP8(U_85,U_84,U_86) )
& ! [U_85,U_84,U_86] :
( U_85 = U_86
| ~ c_Orderings_Oord__class_Oless__eq(U_84,U_86,U_85)
| ~ c_Orderings_Oord__class_Oless__eq(U_84,U_85,U_86)
| ~ sP9(U_85,U_84,U_86) )
& ! [U_85,U_84,U_86] :
( sP8(U_85,U_84,U_86)
| U_85 != U_86
| ~ sP9(U_85,U_84,U_86) )
& ! [U_85,U_84,U_86] :
( sP9(U_85,U_84,U_86)
| ~ class_Orderings_Oorder(U_84) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8,sP9])],[f_30_2]) ).
cnf(f_30_4,plain,
( sP9(U_85,U_84,U_86)
| ~ class_Orderings_Oorder(U_84) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_5,plain,
( sP8(U_85,U_84,U_86)
| U_85 != U_86
| ~ sP9(U_85,U_84,U_86) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_6,plain,
( U_85 = U_86
| ~ c_Orderings_Oord__class_Oless__eq(U_84,U_86,U_85)
| ~ c_Orderings_Oord__class_Oless__eq(U_84,U_85,U_86)
| ~ sP9(U_85,U_84,U_86) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_84,U_85,U_86)
| ~ sP8(U_85,U_84,U_86) ),
inference(clausify,[status(thm)],[f_30_3]) ).
cnf(f_30_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_84,U_86,U_85)
| ~ sP8(U_85,U_84,U_86) ),
inference(clausify,[status(thm)],[f_30_3]) ).
fof(f_31_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_31_2,plain,
! [U_89,U_88,U_87] :
( c_Orderings_Oord__class_Oless__eq(U_87,U_89,U_88)
| c_Orderings_Oord__class_Oless__eq(U_87,U_88,U_89)
| ~ class_Orderings_Olinorder(U_87) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_88,U_87,U_89] :
( c_Orderings_Oord__class_Oless__eq(U_87,U_89,U_88)
| c_Orderings_Oord__class_Oless__eq(U_87,U_88,U_89)
| ~ class_Orderings_Olinorder(U_87) ),
inference(definitional_conversion,[status(esa)],[f_31_2]) ).
cnf(f_31_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_87,U_89,U_88)
| c_Orderings_Oord__class_Oless__eq(U_87,U_88,U_89)
| ~ class_Orderings_Olinorder(U_87) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_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_32_2,plain,
! [U_95,U_94,U_93,U_92] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_93,U_92),U_94,U_95)
| ? [U_91] : ~ c_Orderings_Oord__class_Oless__eq(U_92,hAPP(U_94,U_91),hAPP(U_95,U_91)) )
& ( ! [U_90] : c_Orderings_Oord__class_Oless__eq(U_92,hAPP(U_94,U_90),hAPP(U_95,U_90))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_93,U_92),U_94,U_95) ) )
| ~ class_Orderings_Oord(U_92) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
! [U_95,U_94,U_93,U_92] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_fun(U_93,U_92),U_94,U_95)
| ~ c_Orderings_Oord__class_Oless__eq(U_92,hAPP(U_94,sK4(U_95,U_94,U_93,U_92)),hAPP(U_95,sK4(U_95,U_94,U_93,U_92))) )
& ( ! [U_90] : c_Orderings_Oord__class_Oless__eq(U_92,hAPP(U_94,U_90),hAPP(U_95,U_90))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_93,U_92),U_94,U_95) ) )
| ~ class_Orderings_Oord(U_92) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_91,sK4(U_95,U_94,U_93,U_92))],[f_32_2]) ).
fof(f_32_4,plain,
( ! [U_90,U_92,U_93,U_95,U_94] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_93,U_92),U_94,U_95)
| ~ c_Orderings_Oord__class_Oless__eq(U_92,hAPP(U_94,sK4(U_95,U_94,U_93,U_92)),hAPP(U_95,sK4(U_95,U_94,U_93,U_92)))
| ~ sP10(U_90,U_92,U_93,U_95,U_94) )
& ! [U_90,U_92,U_93,U_95,U_94] :
( c_Orderings_Oord__class_Oless__eq(U_92,hAPP(U_94,U_90),hAPP(U_95,U_90))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_93,U_92),U_94,U_95)
| ~ sP10(U_90,U_92,U_93,U_95,U_94) )
& ! [U_90,U_92,U_93,U_95,U_94] :
( sP10(U_90,U_92,U_93,U_95,U_94)
| ~ class_Orderings_Oord(U_92) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP10])],[f_32_3]) ).
cnf(f_32_5,plain,
( sP10(U_90,U_92,U_93,U_95,U_94)
| ~ class_Orderings_Oord(U_92) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_92,hAPP(U_94,U_90),hAPP(U_95,U_90))
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_93,U_92),U_94,U_95)
| ~ sP10(U_90,U_92,U_93,U_95,U_94) ),
inference(clausify,[status(thm)],[f_32_4]) ).
cnf(f_32_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_93,U_92),U_94,U_95)
| ~ c_Orderings_Oord__class_Oless__eq(U_92,hAPP(U_94,sK4(U_95,U_94,U_93,U_92)),hAPP(U_95,sK4(U_95,U_94,U_93,U_92)))
| ~ sP10(U_90,U_92,U_93,U_95,U_94) ),
inference(clausify,[status(thm)],[f_32_4]) ).
fof(f_33_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_33_2,plain,
! [U_98,U_97,U_96] :
( c_Orderings_Oord__class_Oless(U_96,U_98,U_97)
| U_97 = U_98
| c_Orderings_Oord__class_Oless(U_96,U_97,U_98)
| ~ class_Orderings_Olinorder(U_96) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
! [U_96,U_97,U_98] :
( c_Orderings_Oord__class_Oless(U_96,U_98,U_97)
| U_97 = U_98
| c_Orderings_Oord__class_Oless(U_96,U_97,U_98)
| ~ class_Orderings_Olinorder(U_96) ),
inference(definitional_conversion,[status(esa)],[f_33_2]) ).
cnf(f_33_4,plain,
( c_Orderings_Oord__class_Oless(U_96,U_98,U_97)
| U_97 = U_98
| c_Orderings_Oord__class_Oless(U_96,U_97,U_98)
| ~ class_Orderings_Olinorder(U_96) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_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_34_2,plain,
! [U_101,U_100,U_99] :
( ~ c_Orderings_Oord__class_Oless(U_99,U_101,U_100)
| ~ c_Orderings_Oord__class_Oless(U_99,U_100,U_101)
| ~ class_Orderings_Opreorder(U_99) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
! [U_101,U_100,U_99] :
( ~ c_Orderings_Oord__class_Oless(U_99,U_101,U_100)
| ~ c_Orderings_Oord__class_Oless(U_99,U_100,U_101)
| ~ class_Orderings_Opreorder(U_99) ),
inference(definitional_conversion,[status(esa)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_99,U_101,U_100)
| ~ c_Orderings_Oord__class_Oless(U_99,U_100,U_101)
| ~ class_Orderings_Opreorder(U_99) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_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_35_2,plain,
! [U_105,U_104,U_103,U_102] :
( c_Orderings_Oord__class_Oless(U_102,U_105,U_104)
| ~ c_Orderings_Oord__class_Oless(U_102,U_105,U_103)
| ~ c_Orderings_Oord__class_Oless(U_102,U_103,U_104)
| ~ class_Orderings_Oorder(U_102) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
! [U_103,U_104,U_102,U_105] :
( c_Orderings_Oord__class_Oless(U_102,U_105,U_104)
| ~ c_Orderings_Oord__class_Oless(U_102,U_105,U_103)
| ~ c_Orderings_Oord__class_Oless(U_102,U_103,U_104)
| ~ class_Orderings_Oorder(U_102) ),
inference(definitional_conversion,[status(esa)],[f_35_2]) ).
cnf(f_35_4,plain,
( c_Orderings_Oord__class_Oless(U_102,U_105,U_104)
| ~ c_Orderings_Oord__class_Oless(U_102,U_105,U_103)
| ~ c_Orderings_Oord__class_Oless(U_102,U_103,U_104)
| ~ class_Orderings_Oorder(U_102) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_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_36_2,plain,
! [U_109,U_108,U_107,U_106] :
( c_Orderings_Oord__class_Oless(U_106,U_107,U_109)
| ~ c_Orderings_Oord__class_Oless(U_106,U_108,U_109)
| ~ c_Orderings_Oord__class_Oless(U_106,U_107,U_108)
| ~ class_Orderings_Opreorder(U_106) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_107,U_106,U_108,U_109] :
( c_Orderings_Oord__class_Oless(U_106,U_107,U_109)
| ~ c_Orderings_Oord__class_Oless(U_106,U_108,U_109)
| ~ c_Orderings_Oord__class_Oless(U_106,U_107,U_108)
| ~ class_Orderings_Opreorder(U_106) ),
inference(definitional_conversion,[status(esa)],[f_36_2]) ).
cnf(f_36_4,plain,
( c_Orderings_Oord__class_Oless(U_106,U_107,U_109)
| ~ c_Orderings_Oord__class_Oless(U_106,U_108,U_109)
| ~ c_Orderings_Oord__class_Oless(U_106,U_107,U_108)
| ~ class_Orderings_Opreorder(U_106) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_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_37_2,plain,
! [U_113,U_112,U_111,U_110] :
( c_Orderings_Oord__class_Oless(U_110,U_113,U_112)
| U_111 != U_113
| ~ c_Orderings_Oord__class_Oless(U_110,U_111,U_112)
| ~ class_Orderings_Oorder(U_110) ),
inference(variable_rename,[status(thm)],[f_37_1]) ).
fof(f_37_3,plain,
! [U_111,U_110,U_112,U_113] :
( c_Orderings_Oord__class_Oless(U_110,U_113,U_112)
| U_111 != U_113
| ~ c_Orderings_Oord__class_Oless(U_110,U_111,U_112)
| ~ class_Orderings_Oorder(U_110) ),
inference(definitional_conversion,[status(esa)],[f_37_2]) ).
cnf(f_37_4,plain,
( c_Orderings_Oord__class_Oless(U_110,U_113,U_112)
| U_111 != U_113
| ~ c_Orderings_Oord__class_Oless(U_110,U_111,U_112)
| ~ class_Orderings_Oorder(U_110) ),
inference(clausify,[status(thm)],[f_37_3]) ).
fof(f_38_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_38_2,plain,
! [U_117,U_116,U_115,U_114] :
( c_Orderings_Oord__class_Oless(U_114,U_115,U_117)
| U_116 != U_117
| ~ c_Orderings_Oord__class_Oless(U_114,U_115,U_116)
| ~ class_Orderings_Oord(U_114) ),
inference(variable_rename,[status(thm)],[f_38_1]) ).
fof(f_38_3,plain,
! [U_117,U_116,U_114,U_115] :
( c_Orderings_Oord__class_Oless(U_114,U_115,U_117)
| U_116 != U_117
| ~ c_Orderings_Oord__class_Oless(U_114,U_115,U_116)
| ~ class_Orderings_Oord(U_114) ),
inference(definitional_conversion,[status(esa)],[f_38_2]) ).
cnf(f_38_4,plain,
( c_Orderings_Oord__class_Oless(U_114,U_115,U_117)
| U_116 != U_117
| ~ c_Orderings_Oord__class_Oless(U_114,U_115,U_116)
| ~ class_Orderings_Oord(U_114) ),
inference(clausify,[status(thm)],[f_38_3]) ).
fof(f_39_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_39_2,plain,
! [U_121,U_120,U_119,U_118] :
( c_Orderings_Oord__class_Oless(U_118,U_121,U_119)
| ~ c_Orderings_Oord__class_Oless(U_118,U_121,U_120)
| U_119 != U_120
| ~ class_Orderings_Oorder(U_118) ),
inference(variable_rename,[status(thm)],[f_39_1]) ).
fof(f_39_3,plain,
! [U_118,U_119,U_120,U_121] :
( c_Orderings_Oord__class_Oless(U_118,U_121,U_119)
| ~ c_Orderings_Oord__class_Oless(U_118,U_121,U_120)
| U_119 != U_120
| ~ class_Orderings_Oorder(U_118) ),
inference(definitional_conversion,[status(esa)],[f_39_2]) ).
cnf(f_39_4,plain,
( c_Orderings_Oord__class_Oless(U_118,U_121,U_119)
| ~ c_Orderings_Oord__class_Oless(U_118,U_121,U_120)
| U_119 != U_120
| ~ class_Orderings_Oorder(U_118) ),
inference(clausify,[status(thm)],[f_39_3]) ).
fof(f_40_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_40_2,plain,
! [U_125,U_124,U_123,U_122] :
( c_Orderings_Oord__class_Oless(U_122,U_123,U_125)
| ~ c_Orderings_Oord__class_Oless(U_122,U_124,U_125)
| U_123 != U_124
| ~ class_Orderings_Oord(U_122) ),
inference(variable_rename,[status(thm)],[f_40_1]) ).
fof(f_40_3,plain,
! [U_125,U_122,U_123,U_124] :
( c_Orderings_Oord__class_Oless(U_122,U_123,U_125)
| ~ c_Orderings_Oord__class_Oless(U_122,U_124,U_125)
| U_123 != U_124
| ~ class_Orderings_Oord(U_122) ),
inference(definitional_conversion,[status(esa)],[f_40_2]) ).
cnf(f_40_4,plain,
( c_Orderings_Oord__class_Oless(U_122,U_123,U_125)
| ~ c_Orderings_Oord__class_Oless(U_122,U_124,U_125)
| U_123 != U_124
| ~ class_Orderings_Oord(U_122) ),
inference(clausify,[status(thm)],[f_40_3]) ).
fof(f_41_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_41_2,plain,
! [U_128,U_127,U_126] :
( ~ c_Orderings_Oord__class_Oless(U_126,U_128,U_127)
| ~ c_Orderings_Oord__class_Oless(U_126,U_127,U_128)
| ~ class_Orderings_Oorder(U_126) ),
inference(variable_rename,[status(thm)],[f_41_1]) ).
fof(f_41_3,plain,
! [U_128,U_126,U_127] :
( ~ c_Orderings_Oord__class_Oless(U_126,U_128,U_127)
| ~ c_Orderings_Oord__class_Oless(U_126,U_127,U_128)
| ~ class_Orderings_Oorder(U_126) ),
inference(definitional_conversion,[status(esa)],[f_41_2]) ).
cnf(f_41_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_126,U_128,U_127)
| ~ c_Orderings_Oord__class_Oless(U_126,U_127,U_128)
| ~ class_Orderings_Oorder(U_126) ),
inference(clausify,[status(thm)],[f_41_3]) ).
fof(f_42_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_42_2,plain,
! [U_131,U_130,U_129] :
( ~ c_Orderings_Oord__class_Oless(U_129,U_131,U_130)
| ~ c_Orderings_Oord__class_Oless(U_129,U_130,U_131)
| ~ class_Orderings_Opreorder(U_129) ),
inference(variable_rename,[status(thm)],[f_42_1]) ).
fof(f_42_3,plain,
! [U_131,U_129,U_130] :
( ~ c_Orderings_Oord__class_Oless(U_129,U_131,U_130)
| ~ c_Orderings_Oord__class_Oless(U_129,U_130,U_131)
| ~ class_Orderings_Opreorder(U_129) ),
inference(definitional_conversion,[status(esa)],[f_42_2]) ).
cnf(f_42_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_129,U_131,U_130)
| ~ c_Orderings_Oord__class_Oless(U_129,U_130,U_131)
| ~ class_Orderings_Opreorder(U_129) ),
inference(clausify,[status(thm)],[f_42_3]) ).
fof(f_43_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_43_2,plain,
! [U_134,U_133,U_132] :
( U_134 != U_133
| ~ c_Orderings_Oord__class_Oless(U_132,U_133,U_134)
| ~ class_Orderings_Oorder(U_132) ),
inference(variable_rename,[status(thm)],[f_43_1]) ).
fof(f_43_3,plain,
! [U_132,U_134,U_133] :
( U_134 != U_133
| ~ c_Orderings_Oord__class_Oless(U_132,U_133,U_134)
| ~ class_Orderings_Oorder(U_132) ),
inference(definitional_conversion,[status(esa)],[f_43_2]) ).
cnf(f_43_4,plain,
( U_134 != U_133
| ~ c_Orderings_Oord__class_Oless(U_132,U_133,U_134)
| ~ class_Orderings_Oorder(U_132) ),
inference(clausify,[status(thm)],[f_43_3]) ).
fof(f_44_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_44_2,plain,
! [U_137,U_136,U_135] :
( U_136 != U_137
| ~ c_Orderings_Oord__class_Oless(U_135,U_136,U_137)
| ~ class_Orderings_Oorder(U_135) ),
inference(variable_rename,[status(thm)],[f_44_1]) ).
fof(f_44_3,plain,
! [U_136,U_137,U_135] :
( U_136 != U_137
| ~ c_Orderings_Oord__class_Oless(U_135,U_136,U_137)
| ~ class_Orderings_Oorder(U_135) ),
inference(definitional_conversion,[status(esa)],[f_44_2]) ).
cnf(f_44_4,plain,
( U_136 != U_137
| ~ c_Orderings_Oord__class_Oless(U_135,U_136,U_137)
| ~ class_Orderings_Oorder(U_135) ),
inference(clausify,[status(thm)],[f_44_3]) ).
fof(f_45_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_45_2,plain,
! [U_140,U_139,U_138] :
( ~ c_Orderings_Oord__class_Oless(U_138,U_140,U_139)
| ~ c_Orderings_Oord__class_Oless(U_138,U_139,U_140)
| ~ class_Orderings_Opreorder(U_138) ),
inference(variable_rename,[status(thm)],[f_45_1]) ).
fof(f_45_3,plain,
! [U_140,U_138,U_139] :
( ~ c_Orderings_Oord__class_Oless(U_138,U_140,U_139)
| ~ c_Orderings_Oord__class_Oless(U_138,U_139,U_140)
| ~ class_Orderings_Opreorder(U_138) ),
inference(definitional_conversion,[status(esa)],[f_45_2]) ).
cnf(f_45_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_138,U_140,U_139)
| ~ c_Orderings_Oord__class_Oless(U_138,U_139,U_140)
| ~ class_Orderings_Opreorder(U_138) ),
inference(clausify,[status(thm)],[f_45_3]) ).
fof(f_46_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_46_2,plain,
! [U_143,U_142,U_141] :
( ~ c_Orderings_Oord__class_Oless(U_141,U_143,U_142)
| ~ c_Orderings_Oord__class_Oless(U_141,U_142,U_143)
| ~ class_Orderings_Opreorder(U_141) ),
inference(variable_rename,[status(thm)],[f_46_1]) ).
fof(f_46_3,plain,
! [U_143,U_141,U_142] :
( ~ c_Orderings_Oord__class_Oless(U_141,U_143,U_142)
| ~ c_Orderings_Oord__class_Oless(U_141,U_142,U_143)
| ~ class_Orderings_Opreorder(U_141) ),
inference(definitional_conversion,[status(esa)],[f_46_2]) ).
cnf(f_46_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_141,U_143,U_142)
| ~ c_Orderings_Oord__class_Oless(U_141,U_142,U_143)
| ~ class_Orderings_Opreorder(U_141) ),
inference(clausify,[status(thm)],[f_46_3]) ).
fof(f_47_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_47_2,plain,
! [U_146,U_145,U_144] :
( U_145 != U_146
| ~ c_Orderings_Oord__class_Oless(U_144,U_145,U_146)
| ~ class_Orderings_Oorder(U_144) ),
inference(variable_rename,[status(thm)],[f_47_1]) ).
fof(f_47_3,plain,
! [U_146,U_144,U_145] :
( U_145 != U_146
| ~ c_Orderings_Oord__class_Oless(U_144,U_145,U_146)
| ~ class_Orderings_Oorder(U_144) ),
inference(definitional_conversion,[status(esa)],[f_47_2]) ).
cnf(f_47_4,plain,
( U_145 != U_146
| ~ c_Orderings_Oord__class_Oless(U_144,U_145,U_146)
| ~ class_Orderings_Oorder(U_144) ),
inference(clausify,[status(thm)],[f_47_3]) ).
fof(f_48_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_48_2,plain,
! [U_149,U_148,U_147] :
( c_Orderings_Oord__class_Oless(U_147,U_149,U_148)
| c_Orderings_Oord__class_Oless(U_147,U_148,U_149)
| U_148 = U_149
| ~ class_Orderings_Olinorder(U_147) ),
inference(variable_rename,[status(thm)],[f_48_1]) ).
fof(f_48_3,plain,
! [U_148,U_149,U_147] :
( c_Orderings_Oord__class_Oless(U_147,U_149,U_148)
| c_Orderings_Oord__class_Oless(U_147,U_148,U_149)
| U_148 = U_149
| ~ class_Orderings_Olinorder(U_147) ),
inference(definitional_conversion,[status(esa)],[f_48_2]) ).
cnf(f_48_4,plain,
( c_Orderings_Oord__class_Oless(U_147,U_149,U_148)
| c_Orderings_Oord__class_Oless(U_147,U_148,U_149)
| U_148 = U_149
| ~ class_Orderings_Olinorder(U_147) ),
inference(clausify,[status(thm)],[f_48_3]) ).
fof(f_49_1,plain,
! [V_x_2,V_y_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv3]) ).
fof(f_49_2,plain,
! [U_152,U_151,U_150] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_150,U_152,U_151)
| U_152 != U_151 )
& ( U_152 = U_151
| c_Orderings_Oord__class_Oless(U_150,U_152,U_151) ) )
| c_Orderings_Oord__class_Oless(U_150,U_151,U_152)
| ~ class_Orderings_Olinorder(U_150) ),
inference(variable_rename,[status(thm)],[f_49_1]) ).
fof(f_49_3,plain,
( ! [U_152,U_151,U_150] :
( ~ c_Orderings_Oord__class_Oless(U_150,U_152,U_151)
| U_152 != U_151
| ~ sP11(U_152,U_151,U_150) )
& ! [U_152,U_151,U_150] :
( U_152 = U_151
| c_Orderings_Oord__class_Oless(U_150,U_152,U_151)
| ~ sP11(U_152,U_151,U_150) )
& ! [U_152,U_151,U_150] :
( sP11(U_152,U_151,U_150)
| c_Orderings_Oord__class_Oless(U_150,U_151,U_152)
| ~ class_Orderings_Olinorder(U_150) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP11])],[f_49_2]) ).
cnf(f_49_4,plain,
( sP11(U_152,U_151,U_150)
| c_Orderings_Oord__class_Oless(U_150,U_151,U_152)
| ~ class_Orderings_Olinorder(U_150) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_5,plain,
( U_152 = U_151
| c_Orderings_Oord__class_Oless(U_150,U_152,U_151)
| ~ sP11(U_152,U_151,U_150) ),
inference(clausify,[status(thm)],[f_49_3]) ).
cnf(f_49_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_150,U_152,U_151)
| U_152 != U_151
| ~ sP11(U_152,U_151,U_150) ),
inference(clausify,[status(thm)],[f_49_3]) ).
fof(f_50_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_50_2,plain,
! [U_155,U_154,U_153] :
( c_Orderings_Oord__class_Oless(U_153,U_155,U_154)
| U_154 = U_155
| c_Orderings_Oord__class_Oless(U_153,U_154,U_155)
| ~ class_Orderings_Olinorder(U_153) ),
inference(variable_rename,[status(thm)],[f_50_1]) ).
fof(f_50_3,plain,
! [U_154,U_155,U_153] :
( c_Orderings_Oord__class_Oless(U_153,U_155,U_154)
| U_154 = U_155
| c_Orderings_Oord__class_Oless(U_153,U_154,U_155)
| ~ class_Orderings_Olinorder(U_153) ),
inference(definitional_conversion,[status(esa)],[f_50_2]) ).
cnf(f_50_4,plain,
( c_Orderings_Oord__class_Oless(U_153,U_155,U_154)
| U_154 = U_155
| c_Orderings_Oord__class_Oless(U_153,U_154,U_155)
| ~ class_Orderings_Olinorder(U_153) ),
inference(clausify,[status(thm)],[f_50_3]) ).
fof(f_51_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__less__iff__gr__or__eq]) ).
fof(f_51_2,plain,
! [U_158,U_157,U_156] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_156,U_157,U_158)
| ( U_157 != U_158
& ~ c_Orderings_Oord__class_Oless(U_156,U_158,U_157) ) )
& ( U_157 = U_158
| c_Orderings_Oord__class_Oless(U_156,U_158,U_157)
| c_Orderings_Oord__class_Oless(U_156,U_157,U_158) ) )
| ~ class_Orderings_Olinorder(U_156) ),
inference(variable_rename,[status(thm)],[f_51_1]) ).
fof(f_51_3,plain,
( ! [U_157,U_158,U_156] :
( U_157 != U_158
| ~ sP12(U_157,U_158,U_156) )
& ! [U_157,U_158,U_156] :
( ~ c_Orderings_Oord__class_Oless(U_156,U_158,U_157)
| ~ sP12(U_157,U_158,U_156) )
& ! [U_157,U_158,U_156] :
( ~ c_Orderings_Oord__class_Oless(U_156,U_157,U_158)
| sP12(U_157,U_158,U_156)
| ~ sP13(U_157,U_158,U_156) )
& ! [U_157,U_158,U_156] :
( U_157 = U_158
| c_Orderings_Oord__class_Oless(U_156,U_158,U_157)
| c_Orderings_Oord__class_Oless(U_156,U_157,U_158)
| ~ sP13(U_157,U_158,U_156) )
& ! [U_157,U_158,U_156] :
( sP13(U_157,U_158,U_156)
| ~ class_Orderings_Olinorder(U_156) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12,sP13])],[f_51_2]) ).
cnf(f_51_4,plain,
( sP13(U_157,U_158,U_156)
| ~ class_Orderings_Olinorder(U_156) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_5,plain,
( U_157 = U_158
| c_Orderings_Oord__class_Oless(U_156,U_158,U_157)
| c_Orderings_Oord__class_Oless(U_156,U_157,U_158)
| ~ sP13(U_157,U_158,U_156) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_156,U_157,U_158)
| sP12(U_157,U_158,U_156)
| ~ sP13(U_157,U_158,U_156) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_156,U_158,U_157)
| ~ sP12(U_157,U_158,U_156) ),
inference(clausify,[status(thm)],[f_51_3]) ).
cnf(f_51_8,plain,
( U_157 != U_158
| ~ sP12(U_157,U_158,U_156) ),
inference(clausify,[status(thm)],[f_51_3]) ).
fof(f_52_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( V_x_2 != V_y_2
| ( ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2 ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__neq__iff]) ).
fof(f_52_2,plain,
! [U_161,U_160,U_159] :
( ( ( U_160 != U_161
| ( ~ c_Orderings_Oord__class_Oless(U_159,U_161,U_160)
& ~ c_Orderings_Oord__class_Oless(U_159,U_160,U_161) ) )
& ( c_Orderings_Oord__class_Oless(U_159,U_161,U_160)
| c_Orderings_Oord__class_Oless(U_159,U_160,U_161)
| U_160 = U_161 ) )
| ~ class_Orderings_Olinorder(U_159) ),
inference(variable_rename,[status(thm)],[f_52_1]) ).
fof(f_52_3,plain,
( ! [U_159,U_160,U_161] :
( ~ c_Orderings_Oord__class_Oless(U_159,U_161,U_160)
| ~ sP14(U_159,U_160,U_161) )
& ! [U_159,U_160,U_161] :
( ~ c_Orderings_Oord__class_Oless(U_159,U_160,U_161)
| ~ sP14(U_159,U_160,U_161) )
& ! [U_159,U_160,U_161] :
( U_160 != U_161
| sP14(U_159,U_160,U_161)
| ~ sP15(U_159,U_160,U_161) )
& ! [U_159,U_160,U_161] :
( c_Orderings_Oord__class_Oless(U_159,U_161,U_160)
| c_Orderings_Oord__class_Oless(U_159,U_160,U_161)
| U_160 = U_161
| ~ sP15(U_159,U_160,U_161) )
& ! [U_159,U_160,U_161] :
( sP15(U_159,U_160,U_161)
| ~ class_Orderings_Olinorder(U_159) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14,sP15])],[f_52_2]) ).
cnf(f_52_4,plain,
( sP15(U_159,U_160,U_161)
| ~ class_Orderings_Olinorder(U_159) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_5,plain,
( c_Orderings_Oord__class_Oless(U_159,U_161,U_160)
| c_Orderings_Oord__class_Oless(U_159,U_160,U_161)
| U_160 = U_161
| ~ sP15(U_159,U_160,U_161) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_6,plain,
( U_160 != U_161
| sP14(U_159,U_160,U_161)
| ~ sP15(U_159,U_160,U_161) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_159,U_160,U_161)
| ~ sP14(U_159,U_160,U_161) ),
inference(clausify,[status(thm)],[f_52_3]) ).
cnf(f_52_8,plain,
( ~ c_Orderings_Oord__class_Oless(U_159,U_161,U_160)
| ~ sP14(U_159,U_160,U_161) ),
inference(clausify,[status(thm)],[f_52_3]) ).
fof(f_53_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_53_2,plain,
! [U_163,U_162] :
( ~ c_Orderings_Oord__class_Oless(U_162,U_163,U_163)
| ~ class_Orderings_Opreorder(U_162) ),
inference(variable_rename,[status(thm)],[f_53_1]) ).
fof(f_53_3,plain,
! [U_163,U_162] :
( ~ c_Orderings_Oord__class_Oless(U_162,U_163,U_163)
| ~ class_Orderings_Opreorder(U_162) ),
inference(definitional_conversion,[status(esa)],[f_53_2]) ).
cnf(f_53_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_162,U_163,U_163)
| ~ class_Orderings_Opreorder(U_162) ),
inference(clausify,[status(thm)],[f_53_3]) ).
fof(f_54_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_54_2,plain,
! [U_165,U_164] :
( U_164 = U_165
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_165,U_164)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_164,U_165) ),
inference(variable_rename,[status(thm)],[f_54_1]) ).
fof(f_54_3,plain,
! [U_165,U_164] :
( U_164 = U_165
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_165,U_164)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_164,U_165) ),
inference(definitional_conversion,[status(esa)],[f_54_2]) ).
cnf(f_54_4,plain,
( U_164 = U_165
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_165,U_164)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_164,U_165) ),
inference(clausify,[status(thm)],[f_54_3]) ).
fof(f_55_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_55_2,plain,
! [U_168,U_167,U_166] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_166,U_168)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_167,U_168)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_166,U_167) ),
inference(variable_rename,[status(thm)],[f_55_1]) ).
fof(f_55_3,plain,
! [U_168,U_167,U_166] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_166,U_168)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_167,U_168)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_166,U_167) ),
inference(definitional_conversion,[status(esa)],[f_55_2]) ).
cnf(f_55_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_166,U_168)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_167,U_168)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_166,U_167) ),
inference(clausify,[status(thm)],[f_55_3]) ).
fof(f_56_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_56_2,plain,
! [U_170,U_169] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_170,U_169)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_169,U_170) ),
inference(variable_rename,[status(thm)],[f_56_1]) ).
fof(f_56_3,plain,
! [U_170,U_169] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_170,U_169)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_169,U_170) ),
inference(definitional_conversion,[status(esa)],[f_56_2]) ).
cnf(f_56_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_170,U_169)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_169,U_170) ),
inference(clausify,[status(thm)],[f_56_3]) ).
fof(f_57_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_57_2,plain,
! [U_171] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_171,U_171),
inference(variable_rename,[status(thm)],[f_57_1]) ).
fof(f_57_3,plain,
! [U_171] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_171,U_171),
inference(definitional_conversion,[status(esa)],[f_57_2]) ).
cnf(f_57_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_171,U_171),
inference(clausify,[status(thm)],[f_57_3]) ).
fof(f_58_1,plain,
! [V_q_2,V_b_2,V_pa_2,V_a_2,T_a] :
( ( ( c_Polynomial_OpCons(T_a,V_a_2,V_pa_2) = c_Polynomial_OpCons(T_a,V_b_2,V_q_2)
| V_pa_2 != V_q_2
| V_a_2 != V_b_2 )
& ( ( V_pa_2 = V_q_2
& V_a_2 = V_b_2 )
| c_Polynomial_OpCons(T_a,V_a_2,V_pa_2) != c_Polynomial_OpCons(T_a,V_b_2,V_q_2) ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pCons__eq__iff]) ).
fof(f_58_2,plain,
! [U_176,U_175,U_174,U_173,U_172] :
( ( ( c_Polynomial_OpCons(U_172,U_173,U_174) = c_Polynomial_OpCons(U_172,U_175,U_176)
| U_174 != U_176
| U_173 != U_175 )
& ( ( U_174 = U_176
& U_173 = U_175 )
| c_Polynomial_OpCons(U_172,U_173,U_174) != c_Polynomial_OpCons(U_172,U_175,U_176) ) )
| ~ class_Groups_Ozero(U_172) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ! [U_174,U_175,U_176,U_173] :
( U_174 = U_176
| ~ sP16(U_174,U_175,U_176,U_173) )
& ! [U_174,U_175,U_176,U_173] :
( U_173 = U_175
| ~ sP16(U_174,U_175,U_176,U_173) )
& ! [U_174,U_175,U_176,U_172,U_173] :
( c_Polynomial_OpCons(U_172,U_173,U_174) = c_Polynomial_OpCons(U_172,U_175,U_176)
| U_174 != U_176
| U_173 != U_175
| ~ sP17(U_174,U_175,U_176,U_172,U_173) )
& ! [U_174,U_175,U_176,U_172,U_173] :
( sP16(U_174,U_175,U_176,U_173)
| c_Polynomial_OpCons(U_172,U_173,U_174) != c_Polynomial_OpCons(U_172,U_175,U_176)
| ~ sP17(U_174,U_175,U_176,U_172,U_173) )
& ! [U_174,U_175,U_176,U_172,U_173] :
( sP17(U_174,U_175,U_176,U_172,U_173)
| ~ class_Groups_Ozero(U_172) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16,sP17])],[f_58_2]) ).
cnf(f_58_4,plain,
( sP17(U_174,U_175,U_176,U_172,U_173)
| ~ class_Groups_Ozero(U_172) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_5,plain,
( sP16(U_174,U_175,U_176,U_173)
| c_Polynomial_OpCons(U_172,U_173,U_174) != c_Polynomial_OpCons(U_172,U_175,U_176)
| ~ sP17(U_174,U_175,U_176,U_172,U_173) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_6,plain,
( c_Polynomial_OpCons(U_172,U_173,U_174) = c_Polynomial_OpCons(U_172,U_175,U_176)
| U_174 != U_176
| U_173 != U_175
| ~ sP17(U_174,U_175,U_176,U_172,U_173) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_7,plain,
( U_173 = U_175
| ~ sP16(U_174,U_175,U_176,U_173) ),
inference(clausify,[status(thm)],[f_58_3]) ).
cnf(f_58_8,plain,
( U_174 = U_176
| ~ sP16(U_174,U_175,U_176,U_173) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_59_1,plain,
! [V_q_2,V_pa_2,T_a] :
( ( ( c_Polynomial_Opoly(T_a,V_pa_2) = c_Polynomial_Opoly(T_a,V_q_2)
| V_pa_2 != V_q_2 )
& ( V_pa_2 = V_q_2
| c_Polynomial_Opoly(T_a,V_pa_2) != c_Polynomial_Opoly(T_a,V_q_2) ) )
| ~ class_Rings_Oidom(T_a)
| ~ class_Int_Oring__char__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__eq__iff]) ).
fof(f_59_2,plain,
! [U_179,U_178,U_177] :
( ( ( c_Polynomial_Opoly(U_177,U_178) = c_Polynomial_Opoly(U_177,U_179)
| U_178 != U_179 )
& ( U_178 = U_179
| c_Polynomial_Opoly(U_177,U_178) != c_Polynomial_Opoly(U_177,U_179) ) )
| ~ class_Rings_Oidom(U_177)
| ~ class_Int_Oring__char__0(U_177) ),
inference(variable_rename,[status(thm)],[f_59_1]) ).
fof(f_59_3,plain,
( ! [U_179,U_177,U_178] :
( c_Polynomial_Opoly(U_177,U_178) = c_Polynomial_Opoly(U_177,U_179)
| U_178 != U_179
| ~ sP18(U_179,U_177,U_178) )
& ! [U_179,U_177,U_178] :
( U_178 = U_179
| c_Polynomial_Opoly(U_177,U_178) != c_Polynomial_Opoly(U_177,U_179)
| ~ sP18(U_179,U_177,U_178) )
& ! [U_179,U_177,U_178] :
( sP18(U_179,U_177,U_178)
| ~ class_Rings_Oidom(U_177)
| ~ class_Int_Oring__char__0(U_177) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP18])],[f_59_2]) ).
cnf(f_59_4,plain,
( sP18(U_179,U_177,U_178)
| ~ class_Rings_Oidom(U_177)
| ~ class_Int_Oring__char__0(U_177) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_5,plain,
( U_178 = U_179
| c_Polynomial_Opoly(U_177,U_178) != c_Polynomial_Opoly(U_177,U_179)
| ~ sP18(U_179,U_177,U_178) ),
inference(clausify,[status(thm)],[f_59_3]) ).
cnf(f_59_6,plain,
( c_Polynomial_Opoly(U_177,U_178) = c_Polynomial_Opoly(U_177,U_179)
| U_178 != U_179
| ~ sP18(U_179,U_177,U_178) ),
inference(clausify,[status(thm)],[f_59_3]) ).
fof(f_60_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_60_2,plain,
! [U_183,U_182,U_181,U_180] :
( c_Orderings_Oord__class_Oless(U_180,U_183,U_182)
| ~ c_Orderings_Oord__class_Oless(U_180,U_183,U_181)
| ~ c_Orderings_Oord__class_Oless__eq(U_180,U_181,U_182)
| ~ class_Orderings_Oorder(U_180) ),
inference(variable_rename,[status(thm)],[f_60_1]) ).
fof(f_60_3,plain,
! [U_182,U_180,U_183,U_181] :
( c_Orderings_Oord__class_Oless(U_180,U_183,U_182)
| ~ c_Orderings_Oord__class_Oless(U_180,U_183,U_181)
| ~ c_Orderings_Oord__class_Oless__eq(U_180,U_181,U_182)
| ~ class_Orderings_Oorder(U_180) ),
inference(definitional_conversion,[status(esa)],[f_60_2]) ).
cnf(f_60_4,plain,
( c_Orderings_Oord__class_Oless(U_180,U_183,U_182)
| ~ c_Orderings_Oord__class_Oless(U_180,U_183,U_181)
| ~ c_Orderings_Oord__class_Oless__eq(U_180,U_181,U_182)
| ~ class_Orderings_Oorder(U_180) ),
inference(clausify,[status(thm)],[f_60_3]) ).
fof(f_61_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_61_2,plain,
! [U_187,U_186,U_185,U_184] :
( c_Orderings_Oord__class_Oless(U_184,U_185,U_187)
| ~ c_Orderings_Oord__class_Oless(U_184,U_186,U_187)
| ~ c_Orderings_Oord__class_Oless__eq(U_184,U_185,U_186)
| ~ class_Orderings_Opreorder(U_184) ),
inference(variable_rename,[status(thm)],[f_61_1]) ).
fof(f_61_3,plain,
! [U_186,U_184,U_185,U_187] :
( c_Orderings_Oord__class_Oless(U_184,U_185,U_187)
| ~ c_Orderings_Oord__class_Oless(U_184,U_186,U_187)
| ~ c_Orderings_Oord__class_Oless__eq(U_184,U_185,U_186)
| ~ class_Orderings_Opreorder(U_184) ),
inference(definitional_conversion,[status(esa)],[f_61_2]) ).
cnf(f_61_4,plain,
( c_Orderings_Oord__class_Oless(U_184,U_185,U_187)
| ~ c_Orderings_Oord__class_Oless(U_184,U_186,U_187)
| ~ c_Orderings_Oord__class_Oless__eq(U_184,U_185,U_186)
| ~ class_Orderings_Opreorder(U_184) ),
inference(clausify,[status(thm)],[f_61_3]) ).
fof(f_62_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_62_2,plain,
! [U_191,U_190,U_189,U_188] :
( c_Orderings_Oord__class_Oless(U_188,U_191,U_190)
| ~ c_Orderings_Oord__class_Oless__eq(U_188,U_191,U_189)
| ~ c_Orderings_Oord__class_Oless(U_188,U_189,U_190)
| ~ class_Orderings_Oorder(U_188) ),
inference(variable_rename,[status(thm)],[f_62_1]) ).
fof(f_62_3,plain,
! [U_188,U_189,U_191,U_190] :
( c_Orderings_Oord__class_Oless(U_188,U_191,U_190)
| ~ c_Orderings_Oord__class_Oless__eq(U_188,U_191,U_189)
| ~ c_Orderings_Oord__class_Oless(U_188,U_189,U_190)
| ~ class_Orderings_Oorder(U_188) ),
inference(definitional_conversion,[status(esa)],[f_62_2]) ).
cnf(f_62_4,plain,
( c_Orderings_Oord__class_Oless(U_188,U_191,U_190)
| ~ c_Orderings_Oord__class_Oless__eq(U_188,U_191,U_189)
| ~ c_Orderings_Oord__class_Oless(U_188,U_189,U_190)
| ~ class_Orderings_Oorder(U_188) ),
inference(clausify,[status(thm)],[f_62_3]) ).
fof(f_63_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_63_2,plain,
! [U_195,U_194,U_193,U_192] :
( c_Orderings_Oord__class_Oless(U_192,U_193,U_195)
| ~ c_Orderings_Oord__class_Oless__eq(U_192,U_194,U_195)
| ~ c_Orderings_Oord__class_Oless(U_192,U_193,U_194)
| ~ class_Orderings_Opreorder(U_192) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
fof(f_63_3,plain,
! [U_193,U_194,U_192,U_195] :
( c_Orderings_Oord__class_Oless(U_192,U_193,U_195)
| ~ c_Orderings_Oord__class_Oless__eq(U_192,U_194,U_195)
| ~ c_Orderings_Oord__class_Oless(U_192,U_193,U_194)
| ~ class_Orderings_Opreorder(U_192) ),
inference(definitional_conversion,[status(esa)],[f_63_2]) ).
cnf(f_63_4,plain,
( c_Orderings_Oord__class_Oless(U_192,U_193,U_195)
| ~ c_Orderings_Oord__class_Oless__eq(U_192,U_194,U_195)
| ~ c_Orderings_Oord__class_Oless(U_192,U_193,U_194)
| ~ class_Orderings_Opreorder(U_192) ),
inference(clausify,[status(thm)],[f_63_3]) ).
fof(f_64_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_64_2,plain,
! [U_198,U_197,U_196] :
( c_Orderings_Oord__class_Oless(U_196,U_197,U_198)
| U_198 = U_197
| ~ c_Orderings_Oord__class_Oless__eq(U_196,U_197,U_198)
| ~ class_Orderings_Oorder(U_196) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
fof(f_64_3,plain,
! [U_196,U_198,U_197] :
( c_Orderings_Oord__class_Oless(U_196,U_197,U_198)
| U_198 = U_197
| ~ c_Orderings_Oord__class_Oless__eq(U_196,U_197,U_198)
| ~ class_Orderings_Oorder(U_196) ),
inference(definitional_conversion,[status(esa)],[f_64_2]) ).
cnf(f_64_4,plain,
( c_Orderings_Oord__class_Oless(U_196,U_197,U_198)
| U_198 = U_197
| ~ c_Orderings_Oord__class_Oless__eq(U_196,U_197,U_198)
| ~ class_Orderings_Oorder(U_196) ),
inference(clausify,[status(thm)],[f_64_3]) ).
fof(f_65_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_65_2,plain,
! [U_201,U_200,U_199] :
( c_Orderings_Oord__class_Oless(U_199,U_200,U_201)
| U_200 = U_201
| ~ c_Orderings_Oord__class_Oless__eq(U_199,U_200,U_201)
| ~ class_Orderings_Oorder(U_199) ),
inference(variable_rename,[status(thm)],[f_65_1]) ).
fof(f_65_3,plain,
! [U_200,U_199,U_201] :
( c_Orderings_Oord__class_Oless(U_199,U_200,U_201)
| U_200 = U_201
| ~ c_Orderings_Oord__class_Oless__eq(U_199,U_200,U_201)
| ~ class_Orderings_Oorder(U_199) ),
inference(definitional_conversion,[status(esa)],[f_65_2]) ).
cnf(f_65_4,plain,
( c_Orderings_Oord__class_Oless(U_199,U_200,U_201)
| U_200 = U_201
| ~ c_Orderings_Oord__class_Oless__eq(U_199,U_200,U_201)
| ~ class_Orderings_Oorder(U_199) ),
inference(clausify,[status(thm)],[f_65_3]) ).
fof(f_66_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_66_2,plain,
! [U_204,U_203,U_202] :
( U_203 = U_204
| c_Orderings_Oord__class_Oless(U_202,U_203,U_204)
| ~ c_Orderings_Oord__class_Oless__eq(U_202,U_203,U_204)
| ~ class_Orderings_Oorder(U_202) ),
inference(variable_rename,[status(thm)],[f_66_1]) ).
fof(f_66_3,plain,
! [U_203,U_202,U_204] :
( U_203 = U_204
| c_Orderings_Oord__class_Oless(U_202,U_203,U_204)
| ~ c_Orderings_Oord__class_Oless__eq(U_202,U_203,U_204)
| ~ class_Orderings_Oorder(U_202) ),
inference(definitional_conversion,[status(esa)],[f_66_2]) ).
cnf(f_66_4,plain,
( U_203 = U_204
| c_Orderings_Oord__class_Oless(U_202,U_203,U_204)
| ~ c_Orderings_Oord__class_Oless__eq(U_202,U_203,U_204)
| ~ class_Orderings_Oorder(U_202) ),
inference(clausify,[status(thm)],[f_66_3]) ).
fof(f_67_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv2]) ).
fof(f_67_2,plain,
! [U_207,U_206,U_205] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_205,U_206,U_207)
| U_206 != U_207 )
& ( U_206 = U_207
| c_Orderings_Oord__class_Oless(U_205,U_206,U_207) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_205,U_206,U_207)
| ~ class_Orderings_Olinorder(U_205) ),
inference(variable_rename,[status(thm)],[f_67_1]) ).
fof(f_67_3,plain,
( ! [U_205,U_207,U_206] :
( ~ c_Orderings_Oord__class_Oless(U_205,U_206,U_207)
| U_206 != U_207
| ~ sP19(U_205,U_207,U_206) )
& ! [U_205,U_207,U_206] :
( U_206 = U_207
| c_Orderings_Oord__class_Oless(U_205,U_206,U_207)
| ~ sP19(U_205,U_207,U_206) )
& ! [U_205,U_207,U_206] :
( sP19(U_205,U_207,U_206)
| ~ c_Orderings_Oord__class_Oless__eq(U_205,U_206,U_207)
| ~ class_Orderings_Olinorder(U_205) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_67_2]) ).
cnf(f_67_4,plain,
( sP19(U_205,U_207,U_206)
| ~ c_Orderings_Oord__class_Oless__eq(U_205,U_206,U_207)
| ~ class_Orderings_Olinorder(U_205) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_5,plain,
( U_206 = U_207
| c_Orderings_Oord__class_Oless(U_205,U_206,U_207)
| ~ sP19(U_205,U_207,U_206) ),
inference(clausify,[status(thm)],[f_67_3]) ).
cnf(f_67_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_205,U_206,U_207)
| U_206 != U_207
| ~ sP19(U_205,U_207,U_206) ),
inference(clausify,[status(thm)],[f_67_3]) ).
fof(f_68_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_68_2,plain,
! [U_210,U_209,U_208] :
( c_Orderings_Oord__class_Oless__eq(U_208,U_209,U_210)
| ~ c_Orderings_Oord__class_Oless(U_208,U_209,U_210)
| ~ class_Orderings_Opreorder(U_208) ),
inference(variable_rename,[status(thm)],[f_68_1]) ).
fof(f_68_3,plain,
! [U_210,U_209,U_208] :
( c_Orderings_Oord__class_Oless__eq(U_208,U_209,U_210)
| ~ c_Orderings_Oord__class_Oless(U_208,U_209,U_210)
| ~ class_Orderings_Opreorder(U_208) ),
inference(definitional_conversion,[status(esa)],[f_68_2]) ).
cnf(f_68_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_208,U_209,U_210)
| ~ c_Orderings_Oord__class_Oless(U_208,U_209,U_210)
| ~ class_Orderings_Opreorder(U_208) ),
inference(clausify,[status(thm)],[f_68_3]) ).
fof(f_69_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_69_2,plain,
! [U_213,U_212,U_211] :
( ~ c_Orderings_Oord__class_Oless(U_211,U_213,U_212)
| ~ c_Orderings_Oord__class_Oless__eq(U_211,U_212,U_213)
| ~ class_Orderings_Olinorder(U_211) ),
inference(variable_rename,[status(thm)],[f_69_1]) ).
fof(f_69_3,plain,
! [U_211,U_212,U_213] :
( ~ c_Orderings_Oord__class_Oless(U_211,U_213,U_212)
| ~ c_Orderings_Oord__class_Oless__eq(U_211,U_212,U_213)
| ~ class_Orderings_Olinorder(U_211) ),
inference(definitional_conversion,[status(esa)],[f_69_2]) ).
cnf(f_69_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_211,U_213,U_212)
| ~ c_Orderings_Oord__class_Oless__eq(U_211,U_212,U_213)
| ~ class_Orderings_Olinorder(U_211) ),
inference(clausify,[status(thm)],[f_69_3]) ).
fof(f_70_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_70_2,plain,
! [U_216,U_215,U_214] :
( c_Orderings_Oord__class_Oless(U_214,U_216,U_215)
| ~ c_Orderings_Oord__class_Oless__eq(U_214,U_216,U_215)
| U_215 = U_216
| ~ class_Orderings_Oorder(U_214) ),
inference(variable_rename,[status(thm)],[f_70_1]) ).
fof(f_70_3,plain,
! [U_215,U_214,U_216] :
( c_Orderings_Oord__class_Oless(U_214,U_216,U_215)
| ~ c_Orderings_Oord__class_Oless__eq(U_214,U_216,U_215)
| U_215 = U_216
| ~ class_Orderings_Oorder(U_214) ),
inference(definitional_conversion,[status(esa)],[f_70_2]) ).
cnf(f_70_4,plain,
( c_Orderings_Oord__class_Oless(U_214,U_216,U_215)
| ~ c_Orderings_Oord__class_Oless__eq(U_214,U_216,U_215)
| U_215 = U_216
| ~ class_Orderings_Oorder(U_214) ),
inference(clausify,[status(thm)],[f_70_3]) ).
fof(f_71_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_71_2,plain,
! [U_219,U_218,U_217] :
( c_Orderings_Oord__class_Oless(U_217,U_218,U_219)
| ~ c_Orderings_Oord__class_Oless__eq(U_217,U_218,U_219)
| U_218 = U_219
| ~ class_Orderings_Oorder(U_217) ),
inference(variable_rename,[status(thm)],[f_71_1]) ).
fof(f_71_3,plain,
! [U_218,U_217,U_219] :
( c_Orderings_Oord__class_Oless(U_217,U_218,U_219)
| ~ c_Orderings_Oord__class_Oless__eq(U_217,U_218,U_219)
| U_218 = U_219
| ~ class_Orderings_Oorder(U_217) ),
inference(definitional_conversion,[status(esa)],[f_71_2]) ).
cnf(f_71_4,plain,
( c_Orderings_Oord__class_Oless(U_217,U_218,U_219)
| ~ c_Orderings_Oord__class_Oless__eq(U_217,U_218,U_219)
| U_218 = U_219
| ~ class_Orderings_Oorder(U_217) ),
inference(clausify,[status(thm)],[f_71_3]) ).
fof(f_72_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__antisym__conv1]) ).
fof(f_72_2,plain,
! [U_222,U_221,U_220] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_220,U_221,U_222)
| U_221 != U_222 )
& ( U_221 = U_222
| ~ c_Orderings_Oord__class_Oless__eq(U_220,U_221,U_222) ) )
| c_Orderings_Oord__class_Oless(U_220,U_221,U_222)
| ~ class_Orderings_Olinorder(U_220) ),
inference(variable_rename,[status(thm)],[f_72_1]) ).
fof(f_72_3,plain,
( ! [U_221,U_220,U_222] :
( c_Orderings_Oord__class_Oless__eq(U_220,U_221,U_222)
| U_221 != U_222
| ~ sP20(U_221,U_220,U_222) )
& ! [U_221,U_220,U_222] :
( U_221 = U_222
| ~ c_Orderings_Oord__class_Oless__eq(U_220,U_221,U_222)
| ~ sP20(U_221,U_220,U_222) )
& ! [U_221,U_220,U_222] :
( sP20(U_221,U_220,U_222)
| c_Orderings_Oord__class_Oless(U_220,U_221,U_222)
| ~ class_Orderings_Olinorder(U_220) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_72_2]) ).
cnf(f_72_4,plain,
( sP20(U_221,U_220,U_222)
| c_Orderings_Oord__class_Oless(U_220,U_221,U_222)
| ~ class_Orderings_Olinorder(U_220) ),
inference(clausify,[status(thm)],[f_72_3]) ).
cnf(f_72_5,plain,
( U_221 = U_222
| ~ c_Orderings_Oord__class_Oless__eq(U_220,U_221,U_222)
| ~ sP20(U_221,U_220,U_222) ),
inference(clausify,[status(thm)],[f_72_3]) ).
cnf(f_72_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_220,U_221,U_222)
| U_221 != U_222
| ~ sP20(U_221,U_220,U_222) ),
inference(clausify,[status(thm)],[f_72_3]) ).
fof(f_73_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_73_2,plain,
! [U_225,U_224,U_223] :
( c_Orderings_Oord__class_Oless(U_223,U_225,U_224)
| c_Orderings_Oord__class_Oless__eq(U_223,U_224,U_225)
| ~ class_Orderings_Olinorder(U_223) ),
inference(variable_rename,[status(thm)],[f_73_1]) ).
fof(f_73_3,plain,
! [U_223,U_224,U_225] :
( c_Orderings_Oord__class_Oless(U_223,U_225,U_224)
| c_Orderings_Oord__class_Oless__eq(U_223,U_224,U_225)
| ~ class_Orderings_Olinorder(U_223) ),
inference(definitional_conversion,[status(esa)],[f_73_2]) ).
cnf(f_73_4,plain,
( c_Orderings_Oord__class_Oless(U_223,U_225,U_224)
| c_Orderings_Oord__class_Oless__eq(U_223,U_224,U_225)
| ~ class_Orderings_Olinorder(U_223) ),
inference(clausify,[status(thm)],[f_73_3]) ).
fof(f_74_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_74_2,plain,
! [U_228,U_227,U_226] :
( c_Orderings_Oord__class_Oless__eq(U_226,U_228,U_227)
| c_Orderings_Oord__class_Oless(U_226,U_227,U_228)
| ~ class_Orderings_Olinorder(U_226) ),
inference(variable_rename,[status(thm)],[f_74_1]) ).
fof(f_74_3,plain,
! [U_228,U_226,U_227] :
( c_Orderings_Oord__class_Oless__eq(U_226,U_228,U_227)
| c_Orderings_Oord__class_Oless(U_226,U_227,U_228)
| ~ class_Orderings_Olinorder(U_226) ),
inference(definitional_conversion,[status(esa)],[f_74_2]) ).
cnf(f_74_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_226,U_228,U_227)
| c_Orderings_Oord__class_Oless(U_226,U_227,U_228)
| ~ class_Orderings_Olinorder(U_226) ),
inference(clausify,[status(thm)],[f_74_3]) ).
fof(f_75_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__le__less]) ).
fof(f_75_2,plain,
! [U_231,U_230,U_229] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_229,U_230,U_231)
| ( U_230 != U_231
& ~ c_Orderings_Oord__class_Oless(U_229,U_230,U_231) ) )
& ( U_230 = U_231
| c_Orderings_Oord__class_Oless(U_229,U_230,U_231)
| ~ c_Orderings_Oord__class_Oless__eq(U_229,U_230,U_231) ) )
| ~ class_Orderings_Oorder(U_229) ),
inference(variable_rename,[status(thm)],[f_75_1]) ).
fof(f_75_3,plain,
( ! [U_229,U_230,U_231] :
( U_230 != U_231
| ~ sP21(U_229,U_230,U_231) )
& ! [U_229,U_230,U_231] :
( ~ c_Orderings_Oord__class_Oless(U_229,U_230,U_231)
| ~ sP21(U_229,U_230,U_231) )
& ! [U_229,U_230,U_231] :
( c_Orderings_Oord__class_Oless__eq(U_229,U_230,U_231)
| sP21(U_229,U_230,U_231)
| ~ sP22(U_229,U_230,U_231) )
& ! [U_229,U_230,U_231] :
( U_230 = U_231
| c_Orderings_Oord__class_Oless(U_229,U_230,U_231)
| ~ c_Orderings_Oord__class_Oless__eq(U_229,U_230,U_231)
| ~ sP22(U_229,U_230,U_231) )
& ! [U_229,U_230,U_231] :
( sP22(U_229,U_230,U_231)
| ~ class_Orderings_Oorder(U_229) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21,sP22])],[f_75_2]) ).
cnf(f_75_4,plain,
( sP22(U_229,U_230,U_231)
| ~ class_Orderings_Oorder(U_229) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_5,plain,
( U_230 = U_231
| c_Orderings_Oord__class_Oless(U_229,U_230,U_231)
| ~ c_Orderings_Oord__class_Oless__eq(U_229,U_230,U_231)
| ~ sP22(U_229,U_230,U_231) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_229,U_230,U_231)
| sP21(U_229,U_230,U_231)
| ~ sP22(U_229,U_230,U_231) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_7,plain,
( ~ c_Orderings_Oord__class_Oless(U_229,U_230,U_231)
| ~ sP21(U_229,U_230,U_231) ),
inference(clausify,[status(thm)],[f_75_3]) ).
cnf(f_75_8,plain,
( U_230 != U_231
| ~ sP21(U_229,U_230,U_231) ),
inference(clausify,[status(thm)],[f_75_3]) ).
fof(f_76_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Opreorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__le__not__le]) ).
fof(f_76_2,plain,
! [U_234,U_233,U_232] :
( ( ( c_Orderings_Oord__class_Oless(U_232,U_233,U_234)
| c_Orderings_Oord__class_Oless__eq(U_232,U_234,U_233)
| ~ c_Orderings_Oord__class_Oless__eq(U_232,U_233,U_234) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(U_232,U_234,U_233)
& c_Orderings_Oord__class_Oless__eq(U_232,U_233,U_234) )
| ~ c_Orderings_Oord__class_Oless(U_232,U_233,U_234) ) )
| ~ class_Orderings_Opreorder(U_232) ),
inference(variable_rename,[status(thm)],[f_76_1]) ).
fof(f_76_3,plain,
( ! [U_233,U_232,U_234] :
( ~ c_Orderings_Oord__class_Oless__eq(U_232,U_234,U_233)
| ~ sP23(U_233,U_232,U_234) )
& ! [U_233,U_232,U_234] :
( c_Orderings_Oord__class_Oless__eq(U_232,U_233,U_234)
| ~ sP23(U_233,U_232,U_234) )
& ! [U_233,U_232,U_234] :
( c_Orderings_Oord__class_Oless(U_232,U_233,U_234)
| c_Orderings_Oord__class_Oless__eq(U_232,U_234,U_233)
| ~ c_Orderings_Oord__class_Oless__eq(U_232,U_233,U_234)
| ~ sP24(U_233,U_232,U_234) )
& ! [U_233,U_232,U_234] :
( sP23(U_233,U_232,U_234)
| ~ c_Orderings_Oord__class_Oless(U_232,U_233,U_234)
| ~ sP24(U_233,U_232,U_234) )
& ! [U_233,U_232,U_234] :
( sP24(U_233,U_232,U_234)
| ~ class_Orderings_Opreorder(U_232) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23,sP24])],[f_76_2]) ).
cnf(f_76_4,plain,
( sP24(U_233,U_232,U_234)
| ~ class_Orderings_Opreorder(U_232) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_5,plain,
( sP23(U_233,U_232,U_234)
| ~ c_Orderings_Oord__class_Oless(U_232,U_233,U_234)
| ~ sP24(U_233,U_232,U_234) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_6,plain,
( c_Orderings_Oord__class_Oless(U_232,U_233,U_234)
| c_Orderings_Oord__class_Oless__eq(U_232,U_234,U_233)
| ~ c_Orderings_Oord__class_Oless__eq(U_232,U_233,U_234)
| ~ sP24(U_233,U_232,U_234) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_232,U_233,U_234)
| ~ sP23(U_233,U_232,U_234) ),
inference(clausify,[status(thm)],[f_76_3]) ).
cnf(f_76_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_232,U_234,U_233)
| ~ sP23(U_233,U_232,U_234) ),
inference(clausify,[status(thm)],[f_76_3]) ).
fof(f_77_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__less__le]) ).
fof(f_77_2,plain,
! [U_237,U_236,U_235] :
( ( ( c_Orderings_Oord__class_Oless(U_235,U_236,U_237)
| U_236 = U_237
| ~ c_Orderings_Oord__class_Oless__eq(U_235,U_236,U_237) )
& ( ( U_236 != U_237
& c_Orderings_Oord__class_Oless__eq(U_235,U_236,U_237) )
| ~ c_Orderings_Oord__class_Oless(U_235,U_236,U_237) ) )
| ~ class_Orderings_Oorder(U_235) ),
inference(variable_rename,[status(thm)],[f_77_1]) ).
fof(f_77_3,plain,
( ! [U_237,U_235,U_236] :
( U_236 != U_237
| ~ sP25(U_237,U_235,U_236) )
& ! [U_237,U_235,U_236] :
( c_Orderings_Oord__class_Oless__eq(U_235,U_236,U_237)
| ~ sP25(U_237,U_235,U_236) )
& ! [U_237,U_235,U_236] :
( c_Orderings_Oord__class_Oless(U_235,U_236,U_237)
| U_236 = U_237
| ~ c_Orderings_Oord__class_Oless__eq(U_235,U_236,U_237)
| ~ sP26(U_237,U_235,U_236) )
& ! [U_237,U_235,U_236] :
( sP25(U_237,U_235,U_236)
| ~ c_Orderings_Oord__class_Oless(U_235,U_236,U_237)
| ~ sP26(U_237,U_235,U_236) )
& ! [U_237,U_235,U_236] :
( sP26(U_237,U_235,U_236)
| ~ class_Orderings_Oorder(U_235) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25,sP26])],[f_77_2]) ).
cnf(f_77_4,plain,
( sP26(U_237,U_235,U_236)
| ~ class_Orderings_Oorder(U_235) ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_5,plain,
( sP25(U_237,U_235,U_236)
| ~ c_Orderings_Oord__class_Oless(U_235,U_236,U_237)
| ~ sP26(U_237,U_235,U_236) ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_6,plain,
( c_Orderings_Oord__class_Oless(U_235,U_236,U_237)
| U_236 = U_237
| ~ c_Orderings_Oord__class_Oless__eq(U_235,U_236,U_237)
| ~ sP26(U_237,U_235,U_236) ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_235,U_236,U_237)
| ~ sP25(U_237,U_235,U_236) ),
inference(clausify,[status(thm)],[f_77_3]) ).
cnf(f_77_8,plain,
( U_236 != U_237
| ~ sP25(U_237,U_235,U_236) ),
inference(clausify,[status(thm)],[f_77_3]) ).
fof(f_78_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_78_2,plain,
! [U_240,U_239,U_238] :
( c_Orderings_Oord__class_Oless(U_238,U_240,U_239)
| c_Orderings_Oord__class_Oless__eq(U_238,U_239,U_240)
| ~ class_Orderings_Olinorder(U_238) ),
inference(variable_rename,[status(thm)],[f_78_1]) ).
fof(f_78_3,plain,
! [U_238,U_240,U_239] :
( c_Orderings_Oord__class_Oless(U_238,U_240,U_239)
| c_Orderings_Oord__class_Oless__eq(U_238,U_239,U_240)
| ~ class_Orderings_Olinorder(U_238) ),
inference(definitional_conversion,[status(esa)],[f_78_2]) ).
cnf(f_78_4,plain,
( c_Orderings_Oord__class_Oless(U_238,U_240,U_239)
| c_Orderings_Oord__class_Oless__eq(U_238,U_239,U_240)
| ~ class_Orderings_Olinorder(U_238) ),
inference(clausify,[status(thm)],[f_78_3]) ).
fof(f_79_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless__eq(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__le]) ).
fof(f_79_2,plain,
! [U_243,U_242,U_241] :
( ( ( ~ c_Orderings_Oord__class_Oless__eq(U_241,U_242,U_243)
| ~ c_Orderings_Oord__class_Oless(U_241,U_243,U_242) )
& ( c_Orderings_Oord__class_Oless(U_241,U_243,U_242)
| c_Orderings_Oord__class_Oless__eq(U_241,U_242,U_243) ) )
| ~ class_Orderings_Olinorder(U_241) ),
inference(variable_rename,[status(thm)],[f_79_1]) ).
fof(f_79_3,plain,
( ! [U_241,U_242,U_243] :
( ~ c_Orderings_Oord__class_Oless__eq(U_241,U_242,U_243)
| ~ c_Orderings_Oord__class_Oless(U_241,U_243,U_242)
| ~ sP27(U_241,U_242,U_243) )
& ! [U_241,U_242,U_243] :
( c_Orderings_Oord__class_Oless(U_241,U_243,U_242)
| c_Orderings_Oord__class_Oless__eq(U_241,U_242,U_243)
| ~ sP27(U_241,U_242,U_243) )
& ! [U_241,U_242,U_243] :
( sP27(U_241,U_242,U_243)
| ~ class_Orderings_Olinorder(U_241) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_79_2]) ).
cnf(f_79_4,plain,
( sP27(U_241,U_242,U_243)
| ~ class_Orderings_Olinorder(U_241) ),
inference(clausify,[status(thm)],[f_79_3]) ).
cnf(f_79_5,plain,
( c_Orderings_Oord__class_Oless(U_241,U_243,U_242)
| c_Orderings_Oord__class_Oless__eq(U_241,U_242,U_243)
| ~ sP27(U_241,U_242,U_243) ),
inference(clausify,[status(thm)],[f_79_3]) ).
cnf(f_79_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_241,U_242,U_243)
| ~ c_Orderings_Oord__class_Oless(U_241,U_243,U_242)
| ~ sP27(U_241,U_242,U_243) ),
inference(clausify,[status(thm)],[f_79_3]) ).
fof(f_80_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| c_Orderings_Oord__class_Oless(T_a,V_x_2,V_y_2) ) )
| ~ class_Orderings_Olinorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_linorder__not__less]) ).
fof(f_80_2,plain,
! [U_246,U_245,U_244] :
( ( ( ~ c_Orderings_Oord__class_Oless(U_244,U_245,U_246)
| ~ c_Orderings_Oord__class_Oless__eq(U_244,U_246,U_245) )
& ( c_Orderings_Oord__class_Oless__eq(U_244,U_246,U_245)
| c_Orderings_Oord__class_Oless(U_244,U_245,U_246) ) )
| ~ class_Orderings_Olinorder(U_244) ),
inference(variable_rename,[status(thm)],[f_80_1]) ).
fof(f_80_3,plain,
( ! [U_245,U_246,U_244] :
( ~ c_Orderings_Oord__class_Oless(U_244,U_245,U_246)
| ~ c_Orderings_Oord__class_Oless__eq(U_244,U_246,U_245)
| ~ sP28(U_245,U_246,U_244) )
& ! [U_245,U_246,U_244] :
( c_Orderings_Oord__class_Oless__eq(U_244,U_246,U_245)
| c_Orderings_Oord__class_Oless(U_244,U_245,U_246)
| ~ sP28(U_245,U_246,U_244) )
& ! [U_245,U_246,U_244] :
( sP28(U_245,U_246,U_244)
| ~ class_Orderings_Olinorder(U_244) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_80_2]) ).
cnf(f_80_4,plain,
( sP28(U_245,U_246,U_244)
| ~ class_Orderings_Olinorder(U_244) ),
inference(clausify,[status(thm)],[f_80_3]) ).
cnf(f_80_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_244,U_246,U_245)
| c_Orderings_Oord__class_Oless(U_244,U_245,U_246)
| ~ sP28(U_245,U_246,U_244) ),
inference(clausify,[status(thm)],[f_80_3]) ).
cnf(f_80_6,plain,
( ~ c_Orderings_Oord__class_Oless(U_244,U_245,U_246)
| ~ c_Orderings_Oord__class_Oless__eq(U_244,U_246,U_245)
| ~ sP28(U_245,U_246,U_244) ),
inference(clausify,[status(thm)],[f_80_3]) ).
fof(f_81_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) ) )
& ( V_x_2 = V_y_2
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__real__def]) ).
fof(f_81_2,plain,
! [U_248,U_247] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_247,U_248)
| ( U_247 != U_248
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_247,U_248) ) )
& ( U_247 = U_248
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_247,U_248)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_247,U_248) ) ),
inference(variable_rename,[status(thm)],[f_81_1]) ).
fof(f_81_3,plain,
( ! [U_252,U_250] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_250,U_252)
| ( U_250 != U_252
& ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_250,U_252) ) )
& ! [U_251,U_249] :
( U_249 = U_251
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_249,U_251)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_249,U_251) ) ),
inference(miniscope,[status(thm)],[f_81_2]) ).
fof(f_81_4,plain,
( ! [U_250,U_252] :
( U_250 != U_252
| ~ sP29(U_250,U_252) )
& ! [U_250,U_252] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_250,U_252)
| ~ sP29(U_250,U_252) )
& ! [U_250,U_252] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_250,U_252)
| sP29(U_250,U_252) )
& ! [U_251,U_249] :
( U_249 = U_251
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_249,U_251)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_249,U_251) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_81_3]) ).
cnf(f_81_5,plain,
( U_249 = U_251
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_249,U_251)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_249,U_251) ),
inference(clausify,[status(thm)],[f_81_4]) ).
cnf(f_81_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_250,U_252)
| sP29(U_250,U_252) ),
inference(clausify,[status(thm)],[f_81_4]) ).
cnf(f_81_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_250,U_252)
| ~ sP29(U_250,U_252) ),
inference(clausify,[status(thm)],[f_81_4]) ).
cnf(f_81_8,plain,
( U_250 != U_252
| ~ sP29(U_250,U_252) ),
inference(clausify,[status(thm)],[f_81_4]) ).
fof(f_82_1,plain,
! [V_z_2] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),V_z_2)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_z_2),v_r) ),
inference(fof_nnf,[status(thm)],[fact__096_B_Bz_O_Acmod_Az_A_060_061_Ar_A_061_061_062_Acmod_A_Ipoly_A_IpCons_Ac_Acs_J_Az_J_A_060_061_A1_A_L_Acmod_Ac_A_L_Aabs_A_Ir_A_K_Am_J_096]) ).
fof(f_82_2,plain,
! [U_253] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),U_253)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_253),v_r) ),
inference(variable_rename,[status(thm)],[f_82_1]) ).
fof(f_82_3,plain,
! [U_253] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),U_253)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_253),v_r) ),
inference(definitional_conversion,[status(esa)],[f_82_2]) ).
cnf(f_82_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),U_253)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_253),v_r) ),
inference(clausify,[status(thm)],[f_82_3]) ).
fof(f_83_1,plain,
! [V_pa_2,V_a_2,T_a] :
( ( ( c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_a_2,V_pa_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ~ c_Polynomial_Opos__poly(T_a,V_pa_2) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
& V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
| c_Polynomial_Opos__poly(T_a,V_pa_2)
| ~ c_Polynomial_Opos__poly(T_a,c_Polynomial_OpCons(T_a,V_a_2,V_pa_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__pCons]) ).
fof(f_83_2,plain,
! [U_256,U_255,U_254] :
( ( ( c_Polynomial_Opos__poly(U_254,c_Polynomial_OpCons(U_254,U_255,U_256))
| ( ( ~ c_Orderings_Oord__class_Oless(U_254,c_Groups_Ozero__class_Ozero(U_254),U_255)
| U_256 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_254)) )
& ~ c_Polynomial_Opos__poly(U_254,U_256) ) )
& ( ( c_Orderings_Oord__class_Oless(U_254,c_Groups_Ozero__class_Ozero(U_254),U_255)
& U_256 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_254)) )
| c_Polynomial_Opos__poly(U_254,U_256)
| ~ c_Polynomial_Opos__poly(U_254,c_Polynomial_OpCons(U_254,U_255,U_256)) ) )
| ~ class_Rings_Olinordered__idom(U_254) ),
inference(variable_rename,[status(thm)],[f_83_1]) ).
fof(f_83_3,plain,
( ! [U_254,U_255,U_256] :
( ~ c_Orderings_Oord__class_Oless(U_254,c_Groups_Ozero__class_Ozero(U_254),U_255)
| U_256 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_254))
| ~ sP31(U_254,U_255,U_256) )
& ! [U_254,U_255,U_256] :
( ~ c_Polynomial_Opos__poly(U_254,U_256)
| ~ sP31(U_254,U_255,U_256) )
& ! [U_254,U_255,U_256] :
( c_Orderings_Oord__class_Oless(U_254,c_Groups_Ozero__class_Ozero(U_254),U_255)
| ~ sP30(U_254,U_255,U_256) )
& ! [U_254,U_255,U_256] :
( U_256 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_254))
| ~ sP30(U_254,U_255,U_256) )
& ! [U_254,U_255,U_256] :
( c_Polynomial_Opos__poly(U_254,c_Polynomial_OpCons(U_254,U_255,U_256))
| sP31(U_254,U_255,U_256)
| ~ sP32(U_254,U_255,U_256) )
& ! [U_254,U_255,U_256] :
( sP30(U_254,U_255,U_256)
| c_Polynomial_Opos__poly(U_254,U_256)
| ~ c_Polynomial_Opos__poly(U_254,c_Polynomial_OpCons(U_254,U_255,U_256))
| ~ sP32(U_254,U_255,U_256) )
& ! [U_254,U_255,U_256] :
( sP32(U_254,U_255,U_256)
| ~ class_Rings_Olinordered__idom(U_254) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30,sP31,sP32])],[f_83_2]) ).
cnf(f_83_4,plain,
( sP32(U_254,U_255,U_256)
| ~ class_Rings_Olinordered__idom(U_254) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_5,plain,
( sP30(U_254,U_255,U_256)
| c_Polynomial_Opos__poly(U_254,U_256)
| ~ c_Polynomial_Opos__poly(U_254,c_Polynomial_OpCons(U_254,U_255,U_256))
| ~ sP32(U_254,U_255,U_256) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_6,plain,
( c_Polynomial_Opos__poly(U_254,c_Polynomial_OpCons(U_254,U_255,U_256))
| sP31(U_254,U_255,U_256)
| ~ sP32(U_254,U_255,U_256) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_7,plain,
( U_256 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_254))
| ~ sP30(U_254,U_255,U_256) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_8,plain,
( c_Orderings_Oord__class_Oless(U_254,c_Groups_Ozero__class_Ozero(U_254),U_255)
| ~ sP30(U_254,U_255,U_256) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_9,plain,
( ~ c_Polynomial_Opos__poly(U_254,U_256)
| ~ sP31(U_254,U_255,U_256) ),
inference(clausify,[status(thm)],[f_83_3]) ).
cnf(f_83_10,plain,
( ~ c_Orderings_Oord__class_Oless(U_254,c_Groups_Ozero__class_Ozero(U_254),U_255)
| U_256 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_254))
| ~ sP31(U_254,U_255,U_256) ),
inference(clausify,[status(thm)],[f_83_3]) ).
fof(f_84_1,plain,
! [V_a_2,V_pa_2,T_a] :
( ( ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_pa_2 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
& ( c_Polynomial_Oorder(T_a,V_a_2,V_pa_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_pa_2 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__root]) ).
fof(f_84_2,plain,
! [U_259,U_258,U_257] :
( ( ( hAPP(c_Polynomial_Opoly(U_257,U_258),U_259) = c_Groups_Ozero__class_Ozero(U_257)
| ( c_Polynomial_Oorder(U_257,U_259,U_258) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_258 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_257)) ) )
& ( c_Polynomial_Oorder(U_257,U_259,U_258) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_258 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_257))
| hAPP(c_Polynomial_Opoly(U_257,U_258),U_259) != c_Groups_Ozero__class_Ozero(U_257) ) )
| ~ class_Rings_Oidom(U_257) ),
inference(variable_rename,[status(thm)],[f_84_1]) ).
fof(f_84_3,plain,
( ! [U_257,U_259,U_258] :
( c_Polynomial_Oorder(U_257,U_259,U_258) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP33(U_257,U_259,U_258) )
& ! [U_257,U_259,U_258] :
( U_258 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_257))
| ~ sP33(U_257,U_259,U_258) )
& ! [U_257,U_259,U_258] :
( hAPP(c_Polynomial_Opoly(U_257,U_258),U_259) = c_Groups_Ozero__class_Ozero(U_257)
| sP33(U_257,U_259,U_258)
| ~ sP34(U_257,U_259,U_258) )
& ! [U_257,U_259,U_258] :
( c_Polynomial_Oorder(U_257,U_259,U_258) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_258 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_257))
| hAPP(c_Polynomial_Opoly(U_257,U_258),U_259) != c_Groups_Ozero__class_Ozero(U_257)
| ~ sP34(U_257,U_259,U_258) )
& ! [U_257,U_259,U_258] :
( sP34(U_257,U_259,U_258)
| ~ class_Rings_Oidom(U_257) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP33,sP34])],[f_84_2]) ).
cnf(f_84_4,plain,
( sP34(U_257,U_259,U_258)
| ~ class_Rings_Oidom(U_257) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_5,plain,
( c_Polynomial_Oorder(U_257,U_259,U_258) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_258 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_257))
| hAPP(c_Polynomial_Opoly(U_257,U_258),U_259) != c_Groups_Ozero__class_Ozero(U_257)
| ~ sP34(U_257,U_259,U_258) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_6,plain,
( hAPP(c_Polynomial_Opoly(U_257,U_258),U_259) = c_Groups_Ozero__class_Ozero(U_257)
| sP33(U_257,U_259,U_258)
| ~ sP34(U_257,U_259,U_258) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_7,plain,
( U_258 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_257))
| ~ sP33(U_257,U_259,U_258) ),
inference(clausify,[status(thm)],[f_84_3]) ).
cnf(f_84_8,plain,
( c_Polynomial_Oorder(U_257,U_259,U_258) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP33(U_257,U_259,U_258) ),
inference(clausify,[status(thm)],[f_84_3]) ).
fof(f_85_1,plain,
! [V_pa_2,V_a_2,T_a,V_z_2,V_f_2,T_b] :
( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2))
| hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) != V_z_2
| ~ class_Groups_Ozero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_poly__rec__pCons]) ).
fof(f_85_2,plain,
! [U_265,U_264,U_263,U_262,U_261,U_260] :
( c_Polynomial_Opoly__rec(U_263,U_260,U_262,U_261,c_Polynomial_OpCons(U_260,U_264,U_265)) = hAPP(hAPP(hAPP(U_261,U_264),U_265),c_Polynomial_Opoly__rec(U_263,U_260,U_262,U_261,U_265))
| hAPP(hAPP(hAPP(U_261,c_Groups_Ozero__class_Ozero(U_260)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_260))),U_262) != U_262
| ~ class_Groups_Ozero(U_260) ),
inference(variable_rename,[status(thm)],[f_85_1]) ).
fof(f_85_3,plain,
! [U_265,U_261,U_264,U_263,U_262,U_260] :
( c_Polynomial_Opoly__rec(U_263,U_260,U_262,U_261,c_Polynomial_OpCons(U_260,U_264,U_265)) = hAPP(hAPP(hAPP(U_261,U_264),U_265),c_Polynomial_Opoly__rec(U_263,U_260,U_262,U_261,U_265))
| hAPP(hAPP(hAPP(U_261,c_Groups_Ozero__class_Ozero(U_260)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_260))),U_262) != U_262
| ~ class_Groups_Ozero(U_260) ),
inference(definitional_conversion,[status(esa)],[f_85_2]) ).
cnf(f_85_4,plain,
( c_Polynomial_Opoly__rec(U_263,U_260,U_262,U_261,c_Polynomial_OpCons(U_260,U_264,U_265)) = hAPP(hAPP(hAPP(U_261,U_264),U_265),c_Polynomial_Opoly__rec(U_263,U_260,U_262,U_261,U_265))
| hAPP(hAPP(hAPP(U_261,c_Groups_Ozero__class_Ozero(U_260)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_260))),U_262) != U_262
| ~ class_Groups_Ozero(U_260) ),
inference(clausify,[status(thm)],[f_85_3]) ).
fof(f_86_1,plain,
! [V_pa_2,V_a_2,V_f_2,V_z_2,T_a,T_b] :
( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Polynomial_OpCons(T_b,V_a_2,V_pa_2)) = hAPP(hAPP(hAPP(V_f_2,V_a_2),V_pa_2),c_If(T_a,c_fequal(V_pa_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2,c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,V_pa_2)))
| ~ class_Groups_Ozero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_poly__rec_Osimps]) ).
fof(f_86_2,plain,
! [U_271,U_270,U_269,U_268,U_267,U_266] :
( c_Polynomial_Opoly__rec(U_267,U_266,U_268,U_269,c_Polynomial_OpCons(U_266,U_270,U_271)) = hAPP(hAPP(hAPP(U_269,U_270),U_271),c_If(U_267,c_fequal(U_271,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_266))),U_268,c_Polynomial_Opoly__rec(U_267,U_266,U_268,U_269,U_271)))
| ~ class_Groups_Ozero(U_266) ),
inference(variable_rename,[status(thm)],[f_86_1]) ).
fof(f_86_3,plain,
! [U_267,U_266,U_268,U_269,U_270,U_271] :
( c_Polynomial_Opoly__rec(U_267,U_266,U_268,U_269,c_Polynomial_OpCons(U_266,U_270,U_271)) = hAPP(hAPP(hAPP(U_269,U_270),U_271),c_If(U_267,c_fequal(U_271,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_266))),U_268,c_Polynomial_Opoly__rec(U_267,U_266,U_268,U_269,U_271)))
| ~ class_Groups_Ozero(U_266) ),
inference(definitional_conversion,[status(esa)],[f_86_2]) ).
cnf(f_86_4,plain,
( c_Polynomial_Opoly__rec(U_267,U_266,U_268,U_269,c_Polynomial_OpCons(U_266,U_270,U_271)) = hAPP(hAPP(hAPP(U_269,U_270),U_271),c_If(U_267,c_fequal(U_271,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_266))),U_268,c_Polynomial_Opoly__rec(U_267,U_266,U_268,U_269,U_271)))
| ~ class_Groups_Ozero(U_266) ),
inference(clausify,[status(thm)],[f_86_3]) ).
fof(f_87_1,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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(fof_nnf,[status(thm)],[fact_kp]) ).
fof(f_87_2,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_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(definitional_conversion,[status(esa)],[f_87_1]) ).
cnf(f_87_3,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(clausify,[status(thm)],[f_87_2]) ).
fof(f_88_1,plain,
! [V_c,V_p,V_a,T_a] :
( c_Polynomial_Osynthetic__div(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_c) = c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Polynomial_Osynthetic__div(T_a,V_p,V_c))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_synthetic__div__pCons]) ).
fof(f_88_2,plain,
! [U_275,U_274,U_273,U_272] :
( c_Polynomial_Osynthetic__div(U_272,c_Polynomial_OpCons(U_272,U_273,U_274),U_275) = c_Polynomial_OpCons(U_272,hAPP(c_Polynomial_Opoly(U_272,U_274),U_275),c_Polynomial_Osynthetic__div(U_272,U_274,U_275))
| ~ class_Rings_Ocomm__semiring__0(U_272) ),
inference(variable_rename,[status(thm)],[f_88_1]) ).
fof(f_88_3,plain,
! [U_272,U_273,U_274,U_275] :
( c_Polynomial_Osynthetic__div(U_272,c_Polynomial_OpCons(U_272,U_273,U_274),U_275) = c_Polynomial_OpCons(U_272,hAPP(c_Polynomial_Opoly(U_272,U_274),U_275),c_Polynomial_Osynthetic__div(U_272,U_274,U_275))
| ~ class_Rings_Ocomm__semiring__0(U_272) ),
inference(definitional_conversion,[status(esa)],[f_88_2]) ).
cnf(f_88_4,plain,
( c_Polynomial_Osynthetic__div(U_272,c_Polynomial_OpCons(U_272,U_273,U_274),U_275) = c_Polynomial_OpCons(U_272,hAPP(c_Polynomial_Opoly(U_272,U_274),U_275),c_Polynomial_Osynthetic__div(U_272,U_274,U_275))
| ~ class_Rings_Ocomm__semiring__0(U_272) ),
inference(clausify,[status(thm)],[f_88_3]) ).
fof(f_89_1,plain,
! [T_a,V_z_2,V_f_2,T_b] :
( c_Polynomial_Opoly__rec(T_a,T_b,V_z_2,V_f_2,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))) = V_z_2
| hAPP(hAPP(hAPP(V_f_2,c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_b))),V_z_2) != V_z_2
| ~ class_Groups_Ozero(T_b) ),
inference(fof_nnf,[status(thm)],[fact_poly__rec__0]) ).
fof(f_89_2,plain,
! [U_279,U_278,U_277,U_276] :
( c_Polynomial_Opoly__rec(U_279,U_276,U_278,U_277,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_276))) = U_278
| hAPP(hAPP(hAPP(U_277,c_Groups_Ozero__class_Ozero(U_276)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_276))),U_278) != U_278
| ~ class_Groups_Ozero(U_276) ),
inference(variable_rename,[status(thm)],[f_89_1]) ).
fof(f_89_3,plain,
! [U_276,U_277,U_278,U_279] :
( c_Polynomial_Opoly__rec(U_279,U_276,U_278,U_277,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_276))) = U_278
| hAPP(hAPP(hAPP(U_277,c_Groups_Ozero__class_Ozero(U_276)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_276))),U_278) != U_278
| ~ class_Groups_Ozero(U_276) ),
inference(definitional_conversion,[status(esa)],[f_89_2]) ).
cnf(f_89_4,plain,
( c_Polynomial_Opoly__rec(U_279,U_276,U_278,U_277,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_276))) = U_278
| hAPP(hAPP(hAPP(U_277,c_Groups_Ozero__class_Ozero(U_276)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_276))),U_278) != U_278
| ~ class_Groups_Ozero(U_276) ),
inference(clausify,[status(thm)],[f_89_3]) ).
fof(f_90_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_K] :
( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) )
& ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__def]) ).
fof(f_90_2,plain,
! [U_285,U_284] :
( ( ( c_SEQ_OBseq(U_284,U_285)
| ! [U_283] :
( ? [U_282] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,U_282)),U_283)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_283) ) )
& ( ? [U_281] :
( ! [U_280] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,U_280)),U_281)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_281) )
| ~ c_SEQ_OBseq(U_284,U_285) ) )
| ~ class_RealVector_Oreal__normed__vector(U_284) ),
inference(variable_rename,[status(thm)],[f_90_1]) ).
fof(f_90_3,plain,
! [U_285,U_284] :
( ( ( c_SEQ_OBseq(U_284,U_285)
| ! [U_283] :
( ? [U_282] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,U_282)),U_283)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_283) ) )
& ( ( ! [U_280] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,U_280)),sK5(U_285,U_284))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK5(U_285,U_284)) )
| ~ c_SEQ_OBseq(U_284,U_285) ) )
| ~ class_RealVector_Oreal__normed__vector(U_284) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_281,sK5(U_285,U_284))],[f_90_2]) ).
fof(f_90_4,plain,
! [U_285,U_284] :
( ( ( c_SEQ_OBseq(U_284,U_285)
| ! [U_283] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,sK6(U_285,U_284,U_283))),U_283)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_283) ) )
& ( ( ! [U_280] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,U_280)),sK5(U_285,U_284))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK5(U_285,U_284)) )
| ~ c_SEQ_OBseq(U_284,U_285) ) )
| ~ class_RealVector_Oreal__normed__vector(U_284) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_282,sK6(U_285,U_284,U_283))],[f_90_3]) ).
fof(f_90_5,plain,
( ! [U_280,U_284,U_285] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,U_280)),sK5(U_285,U_284))
| ~ sP35(U_280,U_284,U_285) )
& ! [U_280,U_284,U_285] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK5(U_285,U_284))
| ~ sP35(U_280,U_284,U_285) )
& ! [U_280,U_283,U_284,U_285] :
( c_SEQ_OBseq(U_284,U_285)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,sK6(U_285,U_284,U_283))),U_283)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_283)
| ~ sP36(U_280,U_283,U_284,U_285) )
& ! [U_280,U_283,U_284,U_285] :
( sP35(U_280,U_284,U_285)
| ~ c_SEQ_OBseq(U_284,U_285)
| ~ sP36(U_280,U_283,U_284,U_285) )
& ! [U_280,U_283,U_284,U_285] :
( sP36(U_280,U_283,U_284,U_285)
| ~ class_RealVector_Oreal__normed__vector(U_284) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35,sP36])],[f_90_4]) ).
cnf(f_90_6,plain,
( sP36(U_280,U_283,U_284,U_285)
| ~ class_RealVector_Oreal__normed__vector(U_284) ),
inference(clausify,[status(thm)],[f_90_5]) ).
cnf(f_90_7,plain,
( sP35(U_280,U_284,U_285)
| ~ c_SEQ_OBseq(U_284,U_285)
| ~ sP36(U_280,U_283,U_284,U_285) ),
inference(clausify,[status(thm)],[f_90_5]) ).
cnf(f_90_8,plain,
( c_SEQ_OBseq(U_284,U_285)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,sK6(U_285,U_284,U_283))),U_283)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_283)
| ~ sP36(U_280,U_283,U_284,U_285) ),
inference(clausify,[status(thm)],[f_90_5]) ).
cnf(f_90_9,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK5(U_285,U_284))
| ~ sP35(U_280,U_284,U_285) ),
inference(clausify,[status(thm)],[f_90_5]) ).
cnf(f_90_10,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_284,hAPP(U_285,U_280)),sK5(U_285,U_284))
| ~ sP35(U_280,U_284,U_285) ),
inference(clausify,[status(thm)],[f_90_5]) ).
fof(f_91_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_91_2,plain,
! [U_288,U_287,U_286] :
( c_Orderings_Oord__class_Oless(U_286,U_288,U_287)
| c_Orderings_Oord__class_Oless(U_286,U_287,U_288)
| U_287 = U_288
| ~ class_Rings_Olinordered__idom(U_286) ),
inference(variable_rename,[status(thm)],[f_91_1]) ).
fof(f_91_3,plain,
! [U_288,U_287,U_286] :
( c_Orderings_Oord__class_Oless(U_286,U_288,U_287)
| c_Orderings_Oord__class_Oless(U_286,U_287,U_288)
| U_287 = U_288
| ~ class_Rings_Olinordered__idom(U_286) ),
inference(definitional_conversion,[status(esa)],[f_91_2]) ).
cnf(f_91_4,plain,
( c_Orderings_Oord__class_Oless(U_286,U_288,U_287)
| c_Orderings_Oord__class_Oless(U_286,U_287,U_288)
| U_287 = U_288
| ~ class_Rings_Olinordered__idom(U_286) ),
inference(clausify,[status(thm)],[f_91_3]) ).
fof(f_92_1,plain,
! [V_x_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ozero__class_Ozero(T_a) != V_x_2 ) )
| ~ class_Groups_Ozero(T_a) ),
inference(fof_nnf,[status(thm)],[fact_zero__reorient]) ).
fof(f_92_2,plain,
! [U_290,U_289] :
( ( ( c_Groups_Ozero__class_Ozero(U_289) = U_290
| U_290 != c_Groups_Ozero__class_Ozero(U_289) )
& ( U_290 = c_Groups_Ozero__class_Ozero(U_289)
| c_Groups_Ozero__class_Ozero(U_289) != U_290 ) )
| ~ class_Groups_Ozero(U_289) ),
inference(variable_rename,[status(thm)],[f_92_1]) ).
fof(f_92_3,plain,
( ! [U_289,U_290] :
( c_Groups_Ozero__class_Ozero(U_289) = U_290
| U_290 != c_Groups_Ozero__class_Ozero(U_289)
| ~ sP37(U_289,U_290) )
& ! [U_289,U_290] :
( U_290 = c_Groups_Ozero__class_Ozero(U_289)
| c_Groups_Ozero__class_Ozero(U_289) != U_290
| ~ sP37(U_289,U_290) )
& ! [U_289,U_290] :
( sP37(U_289,U_290)
| ~ class_Groups_Ozero(U_289) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP37])],[f_92_2]) ).
cnf(f_92_4,plain,
( sP37(U_289,U_290)
| ~ class_Groups_Ozero(U_289) ),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_5,plain,
( U_290 = c_Groups_Ozero__class_Ozero(U_289)
| c_Groups_Ozero__class_Ozero(U_289) != U_290
| ~ sP37(U_289,U_290) ),
inference(clausify,[status(thm)],[f_92_3]) ).
cnf(f_92_6,plain,
( c_Groups_Ozero__class_Ozero(U_289) = U_290
| U_290 != c_Groups_Ozero__class_Ozero(U_289)
| ~ sP37(U_289,U_290) ),
inference(clausify,[status(thm)],[f_92_3]) ).
fof(f_93_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_93_2,plain,
! [U_291] : ~ 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_291),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_291),
inference(variable_rename,[status(thm)],[f_93_1]) ).
fof(f_93_3,plain,
! [U_291] : ~ 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_291),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_291),
inference(definitional_conversion,[status(esa)],[f_93_2]) ).
cnf(f_93_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_291),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_291),
inference(clausify,[status(thm)],[f_93_3]) ).
fof(f_94_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_94_2,plain,
! [U_292] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_292) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_292),
inference(variable_rename,[status(thm)],[f_94_1]) ).
fof(f_94_3,plain,
! [U_292] : c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_292) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_292),
inference(definitional_conversion,[status(esa)],[f_94_2]) ).
cnf(f_94_4,plain,
c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,U_292) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_292),
inference(clausify,[status(thm)],[f_94_3]) ).
fof(f_95_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_95_2,plain,
! [U_295,U_294,U_293] :
( c_Orderings_Oord__class_Oless__eq(U_293,c_Groups_Oabs__class_Oabs(U_293,c_Groups_Oplus__class_Oplus(U_293,U_294,U_295)),c_Groups_Oplus__class_Oplus(U_293,c_Groups_Oabs__class_Oabs(U_293,U_294),c_Groups_Oabs__class_Oabs(U_293,U_295)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_293) ),
inference(variable_rename,[status(thm)],[f_95_1]) ).
fof(f_95_3,plain,
! [U_293,U_294,U_295] :
( c_Orderings_Oord__class_Oless__eq(U_293,c_Groups_Oabs__class_Oabs(U_293,c_Groups_Oplus__class_Oplus(U_293,U_294,U_295)),c_Groups_Oplus__class_Oplus(U_293,c_Groups_Oabs__class_Oabs(U_293,U_294),c_Groups_Oabs__class_Oabs(U_293,U_295)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_293) ),
inference(definitional_conversion,[status(esa)],[f_95_2]) ).
cnf(f_95_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_293,c_Groups_Oabs__class_Oabs(U_293,c_Groups_Oplus__class_Oplus(U_293,U_294,U_295)),c_Groups_Oplus__class_Oplus(U_293,c_Groups_Oabs__class_Oabs(U_293,U_294),c_Groups_Oabs__class_Oabs(U_293,U_295)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_293) ),
inference(clausify,[status(thm)],[f_95_3]) ).
fof(f_96_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_96_2,plain,
! [U_296] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_296) = U_296,
inference(variable_rename,[status(thm)],[f_96_1]) ).
fof(f_96_3,plain,
! [U_296] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_296) = U_296,
inference(definitional_conversion,[status(esa)],[f_96_2]) ).
cnf(f_96_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),U_296) = U_296,
inference(clausify,[status(thm)],[f_96_3]) ).
fof(f_97_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_97_2,plain,
! [U_298,U_297] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_297),U_298) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_298),U_297),
inference(variable_rename,[status(thm)],[f_97_1]) ).
fof(f_97_3,plain,
! [U_297,U_298] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_297),U_298) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_298),U_297),
inference(definitional_conversion,[status(esa)],[f_97_2]) ).
cnf(f_97_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_297),U_298) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_298),U_297),
inference(clausify,[status(thm)],[f_97_3]) ).
fof(f_98_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_98_2,plain,
! [U_302,U_301,U_300,U_299] :
( ( ( c_Orderings_Oord__class_Oless(tc_fun(U_300,U_299),U_301,U_302)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_302,U_301)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_301,U_302) )
& ( ( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_302,U_301)
& c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_301,U_302) )
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_300,U_299),U_301,U_302) ) )
| ~ class_Orderings_Oord(U_299) ),
inference(variable_rename,[status(thm)],[f_98_1]) ).
fof(f_98_3,plain,
( ! [U_299,U_300,U_301,U_302] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_302,U_301)
| ~ sP38(U_299,U_300,U_301,U_302) )
& ! [U_299,U_300,U_301,U_302] :
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_301,U_302)
| ~ sP38(U_299,U_300,U_301,U_302) )
& ! [U_299,U_300,U_301,U_302] :
( c_Orderings_Oord__class_Oless(tc_fun(U_300,U_299),U_301,U_302)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_302,U_301)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_301,U_302)
| ~ sP39(U_299,U_300,U_301,U_302) )
& ! [U_299,U_300,U_301,U_302] :
( sP38(U_299,U_300,U_301,U_302)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_300,U_299),U_301,U_302)
| ~ sP39(U_299,U_300,U_301,U_302) )
& ! [U_299,U_300,U_301,U_302] :
( sP39(U_299,U_300,U_301,U_302)
| ~ class_Orderings_Oord(U_299) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP38,sP39])],[f_98_2]) ).
cnf(f_98_4,plain,
( sP39(U_299,U_300,U_301,U_302)
| ~ class_Orderings_Oord(U_299) ),
inference(clausify,[status(thm)],[f_98_3]) ).
cnf(f_98_5,plain,
( sP38(U_299,U_300,U_301,U_302)
| ~ c_Orderings_Oord__class_Oless(tc_fun(U_300,U_299),U_301,U_302)
| ~ sP39(U_299,U_300,U_301,U_302) ),
inference(clausify,[status(thm)],[f_98_3]) ).
cnf(f_98_6,plain,
( c_Orderings_Oord__class_Oless(tc_fun(U_300,U_299),U_301,U_302)
| c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_302,U_301)
| ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_301,U_302)
| ~ sP39(U_299,U_300,U_301,U_302) ),
inference(clausify,[status(thm)],[f_98_3]) ).
cnf(f_98_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_301,U_302)
| ~ sP38(U_299,U_300,U_301,U_302) ),
inference(clausify,[status(thm)],[f_98_3]) ).
cnf(f_98_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_fun(U_300,U_299),U_302,U_301)
| ~ sP38(U_299,U_300,U_301,U_302) ),
inference(clausify,[status(thm)],[f_98_3]) ).
fof(f_99_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_99_2,plain,
! [U_306,U_305,U_304,U_303] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_304),c_Groups_Oplus__class_Oplus(U_303,U_305,U_306)) = c_Groups_Oplus__class_Oplus(U_303,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_304),U_305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_304),U_306))
| ~ class_RealVector_Oreal__normed__algebra(U_303) ),
inference(variable_rename,[status(thm)],[f_99_1]) ).
fof(f_99_3,plain,
! [U_305,U_304,U_306,U_303] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_304),c_Groups_Oplus__class_Oplus(U_303,U_305,U_306)) = c_Groups_Oplus__class_Oplus(U_303,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_304),U_305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_304),U_306))
| ~ class_RealVector_Oreal__normed__algebra(U_303) ),
inference(definitional_conversion,[status(esa)],[f_99_2]) ).
cnf(f_99_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_304),c_Groups_Oplus__class_Oplus(U_303,U_305,U_306)) = c_Groups_Oplus__class_Oplus(U_303,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_304),U_305),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_303),U_304),U_306))
| ~ class_RealVector_Oreal__normed__algebra(U_303) ),
inference(clausify,[status(thm)],[f_99_3]) ).
fof(f_100_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_100_2,plain,
! [U_310,U_309,U_308,U_307] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_308),c_Groups_Oplus__class_Oplus(U_307,U_309,U_310)) = c_Groups_Oplus__class_Oplus(U_307,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_308),U_309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_308),U_310))
| ~ class_RealVector_Oreal__normed__algebra(U_307) ),
inference(variable_rename,[status(thm)],[f_100_1]) ).
fof(f_100_3,plain,
! [U_307,U_308,U_309,U_310] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_308),c_Groups_Oplus__class_Oplus(U_307,U_309,U_310)) = c_Groups_Oplus__class_Oplus(U_307,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_308),U_309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_308),U_310))
| ~ class_RealVector_Oreal__normed__algebra(U_307) ),
inference(definitional_conversion,[status(esa)],[f_100_2]) ).
cnf(f_100_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_308),c_Groups_Oplus__class_Oplus(U_307,U_309,U_310)) = c_Groups_Oplus__class_Oplus(U_307,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_308),U_309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_307),U_308),U_310))
| ~ class_RealVector_Oreal__normed__algebra(U_307) ),
inference(clausify,[status(thm)],[f_100_3]) ).
fof(f_101_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_101_2,plain,
! [U_313,U_312,U_311] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_311),U_312)),U_313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_312),U_313)),
inference(variable_rename,[status(thm)],[f_101_1]) ).
fof(f_101_3,plain,
! [U_311,U_312,U_313] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_311),U_312)),U_313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_312),U_313)),
inference(definitional_conversion,[status(esa)],[f_101_2]) ).
cnf(f_101_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_311),U_312)),U_313) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_311),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_312),U_313)),
inference(clausify,[status(thm)],[f_101_3]) ).
fof(f_102_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_102_2,plain,
! [U_317,U_316,U_315,U_314] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_314),c_Groups_Oplus__class_Oplus(U_314,U_315,U_316)),U_317) = c_Groups_Oplus__class_Oplus(U_314,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_314),U_315),U_317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_314),U_316),U_317))
| ~ class_RealVector_Oreal__normed__algebra(U_314) ),
inference(variable_rename,[status(thm)],[f_102_1]) ).
fof(f_102_3,plain,
! [U_314,U_315,U_316,U_317] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_314),c_Groups_Oplus__class_Oplus(U_314,U_315,U_316)),U_317) = c_Groups_Oplus__class_Oplus(U_314,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_314),U_315),U_317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_314),U_316),U_317))
| ~ class_RealVector_Oreal__normed__algebra(U_314) ),
inference(definitional_conversion,[status(esa)],[f_102_2]) ).
cnf(f_102_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_314),c_Groups_Oplus__class_Oplus(U_314,U_315,U_316)),U_317) = c_Groups_Oplus__class_Oplus(U_314,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_314),U_315),U_317),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_314),U_316),U_317))
| ~ class_RealVector_Oreal__normed__algebra(U_314) ),
inference(clausify,[status(thm)],[f_102_3]) ).
fof(f_103_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_103_2,plain,
! [U_321,U_320,U_319,U_318] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),c_Groups_Oplus__class_Oplus(U_318,U_319,U_320)),U_321) = c_Groups_Oplus__class_Oplus(U_318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),U_319),U_321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),U_320),U_321))
| ~ class_RealVector_Oreal__normed__algebra(U_318) ),
inference(variable_rename,[status(thm)],[f_103_1]) ).
fof(f_103_3,plain,
! [U_318,U_319,U_320,U_321] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),c_Groups_Oplus__class_Oplus(U_318,U_319,U_320)),U_321) = c_Groups_Oplus__class_Oplus(U_318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),U_319),U_321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),U_320),U_321))
| ~ class_RealVector_Oreal__normed__algebra(U_318) ),
inference(definitional_conversion,[status(esa)],[f_103_2]) ).
cnf(f_103_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),c_Groups_Oplus__class_Oplus(U_318,U_319,U_320)),U_321) = c_Groups_Oplus__class_Oplus(U_318,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),U_319),U_321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_318),U_320),U_321))
| ~ class_RealVector_Oreal__normed__algebra(U_318) ),
inference(clausify,[status(thm)],[f_103_3]) ).
fof(f_104_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_104_2,plain,
! [U_324,U_323,U_322] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_322,U_323)),U_324) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_322),U_324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_323),U_324)),
inference(variable_rename,[status(thm)],[f_104_1]) ).
fof(f_104_3,plain,
! [U_322,U_323,U_324] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_322,U_323)),U_324) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_322),U_324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_323),U_324)),
inference(definitional_conversion,[status(esa)],[f_104_2]) ).
cnf(f_104_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_322,U_323)),U_324) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_322),U_324),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_323),U_324)),
inference(clausify,[status(thm)],[f_104_3]) ).
fof(f_105_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_105_2,plain,
! [U_330,U_329,U_328,U_327,U_326,U_325] :
( c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Oplus__class_Oplus(U_325,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_325),U_329),U_326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_325),U_330),U_328)),U_327)
| c_Groups_Oplus__class_Oplus(U_325,U_329,U_330) != c_Groups_Oone__class_Oone(U_325)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ozero__class_Ozero(U_325),U_330)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ozero__class_Ozero(U_325),U_329)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,U_328,U_327)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,U_326,U_327)
| ~ class_Rings_Olinordered__semiring__1(U_325) ),
inference(variable_rename,[status(thm)],[f_105_1]) ).
fof(f_105_3,plain,
! [U_325,U_326,U_327,U_328,U_329,U_330] :
( c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Oplus__class_Oplus(U_325,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_325),U_329),U_326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_325),U_330),U_328)),U_327)
| c_Groups_Oplus__class_Oplus(U_325,U_329,U_330) != c_Groups_Oone__class_Oone(U_325)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ozero__class_Ozero(U_325),U_330)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ozero__class_Ozero(U_325),U_329)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,U_328,U_327)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,U_326,U_327)
| ~ class_Rings_Olinordered__semiring__1(U_325) ),
inference(definitional_conversion,[status(esa)],[f_105_2]) ).
cnf(f_105_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Oplus__class_Oplus(U_325,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_325),U_329),U_326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_325),U_330),U_328)),U_327)
| c_Groups_Oplus__class_Oplus(U_325,U_329,U_330) != c_Groups_Oone__class_Oone(U_325)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ozero__class_Ozero(U_325),U_330)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,c_Groups_Ozero__class_Ozero(U_325),U_329)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,U_328,U_327)
| ~ c_Orderings_Oord__class_Oless__eq(U_325,U_326,U_327)
| ~ class_Rings_Olinordered__semiring__1(U_325) ),
inference(clausify,[status(thm)],[f_105_3]) ).
fof(f_106_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_106_2,plain,
! [U_334,U_333,U_332,U_331] :
( U_332 = U_334
| c_Groups_Oplus__class_Oplus(U_331,U_332,U_333) != c_Groups_Oplus__class_Oplus(U_331,U_334,U_333)
| ~ class_Groups_Ocancel__semigroup__add(U_331) ),
inference(variable_rename,[status(thm)],[f_106_1]) ).
fof(f_106_3,plain,
! [U_333,U_334,U_331,U_332] :
( U_332 = U_334
| c_Groups_Oplus__class_Oplus(U_331,U_332,U_333) != c_Groups_Oplus__class_Oplus(U_331,U_334,U_333)
| ~ class_Groups_Ocancel__semigroup__add(U_331) ),
inference(definitional_conversion,[status(esa)],[f_106_2]) ).
cnf(f_106_4,plain,
( U_332 = U_334
| c_Groups_Oplus__class_Oplus(U_331,U_332,U_333) != c_Groups_Oplus__class_Oplus(U_331,U_334,U_333)
| ~ class_Groups_Ocancel__semigroup__add(U_331) ),
inference(clausify,[status(thm)],[f_106_3]) ).
fof(f_107_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_107_2,plain,
! [U_338,U_337,U_336,U_335] :
( U_337 = U_338
| c_Groups_Oplus__class_Oplus(U_335,U_336,U_337) != c_Groups_Oplus__class_Oplus(U_335,U_336,U_338)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_335) ),
inference(variable_rename,[status(thm)],[f_107_1]) ).
fof(f_107_3,plain,
! [U_336,U_335,U_337,U_338] :
( U_337 = U_338
| c_Groups_Oplus__class_Oplus(U_335,U_336,U_337) != c_Groups_Oplus__class_Oplus(U_335,U_336,U_338)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_335) ),
inference(definitional_conversion,[status(esa)],[f_107_2]) ).
cnf(f_107_4,plain,
( U_337 = U_338
| c_Groups_Oplus__class_Oplus(U_335,U_336,U_337) != c_Groups_Oplus__class_Oplus(U_335,U_336,U_338)
| ~ class_Groups_Ocancel__ab__semigroup__add(U_335) ),
inference(clausify,[status(thm)],[f_107_3]) ).
fof(f_108_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_108_2,plain,
! [U_342,U_341,U_340,U_339] :
( U_341 = U_342
| c_Groups_Oplus__class_Oplus(U_339,U_340,U_341) != c_Groups_Oplus__class_Oplus(U_339,U_340,U_342)
| ~ class_Groups_Ocancel__semigroup__add(U_339) ),
inference(variable_rename,[status(thm)],[f_108_1]) ).
fof(f_108_3,plain,
! [U_339,U_340,U_341,U_342] :
( U_341 = U_342
| c_Groups_Oplus__class_Oplus(U_339,U_340,U_341) != c_Groups_Oplus__class_Oplus(U_339,U_340,U_342)
| ~ class_Groups_Ocancel__semigroup__add(U_339) ),
inference(definitional_conversion,[status(esa)],[f_108_2]) ).
cnf(f_108_4,plain,
( U_341 = U_342
| c_Groups_Oplus__class_Oplus(U_339,U_340,U_341) != c_Groups_Oplus__class_Oplus(U_339,U_340,U_342)
| ~ class_Groups_Ocancel__semigroup__add(U_339) ),
inference(clausify,[status(thm)],[f_108_3]) ).
fof(f_109_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_109_2,plain,
! [U_347,U_346,U_345,U_344,U_343] :
( c_Orderings_Oord__class_Oless(U_343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_343),c_Groups_Oabs__class_Oabs(U_343,U_344)),c_Groups_Oabs__class_Oabs(U_343,U_346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_343),U_345),U_347))
| ~ c_Orderings_Oord__class_Oless(U_343,c_Groups_Oabs__class_Oabs(U_343,U_346),U_347)
| ~ c_Orderings_Oord__class_Oless(U_343,c_Groups_Oabs__class_Oabs(U_343,U_344),U_345)
| ~ class_Rings_Olinordered__idom(U_343) ),
inference(variable_rename,[status(thm)],[f_109_1]) ).
fof(f_109_3,plain,
! [U_344,U_345,U_346,U_347,U_343] :
( c_Orderings_Oord__class_Oless(U_343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_343),c_Groups_Oabs__class_Oabs(U_343,U_344)),c_Groups_Oabs__class_Oabs(U_343,U_346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_343),U_345),U_347))
| ~ c_Orderings_Oord__class_Oless(U_343,c_Groups_Oabs__class_Oabs(U_343,U_346),U_347)
| ~ c_Orderings_Oord__class_Oless(U_343,c_Groups_Oabs__class_Oabs(U_343,U_344),U_345)
| ~ class_Rings_Olinordered__idom(U_343) ),
inference(definitional_conversion,[status(esa)],[f_109_2]) ).
cnf(f_109_4,plain,
( c_Orderings_Oord__class_Oless(U_343,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_343),c_Groups_Oabs__class_Oabs(U_343,U_344)),c_Groups_Oabs__class_Oabs(U_343,U_346)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_343),U_345),U_347))
| ~ c_Orderings_Oord__class_Oless(U_343,c_Groups_Oabs__class_Oabs(U_343,U_346),U_347)
| ~ c_Orderings_Oord__class_Oless(U_343,c_Groups_Oabs__class_Oabs(U_343,U_344),U_345)
| ~ class_Rings_Olinordered__idom(U_343) ),
inference(clausify,[status(thm)],[f_109_3]) ).
fof(f_110_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_110_2,plain,
! [U_350,U_349,U_348] :
( c_Orderings_Oord__class_Oless(U_348,c_Groups_Oone__class_Oone(U_348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_349),U_350))
| ~ c_Orderings_Oord__class_Oless(U_348,c_Groups_Oone__class_Oone(U_348),U_350)
| ~ c_Orderings_Oord__class_Oless(U_348,c_Groups_Oone__class_Oone(U_348),U_349)
| ~ class_Rings_Olinordered__semidom(U_348) ),
inference(variable_rename,[status(thm)],[f_110_1]) ).
fof(f_110_3,plain,
! [U_349,U_348,U_350] :
( c_Orderings_Oord__class_Oless(U_348,c_Groups_Oone__class_Oone(U_348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_349),U_350))
| ~ c_Orderings_Oord__class_Oless(U_348,c_Groups_Oone__class_Oone(U_348),U_350)
| ~ c_Orderings_Oord__class_Oless(U_348,c_Groups_Oone__class_Oone(U_348),U_349)
| ~ class_Rings_Olinordered__semidom(U_348) ),
inference(definitional_conversion,[status(esa)],[f_110_2]) ).
cnf(f_110_4,plain,
( c_Orderings_Oord__class_Oless(U_348,c_Groups_Oone__class_Oone(U_348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_348),U_349),U_350))
| ~ c_Orderings_Oord__class_Oless(U_348,c_Groups_Oone__class_Oone(U_348),U_350)
| ~ c_Orderings_Oord__class_Oless(U_348,c_Groups_Oone__class_Oone(U_348),U_349)
| ~ class_Rings_Olinordered__semidom(U_348) ),
inference(clausify,[status(thm)],[f_110_3]) ).
fof(f_111_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_111_2,plain,
! [U_355,U_354,U_353,U_352,U_351] :
( c_Groups_Oplus__class_Oplus(U_351,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_351),U_352),U_353),c_Groups_Oplus__class_Oplus(U_351,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_351),U_354),U_353),U_355)) = c_Groups_Oplus__class_Oplus(U_351,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_351),c_Groups_Oplus__class_Oplus(U_351,U_352,U_354)),U_353),U_355)
| ~ class_Rings_Osemiring(U_351) ),
inference(variable_rename,[status(thm)],[f_111_1]) ).
fof(f_111_3,plain,
! [U_353,U_351,U_352,U_354,U_355] :
( c_Groups_Oplus__class_Oplus(U_351,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_351),U_352),U_353),c_Groups_Oplus__class_Oplus(U_351,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_351),U_354),U_353),U_355)) = c_Groups_Oplus__class_Oplus(U_351,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_351),c_Groups_Oplus__class_Oplus(U_351,U_352,U_354)),U_353),U_355)
| ~ class_Rings_Osemiring(U_351) ),
inference(definitional_conversion,[status(esa)],[f_111_2]) ).
cnf(f_111_4,plain,
( c_Groups_Oplus__class_Oplus(U_351,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_351),U_352),U_353),c_Groups_Oplus__class_Oplus(U_351,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_351),U_354),U_353),U_355)) = c_Groups_Oplus__class_Oplus(U_351,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_351),c_Groups_Oplus__class_Oplus(U_351,U_352,U_354)),U_353),U_355)
| ~ class_Rings_Osemiring(U_351) ),
inference(clausify,[status(thm)],[f_111_3]) ).
fof(f_112_1,plain,
! [V_ca_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_ca_2,V_a_2)
| V_b_2 != V_ca_2 )
& ( V_b_2 = V_ca_2
| c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_a_2) != c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__right__cancel]) ).
fof(f_112_2,plain,
! [U_359,U_358,U_357,U_356] :
( ( ( c_Groups_Oplus__class_Oplus(U_356,U_357,U_358) = c_Groups_Oplus__class_Oplus(U_356,U_359,U_358)
| U_357 != U_359 )
& ( U_357 = U_359
| c_Groups_Oplus__class_Oplus(U_356,U_357,U_358) != c_Groups_Oplus__class_Oplus(U_356,U_359,U_358) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_356) ),
inference(variable_rename,[status(thm)],[f_112_1]) ).
fof(f_112_3,plain,
( ! [U_359,U_358,U_357,U_356] :
( c_Groups_Oplus__class_Oplus(U_356,U_357,U_358) = c_Groups_Oplus__class_Oplus(U_356,U_359,U_358)
| U_357 != U_359
| ~ sP40(U_359,U_358,U_357,U_356) )
& ! [U_359,U_358,U_357,U_356] :
( U_357 = U_359
| c_Groups_Oplus__class_Oplus(U_356,U_357,U_358) != c_Groups_Oplus__class_Oplus(U_356,U_359,U_358)
| ~ sP40(U_359,U_358,U_357,U_356) )
& ! [U_359,U_358,U_357,U_356] :
( sP40(U_359,U_358,U_357,U_356)
| ~ class_Groups_Ocancel__semigroup__add(U_356) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40])],[f_112_2]) ).
cnf(f_112_4,plain,
( sP40(U_359,U_358,U_357,U_356)
| ~ class_Groups_Ocancel__semigroup__add(U_356) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_5,plain,
( U_357 = U_359
| c_Groups_Oplus__class_Oplus(U_356,U_357,U_358) != c_Groups_Oplus__class_Oplus(U_356,U_359,U_358)
| ~ sP40(U_359,U_358,U_357,U_356) ),
inference(clausify,[status(thm)],[f_112_3]) ).
cnf(f_112_6,plain,
( c_Groups_Oplus__class_Oplus(U_356,U_357,U_358) = c_Groups_Oplus__class_Oplus(U_356,U_359,U_358)
| U_357 != U_359
| ~ sP40(U_359,U_358,U_357,U_356) ),
inference(clausify,[status(thm)],[f_112_3]) ).
fof(f_113_1,plain,
! [V_ca_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_ca_2)
| V_b_2 != V_ca_2 )
& ( V_b_2 = V_ca_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_ca_2) ) )
| ~ class_Groups_Ocancel__semigroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__left__cancel]) ).
fof(f_113_2,plain,
! [U_363,U_362,U_361,U_360] :
( ( ( c_Groups_Oplus__class_Oplus(U_360,U_361,U_362) = c_Groups_Oplus__class_Oplus(U_360,U_361,U_363)
| U_362 != U_363 )
& ( U_362 = U_363
| c_Groups_Oplus__class_Oplus(U_360,U_361,U_362) != c_Groups_Oplus__class_Oplus(U_360,U_361,U_363) ) )
| ~ class_Groups_Ocancel__semigroup__add(U_360) ),
inference(variable_rename,[status(thm)],[f_113_1]) ).
fof(f_113_3,plain,
( ! [U_360,U_361,U_362,U_363] :
( c_Groups_Oplus__class_Oplus(U_360,U_361,U_362) = c_Groups_Oplus__class_Oplus(U_360,U_361,U_363)
| U_362 != U_363
| ~ sP41(U_360,U_361,U_362,U_363) )
& ! [U_360,U_361,U_362,U_363] :
( U_362 = U_363
| c_Groups_Oplus__class_Oplus(U_360,U_361,U_362) != c_Groups_Oplus__class_Oplus(U_360,U_361,U_363)
| ~ sP41(U_360,U_361,U_362,U_363) )
& ! [U_360,U_361,U_362,U_363] :
( sP41(U_360,U_361,U_362,U_363)
| ~ class_Groups_Ocancel__semigroup__add(U_360) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP41])],[f_113_2]) ).
cnf(f_113_4,plain,
( sP41(U_360,U_361,U_362,U_363)
| ~ class_Groups_Ocancel__semigroup__add(U_360) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_5,plain,
( U_362 = U_363
| c_Groups_Oplus__class_Oplus(U_360,U_361,U_362) != c_Groups_Oplus__class_Oplus(U_360,U_361,U_363)
| ~ sP41(U_360,U_361,U_362,U_363) ),
inference(clausify,[status(thm)],[f_113_3]) ).
cnf(f_113_6,plain,
( c_Groups_Oplus__class_Oplus(U_360,U_361,U_362) = c_Groups_Oplus__class_Oplus(U_360,U_361,U_363)
| U_362 != U_363
| ~ sP41(U_360,U_361,U_362,U_363) ),
inference(clausify,[status(thm)],[f_113_3]) ).
fof(f_114_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_114_2,plain,
! [U_367,U_366,U_365,U_364] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_364),c_Groups_Oplus__class_Oplus(U_364,U_365,U_366)),U_367) = c_Groups_Oplus__class_Oplus(U_364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_364),U_365),U_367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_364),U_366),U_367))
| ~ class_Rings_Ocomm__semiring(U_364) ),
inference(variable_rename,[status(thm)],[f_114_1]) ).
fof(f_114_3,plain,
! [U_365,U_364,U_366,U_367] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_364),c_Groups_Oplus__class_Oplus(U_364,U_365,U_366)),U_367) = c_Groups_Oplus__class_Oplus(U_364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_364),U_365),U_367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_364),U_366),U_367))
| ~ class_Rings_Ocomm__semiring(U_364) ),
inference(definitional_conversion,[status(esa)],[f_114_2]) ).
cnf(f_114_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_364),c_Groups_Oplus__class_Oplus(U_364,U_365,U_366)),U_367) = c_Groups_Oplus__class_Oplus(U_364,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_364),U_365),U_367),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_364),U_366),U_367))
| ~ class_Rings_Ocomm__semiring(U_364) ),
inference(clausify,[status(thm)],[f_114_3]) ).
fof(f_115_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_115_2,plain,
! [U_371,U_370,U_369,U_368] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_369),U_370)),U_371) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_370),U_371))
| ~ class_Groups_Oab__semigroup__mult(U_368) ),
inference(variable_rename,[status(thm)],[f_115_1]) ).
fof(f_115_3,plain,
! [U_368,U_369,U_370,U_371] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_369),U_370)),U_371) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_370),U_371))
| ~ class_Groups_Oab__semigroup__mult(U_368) ),
inference(definitional_conversion,[status(esa)],[f_115_2]) ).
cnf(f_115_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_369),U_370)),U_371) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_368),U_370),U_371))
| ~ class_Groups_Oab__semigroup__mult(U_368) ),
inference(clausify,[status(thm)],[f_115_3]) ).
fof(f_116_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_116_2,plain,
! [U_375,U_374,U_373,U_372] :
( c_Groups_Oplus__class_Oplus(U_372,c_Groups_Oplus__class_Oplus(U_372,U_373,U_374),U_375) = c_Groups_Oplus__class_Oplus(U_372,U_373,c_Groups_Oplus__class_Oplus(U_372,U_374,U_375))
| ~ class_Groups_Oab__semigroup__add(U_372) ),
inference(variable_rename,[status(thm)],[f_116_1]) ).
fof(f_116_3,plain,
! [U_373,U_372,U_374,U_375] :
( c_Groups_Oplus__class_Oplus(U_372,c_Groups_Oplus__class_Oplus(U_372,U_373,U_374),U_375) = c_Groups_Oplus__class_Oplus(U_372,U_373,c_Groups_Oplus__class_Oplus(U_372,U_374,U_375))
| ~ class_Groups_Oab__semigroup__add(U_372) ),
inference(definitional_conversion,[status(esa)],[f_116_2]) ).
cnf(f_116_4,plain,
( c_Groups_Oplus__class_Oplus(U_372,c_Groups_Oplus__class_Oplus(U_372,U_373,U_374),U_375) = c_Groups_Oplus__class_Oplus(U_372,U_373,c_Groups_Oplus__class_Oplus(U_372,U_374,U_375))
| ~ class_Groups_Oab__semigroup__add(U_372) ),
inference(clausify,[status(thm)],[f_116_3]) ).
fof(f_117_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_117_2,plain,
! [U_377,U_376] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_376),c_Groups_Oabs__class_Oabs(U_376,U_377)),c_Groups_Oabs__class_Oabs(U_376,U_377)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_376),U_377),U_377)
| ~ class_Rings_Olinordered__idom(U_376) ),
inference(variable_rename,[status(thm)],[f_117_1]) ).
fof(f_117_3,plain,
! [U_376,U_377] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_376),c_Groups_Oabs__class_Oabs(U_376,U_377)),c_Groups_Oabs__class_Oabs(U_376,U_377)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_376),U_377),U_377)
| ~ class_Rings_Olinordered__idom(U_376) ),
inference(definitional_conversion,[status(esa)],[f_117_2]) ).
cnf(f_117_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_376),c_Groups_Oabs__class_Oabs(U_376,U_377)),c_Groups_Oabs__class_Oabs(U_376,U_377)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_376),U_377),U_377)
| ~ class_Rings_Olinordered__idom(U_376) ),
inference(clausify,[status(thm)],[f_117_3]) ).
fof(f_118_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_118_2,plain,
! [U_379,U_378] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_378),U_379),c_Groups_Oone__class_Oone(U_378)) = U_379
| ~ class_Groups_Ocomm__monoid__mult(U_378) ),
inference(variable_rename,[status(thm)],[f_118_1]) ).
fof(f_118_3,plain,
! [U_378,U_379] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_378),U_379),c_Groups_Oone__class_Oone(U_378)) = U_379
| ~ class_Groups_Ocomm__monoid__mult(U_378) ),
inference(definitional_conversion,[status(esa)],[f_118_2]) ).
cnf(f_118_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_378),U_379),c_Groups_Oone__class_Oone(U_378)) = U_379
| ~ class_Groups_Ocomm__monoid__mult(U_378) ),
inference(clausify,[status(thm)],[f_118_3]) ).
fof(f_119_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_119_2,plain,
! [U_381,U_380] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_380),U_381),c_Groups_Oone__class_Oone(U_380)) = U_381
| ~ class_Groups_Omonoid__mult(U_380) ),
inference(variable_rename,[status(thm)],[f_119_1]) ).
fof(f_119_3,plain,
! [U_380,U_381] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_380),U_381),c_Groups_Oone__class_Oone(U_380)) = U_381
| ~ class_Groups_Omonoid__mult(U_380) ),
inference(definitional_conversion,[status(esa)],[f_119_2]) ).
cnf(f_119_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_380),U_381),c_Groups_Oone__class_Oone(U_380)) = U_381
| ~ class_Groups_Omonoid__mult(U_380) ),
inference(clausify,[status(thm)],[f_119_3]) ).
fof(f_120_1,plain,
! [V_x_2,T_a] :
( ( ( c_Groups_Oone__class_Oone(T_a) = V_x_2
| V_x_2 != c_Groups_Oone__class_Oone(T_a) )
& ( V_x_2 = c_Groups_Oone__class_Oone(T_a)
| c_Groups_Oone__class_Oone(T_a) != V_x_2 ) )
| ~ class_Groups_Oone(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__reorient]) ).
fof(f_120_2,plain,
! [U_383,U_382] :
( ( ( c_Groups_Oone__class_Oone(U_382) = U_383
| U_383 != c_Groups_Oone__class_Oone(U_382) )
& ( U_383 = c_Groups_Oone__class_Oone(U_382)
| c_Groups_Oone__class_Oone(U_382) != U_383 ) )
| ~ class_Groups_Oone(U_382) ),
inference(variable_rename,[status(thm)],[f_120_1]) ).
fof(f_120_3,plain,
( ! [U_382,U_383] :
( c_Groups_Oone__class_Oone(U_382) = U_383
| U_383 != c_Groups_Oone__class_Oone(U_382)
| ~ sP42(U_382,U_383) )
& ! [U_382,U_383] :
( U_383 = c_Groups_Oone__class_Oone(U_382)
| c_Groups_Oone__class_Oone(U_382) != U_383
| ~ sP42(U_382,U_383) )
& ! [U_382,U_383] :
( sP42(U_382,U_383)
| ~ class_Groups_Oone(U_382) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP42])],[f_120_2]) ).
cnf(f_120_4,plain,
( sP42(U_382,U_383)
| ~ class_Groups_Oone(U_382) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_5,plain,
( U_383 = c_Groups_Oone__class_Oone(U_382)
| c_Groups_Oone__class_Oone(U_382) != U_383
| ~ sP42(U_382,U_383) ),
inference(clausify,[status(thm)],[f_120_3]) ).
cnf(f_120_6,plain,
( c_Groups_Oone__class_Oone(U_382) = U_383
| U_383 != c_Groups_Oone__class_Oone(U_382)
| ~ sP42(U_382,U_383) ),
inference(clausify,[status(thm)],[f_120_3]) ).
fof(f_121_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_121_2,plain,
! [U_385,U_384] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_384),c_Groups_Oone__class_Oone(U_384)),U_385) = U_385
| ~ class_Groups_Ocomm__monoid__mult(U_384) ),
inference(variable_rename,[status(thm)],[f_121_1]) ).
fof(f_121_3,plain,
! [U_385,U_384] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_384),c_Groups_Oone__class_Oone(U_384)),U_385) = U_385
| ~ class_Groups_Ocomm__monoid__mult(U_384) ),
inference(definitional_conversion,[status(esa)],[f_121_2]) ).
cnf(f_121_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_384),c_Groups_Oone__class_Oone(U_384)),U_385) = U_385
| ~ class_Groups_Ocomm__monoid__mult(U_384) ),
inference(clausify,[status(thm)],[f_121_3]) ).
fof(f_122_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_122_2,plain,
! [U_387,U_386] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_386),c_Groups_Oone__class_Oone(U_386)),U_387) = U_387
| ~ class_Groups_Omonoid__mult(U_386) ),
inference(variable_rename,[status(thm)],[f_122_1]) ).
fof(f_122_3,plain,
! [U_386,U_387] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_386),c_Groups_Oone__class_Oone(U_386)),U_387) = U_387
| ~ class_Groups_Omonoid__mult(U_386) ),
inference(definitional_conversion,[status(esa)],[f_122_2]) ).
cnf(f_122_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_386),c_Groups_Oone__class_Oone(U_386)),U_387) = U_387
| ~ class_Groups_Omonoid__mult(U_386) ),
inference(clausify,[status(thm)],[f_122_3]) ).
fof(f_123_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_123_2,plain,
! [U_390,U_389,U_388] :
( c_Groups_Oabs__class_Oabs(U_388,c_Groups_Oplus__class_Oplus(U_388,c_Groups_Oabs__class_Oabs(U_388,U_389),c_Groups_Oabs__class_Oabs(U_388,U_390))) = c_Groups_Oplus__class_Oplus(U_388,c_Groups_Oabs__class_Oabs(U_388,U_389),c_Groups_Oabs__class_Oabs(U_388,U_390))
| ~ class_Groups_Oordered__ab__group__add__abs(U_388) ),
inference(variable_rename,[status(thm)],[f_123_1]) ).
fof(f_123_3,plain,
! [U_388,U_389,U_390] :
( c_Groups_Oabs__class_Oabs(U_388,c_Groups_Oplus__class_Oplus(U_388,c_Groups_Oabs__class_Oabs(U_388,U_389),c_Groups_Oabs__class_Oabs(U_388,U_390))) = c_Groups_Oplus__class_Oplus(U_388,c_Groups_Oabs__class_Oabs(U_388,U_389),c_Groups_Oabs__class_Oabs(U_388,U_390))
| ~ class_Groups_Oordered__ab__group__add__abs(U_388) ),
inference(definitional_conversion,[status(esa)],[f_123_2]) ).
cnf(f_123_4,plain,
( c_Groups_Oabs__class_Oabs(U_388,c_Groups_Oplus__class_Oplus(U_388,c_Groups_Oabs__class_Oabs(U_388,U_389),c_Groups_Oabs__class_Oabs(U_388,U_390))) = c_Groups_Oplus__class_Oplus(U_388,c_Groups_Oabs__class_Oabs(U_388,U_389),c_Groups_Oabs__class_Oabs(U_388,U_390))
| ~ class_Groups_Oordered__ab__group__add__abs(U_388) ),
inference(clausify,[status(thm)],[f_123_3]) ).
fof(f_124_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_124_2,plain,
! [U_393,U_392,U_391] :
( c_Groups_Oabs__class_Oabs(U_391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_391),U_392),U_393)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_391),c_Groups_Oabs__class_Oabs(U_391,U_392)),c_Groups_Oabs__class_Oabs(U_391,U_393))
| ~ class_Rings_Olinordered__idom(U_391) ),
inference(variable_rename,[status(thm)],[f_124_1]) ).
fof(f_124_3,plain,
! [U_391,U_392,U_393] :
( c_Groups_Oabs__class_Oabs(U_391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_391),U_392),U_393)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_391),c_Groups_Oabs__class_Oabs(U_391,U_392)),c_Groups_Oabs__class_Oabs(U_391,U_393))
| ~ class_Rings_Olinordered__idom(U_391) ),
inference(definitional_conversion,[status(esa)],[f_124_2]) ).
cnf(f_124_4,plain,
( c_Groups_Oabs__class_Oabs(U_391,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_391),U_392),U_393)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_391),c_Groups_Oabs__class_Oabs(U_391,U_392)),c_Groups_Oabs__class_Oabs(U_391,U_393))
| ~ class_Rings_Olinordered__idom(U_391) ),
inference(clausify,[status(thm)],[f_124_3]) ).
fof(f_125_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_125_2,plain,
! [U_395,U_394] :
( c_Groups_Oabs__class_Oabs(U_394,c_Groups_Oabs__class_Oabs(U_394,U_395)) = c_Groups_Oabs__class_Oabs(U_394,U_395)
| ~ class_Groups_Oordered__ab__group__add__abs(U_394) ),
inference(variable_rename,[status(thm)],[f_125_1]) ).
fof(f_125_3,plain,
! [U_394,U_395] :
( c_Groups_Oabs__class_Oabs(U_394,c_Groups_Oabs__class_Oabs(U_394,U_395)) = c_Groups_Oabs__class_Oabs(U_394,U_395)
| ~ class_Groups_Oordered__ab__group__add__abs(U_394) ),
inference(definitional_conversion,[status(esa)],[f_125_2]) ).
cnf(f_125_4,plain,
( c_Groups_Oabs__class_Oabs(U_394,c_Groups_Oabs__class_Oabs(U_394,U_395)) = c_Groups_Oabs__class_Oabs(U_394,U_395)
| ~ class_Groups_Oordered__ab__group__add__abs(U_394) ),
inference(clausify,[status(thm)],[f_125_3]) ).
fof(f_126_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_126_2,plain,
! [U_396] :
( c_Groups_Oabs__class_Oabs(U_396,c_Groups_Oone__class_Oone(U_396)) = c_Groups_Oone__class_Oone(U_396)
| ~ class_Rings_Olinordered__idom(U_396) ),
inference(variable_rename,[status(thm)],[f_126_1]) ).
fof(f_126_3,plain,
! [U_396] :
( c_Groups_Oabs__class_Oabs(U_396,c_Groups_Oone__class_Oone(U_396)) = c_Groups_Oone__class_Oone(U_396)
| ~ class_Rings_Olinordered__idom(U_396) ),
inference(definitional_conversion,[status(esa)],[f_126_2]) ).
cnf(f_126_4,plain,
( c_Groups_Oabs__class_Oabs(U_396,c_Groups_Oone__class_Oone(U_396)) = c_Groups_Oone__class_Oone(U_396)
| ~ class_Rings_Olinordered__idom(U_396) ),
inference(clausify,[status(thm)],[f_126_3]) ).
fof(f_127_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_127_2,plain,
! [U_398,U_397] :
( c_Orderings_Oord__class_Oless(U_397,U_398,c_Groups_Oplus__class_Oplus(U_397,U_398,c_Groups_Oone__class_Oone(U_397)))
| ~ class_Rings_Olinordered__semidom(U_397) ),
inference(variable_rename,[status(thm)],[f_127_1]) ).
fof(f_127_3,plain,
! [U_397,U_398] :
( c_Orderings_Oord__class_Oless(U_397,U_398,c_Groups_Oplus__class_Oplus(U_397,U_398,c_Groups_Oone__class_Oone(U_397)))
| ~ class_Rings_Olinordered__semidom(U_397) ),
inference(definitional_conversion,[status(esa)],[f_127_2]) ).
cnf(f_127_4,plain,
( c_Orderings_Oord__class_Oless(U_397,U_398,c_Groups_Oplus__class_Oplus(U_397,U_398,c_Groups_Oone__class_Oone(U_397)))
| ~ class_Rings_Olinordered__semidom(U_397) ),
inference(clausify,[status(thm)],[f_127_3]) ).
fof(f_128_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_128_2,plain,
! [U_399] :
( c_Groups_Oabs__class_Oabs(U_399,c_Groups_Ozero__class_Ozero(U_399)) = c_Groups_Ozero__class_Ozero(U_399)
| ~ class_Groups_Oordered__ab__group__add__abs(U_399) ),
inference(variable_rename,[status(thm)],[f_128_1]) ).
fof(f_128_3,plain,
! [U_399] :
( c_Groups_Oabs__class_Oabs(U_399,c_Groups_Ozero__class_Ozero(U_399)) = c_Groups_Ozero__class_Ozero(U_399)
| ~ class_Groups_Oordered__ab__group__add__abs(U_399) ),
inference(definitional_conversion,[status(esa)],[f_128_2]) ).
cnf(f_128_4,plain,
( c_Groups_Oabs__class_Oabs(U_399,c_Groups_Ozero__class_Ozero(U_399)) = c_Groups_Ozero__class_Ozero(U_399)
| ~ class_Groups_Oordered__ab__group__add__abs(U_399) ),
inference(clausify,[status(thm)],[f_128_3]) ).
fof(f_129_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_129_2,plain,
! [U_401,U_400] :
( ( ( c_Groups_Oabs__class_Oabs(U_400,U_401) = c_Groups_Ozero__class_Ozero(U_400)
| U_401 != c_Groups_Ozero__class_Ozero(U_400) )
& ( U_401 = c_Groups_Ozero__class_Ozero(U_400)
| c_Groups_Oabs__class_Oabs(U_400,U_401) != c_Groups_Ozero__class_Ozero(U_400) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_400) ),
inference(variable_rename,[status(thm)],[f_129_1]) ).
fof(f_129_3,plain,
( ! [U_400,U_401] :
( c_Groups_Oabs__class_Oabs(U_400,U_401) = c_Groups_Ozero__class_Ozero(U_400)
| U_401 != c_Groups_Ozero__class_Ozero(U_400)
| ~ sP43(U_400,U_401) )
& ! [U_400,U_401] :
( U_401 = c_Groups_Ozero__class_Ozero(U_400)
| c_Groups_Oabs__class_Oabs(U_400,U_401) != c_Groups_Ozero__class_Ozero(U_400)
| ~ sP43(U_400,U_401) )
& ! [U_400,U_401] :
( sP43(U_400,U_401)
| ~ class_Groups_Oordered__ab__group__add__abs(U_400) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP43])],[f_129_2]) ).
cnf(f_129_4,plain,
( sP43(U_400,U_401)
| ~ class_Groups_Oordered__ab__group__add__abs(U_400) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_5,plain,
( U_401 = c_Groups_Ozero__class_Ozero(U_400)
| c_Groups_Oabs__class_Oabs(U_400,U_401) != c_Groups_Ozero__class_Ozero(U_400)
| ~ sP43(U_400,U_401) ),
inference(clausify,[status(thm)],[f_129_3]) ).
cnf(f_129_6,plain,
( c_Groups_Oabs__class_Oabs(U_400,U_401) = c_Groups_Ozero__class_Ozero(U_400)
| U_401 != c_Groups_Ozero__class_Ozero(U_400)
| ~ sP43(U_400,U_401) ),
inference(clausify,[status(thm)],[f_129_3]) ).
fof(f_130_1,plain,
! [V_y_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_y_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__two__squares__add__zero__iff]) ).
fof(f_130_2,plain,
! [U_403,U_402] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_402),U_402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_403),U_403)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_403 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_402 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( ( U_403 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_402 = 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_402),U_402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_403),U_403)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_130_1]) ).
fof(f_130_3,plain,
( ! [U_407,U_405] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_405),U_405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_407),U_407)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_407 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_405 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_406,U_404] :
( ( U_406 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
& U_404 = 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_404),U_404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_406),U_406)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_130_2]) ).
fof(f_130_4,plain,
( ! [U_404,U_406] :
( U_406 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP44(U_404,U_406) )
& ! [U_404,U_406] :
( U_404 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP44(U_404,U_406) )
& ! [U_405,U_407] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_405),U_405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_407),U_407)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_407 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_405 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_404,U_406] :
( sP44(U_404,U_406)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_404),U_404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_406),U_406)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_130_3]) ).
cnf(f_130_5,plain,
( sP44(U_404,U_406)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_404),U_404),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_406),U_406)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_130_4]) ).
cnf(f_130_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_405),U_405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_407),U_407)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_407 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_405 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_130_4]) ).
cnf(f_130_7,plain,
( U_404 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP44(U_404,U_406) ),
inference(clausify,[status(thm)],[f_130_4]) ).
cnf(f_130_8,plain,
( U_406 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| ~ sP44(U_404,U_406) ),
inference(clausify,[status(thm)],[f_130_4]) ).
fof(f_131_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_131_2,plain,
! [U_409,U_408] :
( c_Orderings_Oord__class_Oless__eq(U_408,U_409,c_Groups_Oabs__class_Oabs(U_408,U_409))
| ~ class_Groups_Oordered__ab__group__add__abs(U_408) ),
inference(variable_rename,[status(thm)],[f_131_1]) ).
fof(f_131_3,plain,
! [U_408,U_409] :
( c_Orderings_Oord__class_Oless__eq(U_408,U_409,c_Groups_Oabs__class_Oabs(U_408,U_409))
| ~ class_Groups_Oordered__ab__group__add__abs(U_408) ),
inference(definitional_conversion,[status(esa)],[f_131_2]) ).
cnf(f_131_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_408,U_409,c_Groups_Oabs__class_Oabs(U_408,U_409))
| ~ class_Groups_Oordered__ab__group__add__abs(U_408) ),
inference(clausify,[status(thm)],[f_131_3]) ).
fof(f_132_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_132_2,plain,
! [U_412,U_411,U_410] :
( c_Orderings_Oord__class_Oless__eq(U_410,U_411,U_412)
| ~ c_Orderings_Oord__class_Oless__eq(U_410,c_Groups_Oabs__class_Oabs(U_410,U_411),U_412)
| ~ class_Groups_Oordered__ab__group__add__abs(U_410) ),
inference(variable_rename,[status(thm)],[f_132_1]) ).
fof(f_132_3,plain,
! [U_412,U_410,U_411] :
( c_Orderings_Oord__class_Oless__eq(U_410,U_411,U_412)
| ~ c_Orderings_Oord__class_Oless__eq(U_410,c_Groups_Oabs__class_Oabs(U_410,U_411),U_412)
| ~ class_Groups_Oordered__ab__group__add__abs(U_410) ),
inference(definitional_conversion,[status(esa)],[f_132_2]) ).
cnf(f_132_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_410,U_411,U_412)
| ~ c_Orderings_Oord__class_Oless__eq(U_410,c_Groups_Oabs__class_Oabs(U_410,U_411),U_412)
| ~ class_Groups_Oordered__ab__group__add__abs(U_410) ),
inference(clausify,[status(thm)],[f_132_3]) ).
fof(f_133_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_133_2,plain,
! [U_415,U_414,U_413] :
( c_RealVector_Onorm__class_Onorm(U_413,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_413),U_414),U_415)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_413,U_414)),c_RealVector_Onorm__class_Onorm(U_413,U_415))
| ~ class_RealVector_Oreal__normed__div__algebra(U_413) ),
inference(variable_rename,[status(thm)],[f_133_1]) ).
fof(f_133_3,plain,
! [U_414,U_415,U_413] :
( c_RealVector_Onorm__class_Onorm(U_413,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_413),U_414),U_415)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_413,U_414)),c_RealVector_Onorm__class_Onorm(U_413,U_415))
| ~ class_RealVector_Oreal__normed__div__algebra(U_413) ),
inference(definitional_conversion,[status(esa)],[f_133_2]) ).
cnf(f_133_4,plain,
( c_RealVector_Onorm__class_Onorm(U_413,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_413),U_414),U_415)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_413,U_414)),c_RealVector_Onorm__class_Onorm(U_413,U_415))
| ~ class_RealVector_Oreal__normed__div__algebra(U_413) ),
inference(clausify,[status(thm)],[f_133_3]) ).
fof(f_134_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_134_2,plain,
! [U_416] :
( c_RealVector_Onorm__class_Onorm(U_416,c_Groups_Oone__class_Oone(U_416)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_416) ),
inference(variable_rename,[status(thm)],[f_134_1]) ).
fof(f_134_3,plain,
! [U_416] :
( c_RealVector_Onorm__class_Onorm(U_416,c_Groups_Oone__class_Oone(U_416)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_416) ),
inference(definitional_conversion,[status(esa)],[f_134_2]) ).
cnf(f_134_4,plain,
( c_RealVector_Onorm__class_Onorm(U_416,c_Groups_Oone__class_Oone(U_416)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ class_RealVector_Oreal__normed__algebra__1(U_416) ),
inference(clausify,[status(thm)],[f_134_3]) ).
fof(f_135_1,plain,
! [V_q,V_b,V_p,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__pCons]) ).
fof(f_135_2,plain,
! [U_421,U_420,U_419,U_418,U_417] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_417),c_Polynomial_OpCons(U_417,U_418,U_419),c_Polynomial_OpCons(U_417,U_420,U_421)) = c_Polynomial_OpCons(U_417,c_Groups_Oplus__class_Oplus(U_417,U_418,U_420),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_417),U_419,U_421))
| ~ class_Groups_Ocomm__monoid__add(U_417) ),
inference(variable_rename,[status(thm)],[f_135_1]) ).
fof(f_135_3,plain,
! [U_417,U_418,U_419,U_420,U_421] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_417),c_Polynomial_OpCons(U_417,U_418,U_419),c_Polynomial_OpCons(U_417,U_420,U_421)) = c_Polynomial_OpCons(U_417,c_Groups_Oplus__class_Oplus(U_417,U_418,U_420),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_417),U_419,U_421))
| ~ class_Groups_Ocomm__monoid__add(U_417) ),
inference(definitional_conversion,[status(esa)],[f_135_2]) ).
cnf(f_135_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_417),c_Polynomial_OpCons(U_417,U_418,U_419),c_Polynomial_OpCons(U_417,U_420,U_421)) = c_Polynomial_OpCons(U_417,c_Groups_Oplus__class_Oplus(U_417,U_418,U_420),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_417),U_419,U_421))
| ~ class_Groups_Ocomm__monoid__add(U_417) ),
inference(clausify,[status(thm)],[f_135_3]) ).
fof(f_136_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_136_2,plain,
! [U_423,U_422] :
( c_Groups_Oplus__class_Oplus(U_422,c_Groups_Ozero__class_Ozero(U_422),U_423) = U_423
| ~ class_Groups_Omonoid__add(U_422) ),
inference(variable_rename,[status(thm)],[f_136_1]) ).
fof(f_136_3,plain,
! [U_422,U_423] :
( c_Groups_Oplus__class_Oplus(U_422,c_Groups_Ozero__class_Ozero(U_422),U_423) = U_423
| ~ class_Groups_Omonoid__add(U_422) ),
inference(definitional_conversion,[status(esa)],[f_136_2]) ).
cnf(f_136_4,plain,
( c_Groups_Oplus__class_Oplus(U_422,c_Groups_Ozero__class_Ozero(U_422),U_423) = U_423
| ~ class_Groups_Omonoid__add(U_422) ),
inference(clausify,[status(thm)],[f_136_3]) ).
fof(f_137_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_137_2,plain,
! [U_425,U_424] :
( c_Groups_Oplus__class_Oplus(U_424,c_Groups_Ozero__class_Ozero(U_424),U_425) = U_425
| ~ class_Groups_Ocomm__monoid__add(U_424) ),
inference(variable_rename,[status(thm)],[f_137_1]) ).
fof(f_137_3,plain,
! [U_425,U_424] :
( c_Groups_Oplus__class_Oplus(U_424,c_Groups_Ozero__class_Ozero(U_424),U_425) = U_425
| ~ class_Groups_Ocomm__monoid__add(U_424) ),
inference(definitional_conversion,[status(esa)],[f_137_2]) ).
cnf(f_137_4,plain,
( c_Groups_Oplus__class_Oplus(U_424,c_Groups_Ozero__class_Ozero(U_424),U_425) = U_425
| ~ class_Groups_Ocomm__monoid__add(U_424) ),
inference(clausify,[status(thm)],[f_137_3]) ).
fof(f_138_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_138_2,plain,
! [U_427,U_426] :
( ( ( c_Groups_Ozero__class_Ozero(U_426) = c_Groups_Oplus__class_Oplus(U_426,U_427,U_427)
| U_427 != c_Groups_Ozero__class_Ozero(U_426) )
& ( U_427 = c_Groups_Ozero__class_Ozero(U_426)
| c_Groups_Ozero__class_Ozero(U_426) != c_Groups_Oplus__class_Oplus(U_426,U_427,U_427) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_426) ),
inference(variable_rename,[status(thm)],[f_138_1]) ).
fof(f_138_3,plain,
( ! [U_426,U_427] :
( c_Groups_Ozero__class_Ozero(U_426) = c_Groups_Oplus__class_Oplus(U_426,U_427,U_427)
| U_427 != c_Groups_Ozero__class_Ozero(U_426)
| ~ sP45(U_426,U_427) )
& ! [U_426,U_427] :
( U_427 = c_Groups_Ozero__class_Ozero(U_426)
| c_Groups_Ozero__class_Ozero(U_426) != c_Groups_Oplus__class_Oplus(U_426,U_427,U_427)
| ~ sP45(U_426,U_427) )
& ! [U_426,U_427] :
( sP45(U_426,U_427)
| ~ class_Groups_Olinordered__ab__group__add(U_426) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_138_2]) ).
cnf(f_138_4,plain,
( sP45(U_426,U_427)
| ~ class_Groups_Olinordered__ab__group__add(U_426) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_5,plain,
( U_427 = c_Groups_Ozero__class_Ozero(U_426)
| c_Groups_Ozero__class_Ozero(U_426) != c_Groups_Oplus__class_Oplus(U_426,U_427,U_427)
| ~ sP45(U_426,U_427) ),
inference(clausify,[status(thm)],[f_138_3]) ).
cnf(f_138_6,plain,
( c_Groups_Ozero__class_Ozero(U_426) = c_Groups_Oplus__class_Oplus(U_426,U_427,U_427)
| U_427 != c_Groups_Ozero__class_Ozero(U_426)
| ~ sP45(U_426,U_427) ),
inference(clausify,[status(thm)],[f_138_3]) ).
fof(f_139_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_139_2,plain,
! [U_429,U_428] :
( c_Groups_Oplus__class_Oplus(U_428,U_429,c_Groups_Ozero__class_Ozero(U_428)) = U_429
| ~ class_Groups_Omonoid__add(U_428) ),
inference(variable_rename,[status(thm)],[f_139_1]) ).
fof(f_139_3,plain,
! [U_429,U_428] :
( c_Groups_Oplus__class_Oplus(U_428,U_429,c_Groups_Ozero__class_Ozero(U_428)) = U_429
| ~ class_Groups_Omonoid__add(U_428) ),
inference(definitional_conversion,[status(esa)],[f_139_2]) ).
cnf(f_139_4,plain,
( c_Groups_Oplus__class_Oplus(U_428,U_429,c_Groups_Ozero__class_Ozero(U_428)) = U_429
| ~ class_Groups_Omonoid__add(U_428) ),
inference(clausify,[status(thm)],[f_139_3]) ).
fof(f_140_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_140_2,plain,
! [U_431,U_430] :
( c_Groups_Oplus__class_Oplus(U_430,U_431,c_Groups_Ozero__class_Ozero(U_430)) = U_431
| ~ class_Groups_Ocomm__monoid__add(U_430) ),
inference(variable_rename,[status(thm)],[f_140_1]) ).
fof(f_140_3,plain,
! [U_431,U_430] :
( c_Groups_Oplus__class_Oplus(U_430,U_431,c_Groups_Ozero__class_Ozero(U_430)) = U_431
| ~ class_Groups_Ocomm__monoid__add(U_430) ),
inference(definitional_conversion,[status(esa)],[f_140_2]) ).
cnf(f_140_4,plain,
( c_Groups_Oplus__class_Oplus(U_430,U_431,c_Groups_Ozero__class_Ozero(U_430)) = U_431
| ~ class_Groups_Ocomm__monoid__add(U_430) ),
inference(clausify,[status(thm)],[f_140_3]) ).
fof(f_141_1,plain,
! [V_b_2,V_ca_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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__le__cancel__right]) ).
fof(f_141_2,plain,
! [U_435,U_434,U_433,U_432] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_432,c_Groups_Oplus__class_Oplus(U_432,U_433,U_434),c_Groups_Oplus__class_Oplus(U_432,U_435,U_434))
| ~ c_Orderings_Oord__class_Oless__eq(U_432,U_433,U_435) )
& ( c_Orderings_Oord__class_Oless__eq(U_432,U_433,U_435)
| ~ c_Orderings_Oord__class_Oless__eq(U_432,c_Groups_Oplus__class_Oplus(U_432,U_433,U_434),c_Groups_Oplus__class_Oplus(U_432,U_435,U_434)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_432) ),
inference(variable_rename,[status(thm)],[f_141_1]) ).
fof(f_141_3,plain,
( ! [U_432,U_433,U_434,U_435] :
( c_Orderings_Oord__class_Oless__eq(U_432,c_Groups_Oplus__class_Oplus(U_432,U_433,U_434),c_Groups_Oplus__class_Oplus(U_432,U_435,U_434))
| ~ c_Orderings_Oord__class_Oless__eq(U_432,U_433,U_435)
| ~ sP46(U_432,U_433,U_434,U_435) )
& ! [U_432,U_433,U_434,U_435] :
( c_Orderings_Oord__class_Oless__eq(U_432,U_433,U_435)
| ~ c_Orderings_Oord__class_Oless__eq(U_432,c_Groups_Oplus__class_Oplus(U_432,U_433,U_434),c_Groups_Oplus__class_Oplus(U_432,U_435,U_434))
| ~ sP46(U_432,U_433,U_434,U_435) )
& ! [U_432,U_433,U_434,U_435] :
( sP46(U_432,U_433,U_434,U_435)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_432) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_141_2]) ).
cnf(f_141_4,plain,
( sP46(U_432,U_433,U_434,U_435)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_432) ),
inference(clausify,[status(thm)],[f_141_3]) ).
cnf(f_141_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_432,U_433,U_435)
| ~ c_Orderings_Oord__class_Oless__eq(U_432,c_Groups_Oplus__class_Oplus(U_432,U_433,U_434),c_Groups_Oplus__class_Oplus(U_432,U_435,U_434))
| ~ sP46(U_432,U_433,U_434,U_435) ),
inference(clausify,[status(thm)],[f_141_3]) ).
cnf(f_141_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_432,c_Groups_Oplus__class_Oplus(U_432,U_433,U_434),c_Groups_Oplus__class_Oplus(U_432,U_435,U_434))
| ~ c_Orderings_Oord__class_Oless__eq(U_432,U_433,U_435)
| ~ sP46(U_432,U_433,U_434,U_435) ),
inference(clausify,[status(thm)],[f_141_3]) ).
fof(f_142_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_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_142_2,plain,
! [U_439,U_438,U_437,U_436] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_436,c_Groups_Oplus__class_Oplus(U_436,U_437,U_438),c_Groups_Oplus__class_Oplus(U_436,U_437,U_439))
| ~ c_Orderings_Oord__class_Oless__eq(U_436,U_438,U_439) )
& ( c_Orderings_Oord__class_Oless__eq(U_436,U_438,U_439)
| ~ c_Orderings_Oord__class_Oless__eq(U_436,c_Groups_Oplus__class_Oplus(U_436,U_437,U_438),c_Groups_Oplus__class_Oplus(U_436,U_437,U_439)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_436) ),
inference(variable_rename,[status(thm)],[f_142_1]) ).
fof(f_142_3,plain,
( ! [U_436,U_437,U_438,U_439] :
( c_Orderings_Oord__class_Oless__eq(U_436,c_Groups_Oplus__class_Oplus(U_436,U_437,U_438),c_Groups_Oplus__class_Oplus(U_436,U_437,U_439))
| ~ c_Orderings_Oord__class_Oless__eq(U_436,U_438,U_439)
| ~ sP47(U_436,U_437,U_438,U_439) )
& ! [U_436,U_437,U_438,U_439] :
( c_Orderings_Oord__class_Oless__eq(U_436,U_438,U_439)
| ~ c_Orderings_Oord__class_Oless__eq(U_436,c_Groups_Oplus__class_Oplus(U_436,U_437,U_438),c_Groups_Oplus__class_Oplus(U_436,U_437,U_439))
| ~ sP47(U_436,U_437,U_438,U_439) )
& ! [U_436,U_437,U_438,U_439] :
( sP47(U_436,U_437,U_438,U_439)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_436) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_142_2]) ).
cnf(f_142_4,plain,
( sP47(U_436,U_437,U_438,U_439)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_436) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_436,U_438,U_439)
| ~ c_Orderings_Oord__class_Oless__eq(U_436,c_Groups_Oplus__class_Oplus(U_436,U_437,U_438),c_Groups_Oplus__class_Oplus(U_436,U_437,U_439))
| ~ sP47(U_436,U_437,U_438,U_439) ),
inference(clausify,[status(thm)],[f_142_3]) ).
cnf(f_142_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_436,c_Groups_Oplus__class_Oplus(U_436,U_437,U_438),c_Groups_Oplus__class_Oplus(U_436,U_437,U_439))
| ~ c_Orderings_Oord__class_Oless__eq(U_436,U_438,U_439)
| ~ sP47(U_436,U_437,U_438,U_439) ),
inference(clausify,[status(thm)],[f_142_3]) ).
fof(f_143_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_143_2,plain,
! [U_443,U_442,U_441,U_440] :
( c_Orderings_Oord__class_Oless__eq(U_440,c_Groups_Oplus__class_Oplus(U_440,U_441,U_443),c_Groups_Oplus__class_Oplus(U_440,U_442,U_443))
| ~ c_Orderings_Oord__class_Oless__eq(U_440,U_441,U_442)
| ~ class_Groups_Oordered__ab__semigroup__add(U_440) ),
inference(variable_rename,[status(thm)],[f_143_1]) ).
fof(f_143_3,plain,
! [U_441,U_440,U_442,U_443] :
( c_Orderings_Oord__class_Oless__eq(U_440,c_Groups_Oplus__class_Oplus(U_440,U_441,U_443),c_Groups_Oplus__class_Oplus(U_440,U_442,U_443))
| ~ c_Orderings_Oord__class_Oless__eq(U_440,U_441,U_442)
| ~ class_Groups_Oordered__ab__semigroup__add(U_440) ),
inference(definitional_conversion,[status(esa)],[f_143_2]) ).
cnf(f_143_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_440,c_Groups_Oplus__class_Oplus(U_440,U_441,U_443),c_Groups_Oplus__class_Oplus(U_440,U_442,U_443))
| ~ c_Orderings_Oord__class_Oless__eq(U_440,U_441,U_442)
| ~ class_Groups_Oordered__ab__semigroup__add(U_440) ),
inference(clausify,[status(thm)],[f_143_3]) ).
fof(f_144_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_144_2,plain,
! [U_447,U_446,U_445,U_444] :
( c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Oplus__class_Oplus(U_444,U_447,U_445),c_Groups_Oplus__class_Oplus(U_444,U_447,U_446))
| ~ c_Orderings_Oord__class_Oless__eq(U_444,U_445,U_446)
| ~ class_Groups_Oordered__ab__semigroup__add(U_444) ),
inference(variable_rename,[status(thm)],[f_144_1]) ).
fof(f_144_3,plain,
! [U_445,U_444,U_446,U_447] :
( c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Oplus__class_Oplus(U_444,U_447,U_445),c_Groups_Oplus__class_Oplus(U_444,U_447,U_446))
| ~ c_Orderings_Oord__class_Oless__eq(U_444,U_445,U_446)
| ~ class_Groups_Oordered__ab__semigroup__add(U_444) ),
inference(definitional_conversion,[status(esa)],[f_144_2]) ).
cnf(f_144_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_444,c_Groups_Oplus__class_Oplus(U_444,U_447,U_445),c_Groups_Oplus__class_Oplus(U_444,U_447,U_446))
| ~ c_Orderings_Oord__class_Oless__eq(U_444,U_445,U_446)
| ~ class_Groups_Oordered__ab__semigroup__add(U_444) ),
inference(clausify,[status(thm)],[f_144_3]) ).
fof(f_145_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_145_2,plain,
! [U_452,U_451,U_450,U_449,U_448] :
( c_Orderings_Oord__class_Oless__eq(U_448,c_Groups_Oplus__class_Oplus(U_448,U_449,U_451),c_Groups_Oplus__class_Oplus(U_448,U_450,U_452))
| ~ c_Orderings_Oord__class_Oless__eq(U_448,U_451,U_452)
| ~ c_Orderings_Oord__class_Oless__eq(U_448,U_449,U_450)
| ~ class_Groups_Oordered__ab__semigroup__add(U_448) ),
inference(variable_rename,[status(thm)],[f_145_1]) ).
fof(f_145_3,plain,
! [U_451,U_452,U_450,U_449,U_448] :
( c_Orderings_Oord__class_Oless__eq(U_448,c_Groups_Oplus__class_Oplus(U_448,U_449,U_451),c_Groups_Oplus__class_Oplus(U_448,U_450,U_452))
| ~ c_Orderings_Oord__class_Oless__eq(U_448,U_451,U_452)
| ~ c_Orderings_Oord__class_Oless__eq(U_448,U_449,U_450)
| ~ class_Groups_Oordered__ab__semigroup__add(U_448) ),
inference(definitional_conversion,[status(esa)],[f_145_2]) ).
cnf(f_145_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_448,c_Groups_Oplus__class_Oplus(U_448,U_449,U_451),c_Groups_Oplus__class_Oplus(U_448,U_450,U_452))
| ~ c_Orderings_Oord__class_Oless__eq(U_448,U_451,U_452)
| ~ c_Orderings_Oord__class_Oless__eq(U_448,U_449,U_450)
| ~ class_Groups_Oordered__ab__semigroup__add(U_448) ),
inference(clausify,[status(thm)],[f_145_3]) ).
fof(f_146_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_146_2,plain,
! [U_456,U_455,U_454,U_453] :
( c_Orderings_Oord__class_Oless__eq(U_453,U_454,U_456)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,c_Groups_Oplus__class_Oplus(U_453,U_454,U_455),c_Groups_Oplus__class_Oplus(U_453,U_456,U_455))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_453) ),
inference(variable_rename,[status(thm)],[f_146_1]) ).
fof(f_146_3,plain,
! [U_456,U_455,U_453,U_454] :
( c_Orderings_Oord__class_Oless__eq(U_453,U_454,U_456)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,c_Groups_Oplus__class_Oplus(U_453,U_454,U_455),c_Groups_Oplus__class_Oplus(U_453,U_456,U_455))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_453) ),
inference(definitional_conversion,[status(esa)],[f_146_2]) ).
cnf(f_146_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_453,U_454,U_456)
| ~ c_Orderings_Oord__class_Oless__eq(U_453,c_Groups_Oplus__class_Oplus(U_453,U_454,U_455),c_Groups_Oplus__class_Oplus(U_453,U_456,U_455))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_453) ),
inference(clausify,[status(thm)],[f_146_3]) ).
fof(f_147_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_147_2,plain,
! [U_460,U_459,U_458,U_457] :
( c_Orderings_Oord__class_Oless__eq(U_457,U_459,U_460)
| ~ c_Orderings_Oord__class_Oless__eq(U_457,c_Groups_Oplus__class_Oplus(U_457,U_458,U_459),c_Groups_Oplus__class_Oplus(U_457,U_458,U_460))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_457) ),
inference(variable_rename,[status(thm)],[f_147_1]) ).
fof(f_147_3,plain,
! [U_459,U_458,U_457,U_460] :
( c_Orderings_Oord__class_Oless__eq(U_457,U_459,U_460)
| ~ c_Orderings_Oord__class_Oless__eq(U_457,c_Groups_Oplus__class_Oplus(U_457,U_458,U_459),c_Groups_Oplus__class_Oplus(U_457,U_458,U_460))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_457) ),
inference(definitional_conversion,[status(esa)],[f_147_2]) ).
cnf(f_147_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_457,U_459,U_460)
| ~ c_Orderings_Oord__class_Oless__eq(U_457,c_Groups_Oplus__class_Oplus(U_457,U_458,U_459),c_Groups_Oplus__class_Oplus(U_457,U_458,U_460))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_457) ),
inference(clausify,[status(thm)],[f_147_3]) ).
fof(f_148_1,plain,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_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_ca_2),c_Groups_Oplus__class_Oplus(T_a,V_b_2,V_ca_2)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__less__cancel__right]) ).
fof(f_148_2,plain,
! [U_464,U_463,U_462,U_461] :
( ( ( c_Orderings_Oord__class_Oless(U_461,c_Groups_Oplus__class_Oplus(U_461,U_462,U_463),c_Groups_Oplus__class_Oplus(U_461,U_464,U_463))
| ~ c_Orderings_Oord__class_Oless(U_461,U_462,U_464) )
& ( c_Orderings_Oord__class_Oless(U_461,U_462,U_464)
| ~ c_Orderings_Oord__class_Oless(U_461,c_Groups_Oplus__class_Oplus(U_461,U_462,U_463),c_Groups_Oplus__class_Oplus(U_461,U_464,U_463)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_461) ),
inference(variable_rename,[status(thm)],[f_148_1]) ).
fof(f_148_3,plain,
( ! [U_463,U_461,U_462,U_464] :
( c_Orderings_Oord__class_Oless(U_461,c_Groups_Oplus__class_Oplus(U_461,U_462,U_463),c_Groups_Oplus__class_Oplus(U_461,U_464,U_463))
| ~ c_Orderings_Oord__class_Oless(U_461,U_462,U_464)
| ~ sP48(U_463,U_461,U_462,U_464) )
& ! [U_463,U_461,U_462,U_464] :
( c_Orderings_Oord__class_Oless(U_461,U_462,U_464)
| ~ c_Orderings_Oord__class_Oless(U_461,c_Groups_Oplus__class_Oplus(U_461,U_462,U_463),c_Groups_Oplus__class_Oplus(U_461,U_464,U_463))
| ~ sP48(U_463,U_461,U_462,U_464) )
& ! [U_463,U_461,U_462,U_464] :
( sP48(U_463,U_461,U_462,U_464)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_461) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_148_2]) ).
cnf(f_148_4,plain,
( sP48(U_463,U_461,U_462,U_464)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_461) ),
inference(clausify,[status(thm)],[f_148_3]) ).
cnf(f_148_5,plain,
( c_Orderings_Oord__class_Oless(U_461,U_462,U_464)
| ~ c_Orderings_Oord__class_Oless(U_461,c_Groups_Oplus__class_Oplus(U_461,U_462,U_463),c_Groups_Oplus__class_Oplus(U_461,U_464,U_463))
| ~ sP48(U_463,U_461,U_462,U_464) ),
inference(clausify,[status(thm)],[f_148_3]) ).
cnf(f_148_6,plain,
( c_Orderings_Oord__class_Oless(U_461,c_Groups_Oplus__class_Oplus(U_461,U_462,U_463),c_Groups_Oplus__class_Oplus(U_461,U_464,U_463))
| ~ c_Orderings_Oord__class_Oless(U_461,U_462,U_464)
| ~ sP48(U_463,U_461,U_462,U_464) ),
inference(clausify,[status(thm)],[f_148_3]) ).
fof(f_149_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oplus__class_Oplus(T_a,V_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_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_ca_2,V_a_2),c_Groups_Oplus__class_Oplus(T_a,V_ca_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_149_2,plain,
! [U_468,U_467,U_466,U_465] :
( ( ( c_Orderings_Oord__class_Oless(U_465,c_Groups_Oplus__class_Oplus(U_465,U_466,U_467),c_Groups_Oplus__class_Oplus(U_465,U_466,U_468))
| ~ c_Orderings_Oord__class_Oless(U_465,U_467,U_468) )
& ( c_Orderings_Oord__class_Oless(U_465,U_467,U_468)
| ~ c_Orderings_Oord__class_Oless(U_465,c_Groups_Oplus__class_Oplus(U_465,U_466,U_467),c_Groups_Oplus__class_Oplus(U_465,U_466,U_468)) ) )
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_465) ),
inference(variable_rename,[status(thm)],[f_149_1]) ).
fof(f_149_3,plain,
( ! [U_468,U_466,U_465,U_467] :
( c_Orderings_Oord__class_Oless(U_465,c_Groups_Oplus__class_Oplus(U_465,U_466,U_467),c_Groups_Oplus__class_Oplus(U_465,U_466,U_468))
| ~ c_Orderings_Oord__class_Oless(U_465,U_467,U_468)
| ~ sP49(U_468,U_466,U_465,U_467) )
& ! [U_468,U_466,U_465,U_467] :
( c_Orderings_Oord__class_Oless(U_465,U_467,U_468)
| ~ c_Orderings_Oord__class_Oless(U_465,c_Groups_Oplus__class_Oplus(U_465,U_466,U_467),c_Groups_Oplus__class_Oplus(U_465,U_466,U_468))
| ~ sP49(U_468,U_466,U_465,U_467) )
& ! [U_468,U_466,U_465,U_467] :
( sP49(U_468,U_466,U_465,U_467)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_465) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_149_2]) ).
cnf(f_149_4,plain,
( sP49(U_468,U_466,U_465,U_467)
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_465) ),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_5,plain,
( c_Orderings_Oord__class_Oless(U_465,U_467,U_468)
| ~ c_Orderings_Oord__class_Oless(U_465,c_Groups_Oplus__class_Oplus(U_465,U_466,U_467),c_Groups_Oplus__class_Oplus(U_465,U_466,U_468))
| ~ sP49(U_468,U_466,U_465,U_467) ),
inference(clausify,[status(thm)],[f_149_3]) ).
cnf(f_149_6,plain,
( c_Orderings_Oord__class_Oless(U_465,c_Groups_Oplus__class_Oplus(U_465,U_466,U_467),c_Groups_Oplus__class_Oplus(U_465,U_466,U_468))
| ~ c_Orderings_Oord__class_Oless(U_465,U_467,U_468)
| ~ sP49(U_468,U_466,U_465,U_467) ),
inference(clausify,[status(thm)],[f_149_3]) ).
fof(f_150_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_150_2,plain,
! [U_472,U_471,U_470,U_469] :
( c_Orderings_Oord__class_Oless(U_469,c_Groups_Oplus__class_Oplus(U_469,U_470,U_472),c_Groups_Oplus__class_Oplus(U_469,U_471,U_472))
| ~ c_Orderings_Oord__class_Oless(U_469,U_470,U_471)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_469) ),
inference(variable_rename,[status(thm)],[f_150_1]) ).
fof(f_150_3,plain,
! [U_470,U_469,U_472,U_471] :
( c_Orderings_Oord__class_Oless(U_469,c_Groups_Oplus__class_Oplus(U_469,U_470,U_472),c_Groups_Oplus__class_Oplus(U_469,U_471,U_472))
| ~ c_Orderings_Oord__class_Oless(U_469,U_470,U_471)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_469) ),
inference(definitional_conversion,[status(esa)],[f_150_2]) ).
cnf(f_150_4,plain,
( c_Orderings_Oord__class_Oless(U_469,c_Groups_Oplus__class_Oplus(U_469,U_470,U_472),c_Groups_Oplus__class_Oplus(U_469,U_471,U_472))
| ~ c_Orderings_Oord__class_Oless(U_469,U_470,U_471)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_469) ),
inference(clausify,[status(thm)],[f_150_3]) ).
fof(f_151_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_151_2,plain,
! [U_476,U_475,U_474,U_473] :
( c_Orderings_Oord__class_Oless(U_473,c_Groups_Oplus__class_Oplus(U_473,U_476,U_474),c_Groups_Oplus__class_Oplus(U_473,U_476,U_475))
| ~ c_Orderings_Oord__class_Oless(U_473,U_474,U_475)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_473) ),
inference(variable_rename,[status(thm)],[f_151_1]) ).
fof(f_151_3,plain,
! [U_475,U_476,U_474,U_473] :
( c_Orderings_Oord__class_Oless(U_473,c_Groups_Oplus__class_Oplus(U_473,U_476,U_474),c_Groups_Oplus__class_Oplus(U_473,U_476,U_475))
| ~ c_Orderings_Oord__class_Oless(U_473,U_474,U_475)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_473) ),
inference(definitional_conversion,[status(esa)],[f_151_2]) ).
cnf(f_151_4,plain,
( c_Orderings_Oord__class_Oless(U_473,c_Groups_Oplus__class_Oplus(U_473,U_476,U_474),c_Groups_Oplus__class_Oplus(U_473,U_476,U_475))
| ~ c_Orderings_Oord__class_Oless(U_473,U_474,U_475)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_473) ),
inference(clausify,[status(thm)],[f_151_3]) ).
fof(f_152_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_152_2,plain,
! [U_481,U_480,U_479,U_478,U_477] :
( c_Orderings_Oord__class_Oless(U_477,c_Groups_Oplus__class_Oplus(U_477,U_478,U_480),c_Groups_Oplus__class_Oplus(U_477,U_479,U_481))
| ~ c_Orderings_Oord__class_Oless(U_477,U_480,U_481)
| ~ c_Orderings_Oord__class_Oless(U_477,U_478,U_479)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_477) ),
inference(variable_rename,[status(thm)],[f_152_1]) ).
fof(f_152_3,plain,
! [U_479,U_478,U_477,U_480,U_481] :
( c_Orderings_Oord__class_Oless(U_477,c_Groups_Oplus__class_Oplus(U_477,U_478,U_480),c_Groups_Oplus__class_Oplus(U_477,U_479,U_481))
| ~ c_Orderings_Oord__class_Oless(U_477,U_480,U_481)
| ~ c_Orderings_Oord__class_Oless(U_477,U_478,U_479)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_477) ),
inference(definitional_conversion,[status(esa)],[f_152_2]) ).
cnf(f_152_4,plain,
( c_Orderings_Oord__class_Oless(U_477,c_Groups_Oplus__class_Oplus(U_477,U_478,U_480),c_Groups_Oplus__class_Oplus(U_477,U_479,U_481))
| ~ c_Orderings_Oord__class_Oless(U_477,U_480,U_481)
| ~ c_Orderings_Oord__class_Oless(U_477,U_478,U_479)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_477) ),
inference(clausify,[status(thm)],[f_152_3]) ).
fof(f_153_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_153_2,plain,
! [U_485,U_484,U_483,U_482] :
( c_Orderings_Oord__class_Oless(U_482,U_483,U_485)
| ~ c_Orderings_Oord__class_Oless(U_482,c_Groups_Oplus__class_Oplus(U_482,U_483,U_484),c_Groups_Oplus__class_Oplus(U_482,U_485,U_484))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_482) ),
inference(variable_rename,[status(thm)],[f_153_1]) ).
fof(f_153_3,plain,
! [U_484,U_482,U_483,U_485] :
( c_Orderings_Oord__class_Oless(U_482,U_483,U_485)
| ~ c_Orderings_Oord__class_Oless(U_482,c_Groups_Oplus__class_Oplus(U_482,U_483,U_484),c_Groups_Oplus__class_Oplus(U_482,U_485,U_484))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_482) ),
inference(definitional_conversion,[status(esa)],[f_153_2]) ).
cnf(f_153_4,plain,
( c_Orderings_Oord__class_Oless(U_482,U_483,U_485)
| ~ c_Orderings_Oord__class_Oless(U_482,c_Groups_Oplus__class_Oplus(U_482,U_483,U_484),c_Groups_Oplus__class_Oplus(U_482,U_485,U_484))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_482) ),
inference(clausify,[status(thm)],[f_153_3]) ).
fof(f_154_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_154_2,plain,
! [U_489,U_488,U_487,U_486] :
( c_Orderings_Oord__class_Oless(U_486,U_488,U_489)
| ~ c_Orderings_Oord__class_Oless(U_486,c_Groups_Oplus__class_Oplus(U_486,U_487,U_488),c_Groups_Oplus__class_Oplus(U_486,U_487,U_489))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_486) ),
inference(variable_rename,[status(thm)],[f_154_1]) ).
fof(f_154_3,plain,
! [U_486,U_488,U_487,U_489] :
( c_Orderings_Oord__class_Oless(U_486,U_488,U_489)
| ~ c_Orderings_Oord__class_Oless(U_486,c_Groups_Oplus__class_Oplus(U_486,U_487,U_488),c_Groups_Oplus__class_Oplus(U_486,U_487,U_489))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_486) ),
inference(definitional_conversion,[status(esa)],[f_154_2]) ).
cnf(f_154_4,plain,
( c_Orderings_Oord__class_Oless(U_486,U_488,U_489)
| ~ c_Orderings_Oord__class_Oless(U_486,c_Groups_Oplus__class_Oplus(U_486,U_487,U_488),c_Groups_Oplus__class_Oplus(U_486,U_487,U_489))
| ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_486) ),
inference(clausify,[status(thm)],[f_154_3]) ).
fof(f_155_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_155_2,plain,
! [U_491,U_490] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_490),c_Groups_Ozero__class_Ozero(U_490)),U_491) = c_Groups_Ozero__class_Ozero(U_490)
| ~ class_Rings_Omult__zero(U_490) ),
inference(variable_rename,[status(thm)],[f_155_1]) ).
fof(f_155_3,plain,
! [U_490,U_491] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_490),c_Groups_Ozero__class_Ozero(U_490)),U_491) = c_Groups_Ozero__class_Ozero(U_490)
| ~ class_Rings_Omult__zero(U_490) ),
inference(definitional_conversion,[status(esa)],[f_155_2]) ).
cnf(f_155_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_490),c_Groups_Ozero__class_Ozero(U_490)),U_491) = c_Groups_Ozero__class_Ozero(U_490)
| ~ class_Rings_Omult__zero(U_490) ),
inference(clausify,[status(thm)],[f_155_3]) ).
fof(f_156_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_156_2,plain,
! [U_493,U_492] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_492),U_493),c_Groups_Ozero__class_Ozero(U_492)) = c_Groups_Ozero__class_Ozero(U_492)
| ~ class_Rings_Omult__zero(U_492) ),
inference(variable_rename,[status(thm)],[f_156_1]) ).
fof(f_156_3,plain,
! [U_492,U_493] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_492),U_493),c_Groups_Ozero__class_Ozero(U_492)) = c_Groups_Ozero__class_Ozero(U_492)
| ~ class_Rings_Omult__zero(U_492) ),
inference(definitional_conversion,[status(esa)],[f_156_2]) ).
cnf(f_156_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_492),U_493),c_Groups_Ozero__class_Ozero(U_492)) = c_Groups_Ozero__class_Ozero(U_492)
| ~ class_Rings_Omult__zero(U_492) ),
inference(clausify,[status(thm)],[f_156_3]) ).
fof(f_157_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_157_2,plain,
! [U_496,U_495,U_494] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_494),U_495),U_496) = c_Groups_Ozero__class_Ozero(U_494)
| ( U_496 != c_Groups_Ozero__class_Ozero(U_494)
& U_495 != c_Groups_Ozero__class_Ozero(U_494) ) )
& ( U_496 = c_Groups_Ozero__class_Ozero(U_494)
| U_495 = c_Groups_Ozero__class_Ozero(U_494)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_494),U_495),U_496) != c_Groups_Ozero__class_Ozero(U_494) ) )
| ~ class_Rings_Oring__no__zero__divisors(U_494) ),
inference(variable_rename,[status(thm)],[f_157_1]) ).
fof(f_157_3,plain,
( ! [U_494,U_495,U_496] :
( U_496 != c_Groups_Ozero__class_Ozero(U_494)
| ~ sP50(U_494,U_495,U_496) )
& ! [U_494,U_495,U_496] :
( U_495 != c_Groups_Ozero__class_Ozero(U_494)
| ~ sP50(U_494,U_495,U_496) )
& ! [U_494,U_495,U_496] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_494),U_495),U_496) = c_Groups_Ozero__class_Ozero(U_494)
| sP50(U_494,U_495,U_496)
| ~ sP51(U_494,U_495,U_496) )
& ! [U_494,U_495,U_496] :
( U_496 = c_Groups_Ozero__class_Ozero(U_494)
| U_495 = c_Groups_Ozero__class_Ozero(U_494)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_494),U_495),U_496) != c_Groups_Ozero__class_Ozero(U_494)
| ~ sP51(U_494,U_495,U_496) )
& ! [U_494,U_495,U_496] :
( sP51(U_494,U_495,U_496)
| ~ class_Rings_Oring__no__zero__divisors(U_494) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50,sP51])],[f_157_2]) ).
cnf(f_157_4,plain,
( sP51(U_494,U_495,U_496)
| ~ class_Rings_Oring__no__zero__divisors(U_494) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_5,plain,
( U_496 = c_Groups_Ozero__class_Ozero(U_494)
| U_495 = c_Groups_Ozero__class_Ozero(U_494)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_494),U_495),U_496) != c_Groups_Ozero__class_Ozero(U_494)
| ~ sP51(U_494,U_495,U_496) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_494),U_495),U_496) = c_Groups_Ozero__class_Ozero(U_494)
| sP50(U_494,U_495,U_496)
| ~ sP51(U_494,U_495,U_496) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_7,plain,
( U_495 != c_Groups_Ozero__class_Ozero(U_494)
| ~ sP50(U_494,U_495,U_496) ),
inference(clausify,[status(thm)],[f_157_3]) ).
cnf(f_157_8,plain,
( U_496 != c_Groups_Ozero__class_Ozero(U_494)
| ~ sP50(U_494,U_495,U_496) ),
inference(clausify,[status(thm)],[f_157_3]) ).
fof(f_158_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_158_2,plain,
! [U_499,U_498,U_497] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_497),U_498),U_499) != c_Groups_Ozero__class_Ozero(U_497)
| U_499 = c_Groups_Ozero__class_Ozero(U_497)
| U_498 = c_Groups_Ozero__class_Ozero(U_497)
| ~ class_Rings_Ono__zero__divisors(U_497) ),
inference(variable_rename,[status(thm)],[f_158_1]) ).
fof(f_158_3,plain,
! [U_498,U_497,U_499] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_497),U_498),U_499) != c_Groups_Ozero__class_Ozero(U_497)
| U_499 = c_Groups_Ozero__class_Ozero(U_497)
| U_498 = c_Groups_Ozero__class_Ozero(U_497)
| ~ class_Rings_Ono__zero__divisors(U_497) ),
inference(definitional_conversion,[status(esa)],[f_158_2]) ).
cnf(f_158_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_497),U_498),U_499) != c_Groups_Ozero__class_Ozero(U_497)
| U_499 = c_Groups_Ozero__class_Ozero(U_497)
| U_498 = c_Groups_Ozero__class_Ozero(U_497)
| ~ class_Rings_Ono__zero__divisors(U_497) ),
inference(clausify,[status(thm)],[f_158_3]) ).
fof(f_159_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_159_2,plain,
! [U_502,U_501,U_500] :
( U_502 = c_Groups_Ozero__class_Ozero(U_500)
| U_501 = c_Groups_Ozero__class_Ozero(U_500)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),U_501),U_502) != c_Groups_Ozero__class_Ozero(U_500)
| ~ class_Rings_Ono__zero__divisors(U_500) ),
inference(variable_rename,[status(thm)],[f_159_1]) ).
fof(f_159_3,plain,
! [U_502,U_501,U_500] :
( U_502 = c_Groups_Ozero__class_Ozero(U_500)
| U_501 = c_Groups_Ozero__class_Ozero(U_500)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),U_501),U_502) != c_Groups_Ozero__class_Ozero(U_500)
| ~ class_Rings_Ono__zero__divisors(U_500) ),
inference(definitional_conversion,[status(esa)],[f_159_2]) ).
cnf(f_159_4,plain,
( U_502 = c_Groups_Ozero__class_Ozero(U_500)
| U_501 = c_Groups_Ozero__class_Ozero(U_500)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_500),U_501),U_502) != c_Groups_Ozero__class_Ozero(U_500)
| ~ class_Rings_Ono__zero__divisors(U_500) ),
inference(clausify,[status(thm)],[f_159_3]) ).
fof(f_160_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_160_2,plain,
! [U_503] :
( c_Groups_Oone__class_Oone(U_503) != c_Groups_Ozero__class_Ozero(U_503)
| ~ class_Rings_Ozero__neq__one(U_503) ),
inference(variable_rename,[status(thm)],[f_160_1]) ).
fof(f_160_3,plain,
! [U_503] :
( c_Groups_Oone__class_Oone(U_503) != c_Groups_Ozero__class_Ozero(U_503)
| ~ class_Rings_Ozero__neq__one(U_503) ),
inference(definitional_conversion,[status(esa)],[f_160_2]) ).
cnf(f_160_4,plain,
( c_Groups_Oone__class_Oone(U_503) != c_Groups_Ozero__class_Ozero(U_503)
| ~ class_Rings_Ozero__neq__one(U_503) ),
inference(clausify,[status(thm)],[f_160_3]) ).
fof(f_161_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_161_2,plain,
! [U_504] :
( c_Groups_Ozero__class_Ozero(U_504) != c_Groups_Oone__class_Oone(U_504)
| ~ class_Rings_Ozero__neq__one(U_504) ),
inference(variable_rename,[status(thm)],[f_161_1]) ).
fof(f_161_3,plain,
! [U_504] :
( c_Groups_Ozero__class_Ozero(U_504) != c_Groups_Oone__class_Oone(U_504)
| ~ class_Rings_Ozero__neq__one(U_504) ),
inference(definitional_conversion,[status(esa)],[f_161_2]) ).
cnf(f_161_4,plain,
( c_Groups_Ozero__class_Ozero(U_504) != c_Groups_Oone__class_Oone(U_504)
| ~ class_Rings_Ozero__neq__one(U_504) ),
inference(clausify,[status(thm)],[f_161_3]) ).
fof(f_162_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Oplus__class_Oplus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__add]) ).
fof(f_162_2,plain,
! [U_508,U_507,U_506,U_505] :
( hAPP(c_Polynomial_Opoly(U_505,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_505),U_506,U_507)),U_508) = c_Groups_Oplus__class_Oplus(U_505,hAPP(c_Polynomial_Opoly(U_505,U_506),U_508),hAPP(c_Polynomial_Opoly(U_505,U_507),U_508))
| ~ class_Rings_Ocomm__semiring__0(U_505) ),
inference(variable_rename,[status(thm)],[f_162_1]) ).
fof(f_162_3,plain,
! [U_505,U_506,U_507,U_508] :
( hAPP(c_Polynomial_Opoly(U_505,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_505),U_506,U_507)),U_508) = c_Groups_Oplus__class_Oplus(U_505,hAPP(c_Polynomial_Opoly(U_505,U_506),U_508),hAPP(c_Polynomial_Opoly(U_505,U_507),U_508))
| ~ class_Rings_Ocomm__semiring__0(U_505) ),
inference(definitional_conversion,[status(esa)],[f_162_2]) ).
cnf(f_162_4,plain,
( hAPP(c_Polynomial_Opoly(U_505,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_505),U_506,U_507)),U_508) = c_Groups_Oplus__class_Oplus(U_505,hAPP(c_Polynomial_Opoly(U_505,U_506),U_508),hAPP(c_Polynomial_Opoly(U_505,U_507),U_508))
| ~ class_Rings_Ocomm__semiring__0(U_505) ),
inference(clausify,[status(thm)],[f_162_3]) ).
fof(f_163_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q)),V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__mult]) ).
fof(f_163_2,plain,
! [U_512,U_511,U_510,U_509] :
( hAPP(c_Polynomial_Opoly(U_509,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_509)),U_510),U_511)),U_512) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_509),hAPP(c_Polynomial_Opoly(U_509,U_510),U_512)),hAPP(c_Polynomial_Opoly(U_509,U_511),U_512))
| ~ class_Rings_Ocomm__semiring__0(U_509) ),
inference(variable_rename,[status(thm)],[f_163_1]) ).
fof(f_163_3,plain,
! [U_509,U_510,U_511,U_512] :
( hAPP(c_Polynomial_Opoly(U_509,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_509)),U_510),U_511)),U_512) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_509),hAPP(c_Polynomial_Opoly(U_509,U_510),U_512)),hAPP(c_Polynomial_Opoly(U_509,U_511),U_512))
| ~ class_Rings_Ocomm__semiring__0(U_509) ),
inference(definitional_conversion,[status(esa)],[f_163_2]) ).
cnf(f_163_4,plain,
( hAPP(c_Polynomial_Opoly(U_509,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_509)),U_510),U_511)),U_512) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_509),hAPP(c_Polynomial_Opoly(U_509,U_510),U_512)),hAPP(c_Polynomial_Opoly(U_509,U_511),U_512))
| ~ class_Rings_Ocomm__semiring__0(U_509) ),
inference(clausify,[status(thm)],[f_163_3]) ).
fof(f_164_1,plain,
! [V_x,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))),V_x) = c_Groups_Oone__class_Oone(T_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__1]) ).
fof(f_164_2,plain,
! [U_514,U_513] :
( hAPP(c_Polynomial_Opoly(U_513,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_513))),U_514) = c_Groups_Oone__class_Oone(U_513)
| ~ class_Rings_Ocomm__semiring__1(U_513) ),
inference(variable_rename,[status(thm)],[f_164_1]) ).
fof(f_164_3,plain,
! [U_513,U_514] :
( hAPP(c_Polynomial_Opoly(U_513,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_513))),U_514) = c_Groups_Oone__class_Oone(U_513)
| ~ class_Rings_Ocomm__semiring__1(U_513) ),
inference(definitional_conversion,[status(esa)],[f_164_2]) ).
cnf(f_164_4,plain,
( hAPP(c_Polynomial_Opoly(U_513,c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_513))),U_514) = c_Groups_Oone__class_Oone(U_513)
| ~ class_Rings_Ocomm__semiring__1(U_513) ),
inference(clausify,[status(thm)],[f_164_3]) ).
fof(f_165_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_165_2,plain,
! [U_515] : 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_515))),
inference(variable_rename,[status(thm)],[f_165_1]) ).
fof(f_165_3,plain,
! [U_515] : 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_515))),
inference(definitional_conversion,[status(esa)],[f_165_2]) ).
cnf(f_165_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_515))),
inference(clausify,[status(thm)],[f_165_3]) ).
fof(f_166_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_166_2,plain,
! [U_518,U_517,U_516] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),c_Groups_Oabs__class_Oabs(U_516,U_518)),U_517) = c_Groups_Oabs__class_Oabs(U_516,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_518),U_517))
| ~ c_Orderings_Oord__class_Oless__eq(U_516,c_Groups_Ozero__class_Ozero(U_516),U_517)
| ~ class_Rings_Olinordered__idom(U_516) ),
inference(variable_rename,[status(thm)],[f_166_1]) ).
fof(f_166_3,plain,
! [U_517,U_518,U_516] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),c_Groups_Oabs__class_Oabs(U_516,U_518)),U_517) = c_Groups_Oabs__class_Oabs(U_516,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_518),U_517))
| ~ c_Orderings_Oord__class_Oless__eq(U_516,c_Groups_Ozero__class_Ozero(U_516),U_517)
| ~ class_Rings_Olinordered__idom(U_516) ),
inference(definitional_conversion,[status(esa)],[f_166_2]) ).
cnf(f_166_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),c_Groups_Oabs__class_Oabs(U_516,U_518)),U_517) = c_Groups_Oabs__class_Oabs(U_516,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_516),U_518),U_517))
| ~ c_Orderings_Oord__class_Oless__eq(U_516,c_Groups_Ozero__class_Ozero(U_516),U_517)
| ~ class_Rings_Olinordered__idom(U_516) ),
inference(clausify,[status(thm)],[f_166_3]) ).
fof(f_167_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_167_2,plain,
! [U_521,U_520,U_519] :
( c_Groups_Oabs__class_Oabs(U_519,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_519),U_520),U_521)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_519),c_Groups_Oabs__class_Oabs(U_519,U_520)),c_Groups_Oabs__class_Oabs(U_519,U_521))
| ( ~ c_Orderings_Oord__class_Oless__eq(U_519,U_521,c_Groups_Ozero__class_Ozero(U_519))
& ~ c_Orderings_Oord__class_Oless__eq(U_519,c_Groups_Ozero__class_Ozero(U_519),U_521) )
| ( ~ c_Orderings_Oord__class_Oless__eq(U_519,U_520,c_Groups_Ozero__class_Ozero(U_519))
& ~ c_Orderings_Oord__class_Oless__eq(U_519,c_Groups_Ozero__class_Ozero(U_519),U_520) )
| ~ class_Rings_Oordered__ring__abs(U_519) ),
inference(variable_rename,[status(thm)],[f_167_1]) ).
fof(f_167_3,plain,
( ! [U_519,U_521] :
( ~ c_Orderings_Oord__class_Oless__eq(U_519,U_521,c_Groups_Ozero__class_Ozero(U_519))
| ~ sP53(U_519,U_521) )
& ! [U_519,U_521] :
( ~ c_Orderings_Oord__class_Oless__eq(U_519,c_Groups_Ozero__class_Ozero(U_519),U_521)
| ~ sP53(U_519,U_521) )
& ! [U_519,U_520] :
( ~ c_Orderings_Oord__class_Oless__eq(U_519,U_520,c_Groups_Ozero__class_Ozero(U_519))
| ~ sP52(U_519,U_520) )
& ! [U_519,U_520] :
( ~ c_Orderings_Oord__class_Oless__eq(U_519,c_Groups_Ozero__class_Ozero(U_519),U_520)
| ~ sP52(U_519,U_520) )
& ! [U_519,U_520,U_521] :
( c_Groups_Oabs__class_Oabs(U_519,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_519),U_520),U_521)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_519),c_Groups_Oabs__class_Oabs(U_519,U_520)),c_Groups_Oabs__class_Oabs(U_519,U_521))
| sP53(U_519,U_521)
| sP52(U_519,U_520)
| ~ class_Rings_Oordered__ring__abs(U_519) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52,sP53])],[f_167_2]) ).
cnf(f_167_4,plain,
( c_Groups_Oabs__class_Oabs(U_519,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_519),U_520),U_521)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_519),c_Groups_Oabs__class_Oabs(U_519,U_520)),c_Groups_Oabs__class_Oabs(U_519,U_521))
| sP53(U_519,U_521)
| sP52(U_519,U_520)
| ~ class_Rings_Oordered__ring__abs(U_519) ),
inference(clausify,[status(thm)],[f_167_3]) ).
cnf(f_167_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_519,c_Groups_Ozero__class_Ozero(U_519),U_520)
| ~ sP52(U_519,U_520) ),
inference(clausify,[status(thm)],[f_167_3]) ).
cnf(f_167_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_519,U_520,c_Groups_Ozero__class_Ozero(U_519))
| ~ sP52(U_519,U_520) ),
inference(clausify,[status(thm)],[f_167_3]) ).
cnf(f_167_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_519,c_Groups_Ozero__class_Ozero(U_519),U_521)
| ~ sP53(U_519,U_521) ),
inference(clausify,[status(thm)],[f_167_3]) ).
cnf(f_167_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_519,U_521,c_Groups_Ozero__class_Ozero(U_519))
| ~ sP53(U_519,U_521) ),
inference(clausify,[status(thm)],[f_167_3]) ).
fof(f_168_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_168_2,plain,
! [U_522] :
( c_Orderings_Oord__class_Oless(U_522,c_Groups_Ozero__class_Ozero(U_522),c_Groups_Oplus__class_Oplus(U_522,c_Groups_Oone__class_Oone(U_522),c_Groups_Oone__class_Oone(U_522)))
| ~ class_Rings_Olinordered__semidom(U_522) ),
inference(variable_rename,[status(thm)],[f_168_1]) ).
fof(f_168_3,plain,
! [U_522] :
( c_Orderings_Oord__class_Oless(U_522,c_Groups_Ozero__class_Ozero(U_522),c_Groups_Oplus__class_Oplus(U_522,c_Groups_Oone__class_Oone(U_522),c_Groups_Oone__class_Oone(U_522)))
| ~ class_Rings_Olinordered__semidom(U_522) ),
inference(definitional_conversion,[status(esa)],[f_168_2]) ).
cnf(f_168_4,plain,
( c_Orderings_Oord__class_Oless(U_522,c_Groups_Ozero__class_Ozero(U_522),c_Groups_Oplus__class_Oplus(U_522,c_Groups_Oone__class_Oone(U_522),c_Groups_Oone__class_Oone(U_522)))
| ~ class_Rings_Olinordered__semidom(U_522) ),
inference(clausify,[status(thm)],[f_168_3]) ).
fof(f_169_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_169_2,plain,
! [U_525,U_524,U_523] :
( c_Orderings_Oord__class_Oless__eq(U_523,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_523),U_524),U_525),U_524)
| ~ c_Orderings_Oord__class_Oless__eq(U_523,U_525,c_Groups_Oone__class_Oone(U_523))
| ~ c_Orderings_Oord__class_Oless__eq(U_523,c_Groups_Ozero__class_Ozero(U_523),U_525)
| ~ c_Orderings_Oord__class_Oless__eq(U_523,c_Groups_Ozero__class_Ozero(U_523),U_524)
| ~ class_Rings_Olinordered__idom(U_523) ),
inference(variable_rename,[status(thm)],[f_169_1]) ).
fof(f_169_3,plain,
! [U_524,U_523,U_525] :
( c_Orderings_Oord__class_Oless__eq(U_523,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_523),U_524),U_525),U_524)
| ~ c_Orderings_Oord__class_Oless__eq(U_523,U_525,c_Groups_Oone__class_Oone(U_523))
| ~ c_Orderings_Oord__class_Oless__eq(U_523,c_Groups_Ozero__class_Ozero(U_523),U_525)
| ~ c_Orderings_Oord__class_Oless__eq(U_523,c_Groups_Ozero__class_Ozero(U_523),U_524)
| ~ class_Rings_Olinordered__idom(U_523) ),
inference(definitional_conversion,[status(esa)],[f_169_2]) ).
cnf(f_169_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_523,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_523),U_524),U_525),U_524)
| ~ c_Orderings_Oord__class_Oless__eq(U_523,U_525,c_Groups_Oone__class_Oone(U_523))
| ~ c_Orderings_Oord__class_Oless__eq(U_523,c_Groups_Ozero__class_Ozero(U_523),U_525)
| ~ c_Orderings_Oord__class_Oless__eq(U_523,c_Groups_Ozero__class_Ozero(U_523),U_524)
| ~ class_Rings_Olinordered__idom(U_523) ),
inference(clausify,[status(thm)],[f_169_3]) ).
fof(f_170_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_170_2,plain,
! [U_528,U_527,U_526] :
( c_Orderings_Oord__class_Oless__eq(U_526,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),U_528),U_527),U_527)
| ~ c_Orderings_Oord__class_Oless__eq(U_526,U_528,c_Groups_Oone__class_Oone(U_526))
| ~ c_Orderings_Oord__class_Oless__eq(U_526,c_Groups_Ozero__class_Ozero(U_526),U_528)
| ~ c_Orderings_Oord__class_Oless__eq(U_526,c_Groups_Ozero__class_Ozero(U_526),U_527)
| ~ class_Rings_Olinordered__idom(U_526) ),
inference(variable_rename,[status(thm)],[f_170_1]) ).
fof(f_170_3,plain,
! [U_526,U_527,U_528] :
( c_Orderings_Oord__class_Oless__eq(U_526,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),U_528),U_527),U_527)
| ~ c_Orderings_Oord__class_Oless__eq(U_526,U_528,c_Groups_Oone__class_Oone(U_526))
| ~ c_Orderings_Oord__class_Oless__eq(U_526,c_Groups_Ozero__class_Ozero(U_526),U_528)
| ~ c_Orderings_Oord__class_Oless__eq(U_526,c_Groups_Ozero__class_Ozero(U_526),U_527)
| ~ class_Rings_Olinordered__idom(U_526) ),
inference(definitional_conversion,[status(esa)],[f_170_2]) ).
cnf(f_170_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_526,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_526),U_528),U_527),U_527)
| ~ c_Orderings_Oord__class_Oless__eq(U_526,U_528,c_Groups_Oone__class_Oone(U_526))
| ~ c_Orderings_Oord__class_Oless__eq(U_526,c_Groups_Ozero__class_Ozero(U_526),U_528)
| ~ c_Orderings_Oord__class_Oless__eq(U_526,c_Groups_Ozero__class_Ozero(U_526),U_527)
| ~ class_Rings_Olinordered__idom(U_526) ),
inference(clausify,[status(thm)],[f_170_3]) ).
fof(f_171_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_171_2,plain,
! [U_534,U_533,U_532,U_531,U_530,U_529] :
( c_Orderings_Oord__class_Oless(U_529,c_Groups_Oplus__class_Oplus(U_529,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_529),U_533),U_530),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_529),U_534),U_532)),U_531)
| c_Groups_Oplus__class_Oplus(U_529,U_533,U_534) != c_Groups_Oone__class_Oone(U_529)
| ~ c_Orderings_Oord__class_Oless__eq(U_529,c_Groups_Ozero__class_Ozero(U_529),U_534)
| ~ c_Orderings_Oord__class_Oless__eq(U_529,c_Groups_Ozero__class_Ozero(U_529),U_533)
| ~ c_Orderings_Oord__class_Oless(U_529,U_532,U_531)
| ~ c_Orderings_Oord__class_Oless(U_529,U_530,U_531)
| ~ class_Rings_Olinordered__semiring__1__strict(U_529) ),
inference(variable_rename,[status(thm)],[f_171_1]) ).
fof(f_171_3,plain,
! [U_529,U_530,U_531,U_532,U_533,U_534] :
( c_Orderings_Oord__class_Oless(U_529,c_Groups_Oplus__class_Oplus(U_529,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_529),U_533),U_530),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_529),U_534),U_532)),U_531)
| c_Groups_Oplus__class_Oplus(U_529,U_533,U_534) != c_Groups_Oone__class_Oone(U_529)
| ~ c_Orderings_Oord__class_Oless__eq(U_529,c_Groups_Ozero__class_Ozero(U_529),U_534)
| ~ c_Orderings_Oord__class_Oless__eq(U_529,c_Groups_Ozero__class_Ozero(U_529),U_533)
| ~ c_Orderings_Oord__class_Oless(U_529,U_532,U_531)
| ~ c_Orderings_Oord__class_Oless(U_529,U_530,U_531)
| ~ class_Rings_Olinordered__semiring__1__strict(U_529) ),
inference(definitional_conversion,[status(esa)],[f_171_2]) ).
cnf(f_171_4,plain,
( c_Orderings_Oord__class_Oless(U_529,c_Groups_Oplus__class_Oplus(U_529,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_529),U_533),U_530),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_529),U_534),U_532)),U_531)
| c_Groups_Oplus__class_Oplus(U_529,U_533,U_534) != c_Groups_Oone__class_Oone(U_529)
| ~ c_Orderings_Oord__class_Oless__eq(U_529,c_Groups_Ozero__class_Ozero(U_529),U_534)
| ~ c_Orderings_Oord__class_Oless__eq(U_529,c_Groups_Ozero__class_Ozero(U_529),U_533)
| ~ c_Orderings_Oord__class_Oless(U_529,U_532,U_531)
| ~ c_Orderings_Oord__class_Oless(U_529,U_530,U_531)
| ~ class_Rings_Olinordered__semiring__1__strict(U_529) ),
inference(clausify,[status(thm)],[f_171_3]) ).
fof(f_172_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_172_2,plain,
! [U_537,U_536,U_535] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_535,c_Groups_Oplus__class_Oplus(U_535,U_536,U_537)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_535,U_536),c_RealVector_Onorm__class_Onorm(U_535,U_537)))
| ~ class_RealVector_Oreal__normed__vector(U_535) ),
inference(variable_rename,[status(thm)],[f_172_1]) ).
fof(f_172_3,plain,
! [U_535,U_537,U_536] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_535,c_Groups_Oplus__class_Oplus(U_535,U_536,U_537)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_535,U_536),c_RealVector_Onorm__class_Onorm(U_535,U_537)))
| ~ class_RealVector_Oreal__normed__vector(U_535) ),
inference(definitional_conversion,[status(esa)],[f_172_2]) ).
cnf(f_172_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_535,c_Groups_Oplus__class_Oplus(U_535,U_536,U_537)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_535,U_536),c_RealVector_Onorm__class_Onorm(U_535,U_537)))
| ~ class_RealVector_Oreal__normed__vector(U_535) ),
inference(clausify,[status(thm)],[f_172_3]) ).
fof(f_173_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_173_2,plain,
! [U_542,U_541,U_540,U_539,U_538] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_538,c_Groups_Oplus__class_Oplus(U_538,U_539,U_541)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_540,U_542))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_538,U_541),U_542)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_538,U_539),U_540)
| ~ class_RealVector_Oreal__normed__vector(U_538) ),
inference(variable_rename,[status(thm)],[f_173_1]) ).
fof(f_173_3,plain,
! [U_538,U_539,U_540,U_541,U_542] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_538,c_Groups_Oplus__class_Oplus(U_538,U_539,U_541)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_540,U_542))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_538,U_541),U_542)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_538,U_539),U_540)
| ~ class_RealVector_Oreal__normed__vector(U_538) ),
inference(definitional_conversion,[status(esa)],[f_173_2]) ).
cnf(f_173_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_538,c_Groups_Oplus__class_Oplus(U_538,U_539,U_541)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_540,U_542))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_538,U_541),U_542)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_538,U_539),U_540)
| ~ class_RealVector_Oreal__normed__vector(U_538) ),
inference(clausify,[status(thm)],[f_173_3]) ).
fof(f_174_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_174_2,plain,
! [U_545,U_544,U_543] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_543,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_543),U_544),U_545)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_543,U_544)),c_RealVector_Onorm__class_Onorm(U_543,U_545)))
| ~ class_RealVector_Oreal__normed__algebra(U_543) ),
inference(variable_rename,[status(thm)],[f_174_1]) ).
fof(f_174_3,plain,
! [U_543,U_544,U_545] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_543,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_543),U_544),U_545)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_543,U_544)),c_RealVector_Onorm__class_Onorm(U_543,U_545)))
| ~ class_RealVector_Oreal__normed__algebra(U_543) ),
inference(definitional_conversion,[status(esa)],[f_174_2]) ).
cnf(f_174_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_543,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_543),U_544),U_545)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_543,U_544)),c_RealVector_Onorm__class_Onorm(U_543,U_545)))
| ~ class_RealVector_Oreal__normed__algebra(U_543) ),
inference(clausify,[status(thm)],[f_174_3]) ).
fof(f_175_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_175_2,plain,
! [U_550,U_549,U_548,U_547,U_546] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_546,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_546),U_547),U_549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_548),U_550))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_546,U_549),U_550)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_546,U_547),U_548)
| ~ class_RealVector_Oreal__normed__algebra(U_546) ),
inference(variable_rename,[status(thm)],[f_175_1]) ).
fof(f_175_3,plain,
! [U_546,U_547,U_548,U_549,U_550] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_546,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_546),U_547),U_549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_548),U_550))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_546,U_549),U_550)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_546,U_547),U_548)
| ~ class_RealVector_Oreal__normed__algebra(U_546) ),
inference(definitional_conversion,[status(esa)],[f_175_2]) ).
cnf(f_175_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_546,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_546),U_547),U_549)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_548),U_550))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_546,U_549),U_550)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_546,U_547),U_548)
| ~ class_RealVector_Oreal__normed__algebra(U_546) ),
inference(clausify,[status(thm)],[f_175_3]) ).
fof(f_176_1,plain,
! [T_a] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)) = c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__poly__def]) ).
fof(f_176_2,plain,
! [U_551] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_551)) = c_Polynomial_OpCons(U_551,c_Groups_Oone__class_Oone(U_551),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_551)))
| ~ class_Rings_Ocomm__semiring__1(U_551) ),
inference(variable_rename,[status(thm)],[f_176_1]) ).
fof(f_176_3,plain,
! [U_551] :
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_551)) = c_Polynomial_OpCons(U_551,c_Groups_Oone__class_Oone(U_551),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_551)))
| ~ class_Rings_Ocomm__semiring__1(U_551) ),
inference(definitional_conversion,[status(esa)],[f_176_2]) ).
cnf(f_176_4,plain,
( c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_551)) = c_Polynomial_OpCons(U_551,c_Groups_Oone__class_Oone(U_551),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_551)))
| ~ class_Rings_Ocomm__semiring__1(U_551) ),
inference(clausify,[status(thm)],[f_176_3]) ).
fof(f_177_1,plain,
! [V_x,V_p,V_a,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_OpCons(T_a,V_a,V_p)),V_x) = c_Groups_Oplus__class_Oplus(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__pCons]) ).
fof(f_177_2,plain,
! [U_555,U_554,U_553,U_552] :
( hAPP(c_Polynomial_Opoly(U_552,c_Polynomial_OpCons(U_552,U_553,U_554)),U_555) = c_Groups_Oplus__class_Oplus(U_552,U_553,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_552),U_555),hAPP(c_Polynomial_Opoly(U_552,U_554),U_555)))
| ~ class_Rings_Ocomm__semiring__0(U_552) ),
inference(variable_rename,[status(thm)],[f_177_1]) ).
fof(f_177_3,plain,
! [U_552,U_553,U_554,U_555] :
( hAPP(c_Polynomial_Opoly(U_552,c_Polynomial_OpCons(U_552,U_553,U_554)),U_555) = c_Groups_Oplus__class_Oplus(U_552,U_553,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_552),U_555),hAPP(c_Polynomial_Opoly(U_552,U_554),U_555)))
| ~ class_Rings_Ocomm__semiring__0(U_552) ),
inference(definitional_conversion,[status(esa)],[f_177_2]) ).
cnf(f_177_4,plain,
( hAPP(c_Polynomial_Opoly(U_552,c_Polynomial_OpCons(U_552,U_553,U_554)),U_555) = c_Groups_Oplus__class_Oplus(U_552,U_553,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_552),U_555),hAPP(c_Polynomial_Opoly(U_552,U_554),U_555)))
| ~ class_Rings_Ocomm__semiring__0(U_552) ),
inference(clausify,[status(thm)],[f_177_3]) ).
fof(f_178_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_178_2,plain,
! [U_557,U_556] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_556),c_Groups_Ozero__class_Ozero(U_556)),U_557) = c_Groups_Ozero__class_Ozero(U_556)
| ~ class_RealVector_Oreal__normed__algebra(U_556) ),
inference(variable_rename,[status(thm)],[f_178_1]) ).
fof(f_178_3,plain,
! [U_556,U_557] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_556),c_Groups_Ozero__class_Ozero(U_556)),U_557) = c_Groups_Ozero__class_Ozero(U_556)
| ~ class_RealVector_Oreal__normed__algebra(U_556) ),
inference(definitional_conversion,[status(esa)],[f_178_2]) ).
cnf(f_178_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_556),c_Groups_Ozero__class_Ozero(U_556)),U_557) = c_Groups_Ozero__class_Ozero(U_556)
| ~ class_RealVector_Oreal__normed__algebra(U_556) ),
inference(clausify,[status(thm)],[f_178_3]) ).
fof(f_179_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_179_2,plain,
! [U_559,U_558] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_558),c_Groups_Ozero__class_Ozero(U_558)),U_559) = c_Groups_Ozero__class_Ozero(U_558)
| ~ class_RealVector_Oreal__normed__algebra(U_558) ),
inference(variable_rename,[status(thm)],[f_179_1]) ).
fof(f_179_3,plain,
! [U_558,U_559] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_558),c_Groups_Ozero__class_Ozero(U_558)),U_559) = c_Groups_Ozero__class_Ozero(U_558)
| ~ class_RealVector_Oreal__normed__algebra(U_558) ),
inference(definitional_conversion,[status(esa)],[f_179_2]) ).
cnf(f_179_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_558),c_Groups_Ozero__class_Ozero(U_558)),U_559) = c_Groups_Ozero__class_Ozero(U_558)
| ~ class_RealVector_Oreal__normed__algebra(U_558) ),
inference(clausify,[status(thm)],[f_179_3]) ).
fof(f_180_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_180_2,plain,
! [U_561,U_560] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_560),U_561),c_Groups_Ozero__class_Ozero(U_560)) = c_Groups_Ozero__class_Ozero(U_560)
| ~ class_RealVector_Oreal__normed__algebra(U_560) ),
inference(variable_rename,[status(thm)],[f_180_1]) ).
fof(f_180_3,plain,
! [U_560,U_561] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_560),U_561),c_Groups_Ozero__class_Ozero(U_560)) = c_Groups_Ozero__class_Ozero(U_560)
| ~ class_RealVector_Oreal__normed__algebra(U_560) ),
inference(definitional_conversion,[status(esa)],[f_180_2]) ).
cnf(f_180_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_560),U_561),c_Groups_Ozero__class_Ozero(U_560)) = c_Groups_Ozero__class_Ozero(U_560)
| ~ class_RealVector_Oreal__normed__algebra(U_560) ),
inference(clausify,[status(thm)],[f_180_3]) ).
fof(f_181_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_181_2,plain,
! [U_563,U_562] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_562),U_563),c_Groups_Ozero__class_Ozero(U_562)) = c_Groups_Ozero__class_Ozero(U_562)
| ~ class_RealVector_Oreal__normed__algebra(U_562) ),
inference(variable_rename,[status(thm)],[f_181_1]) ).
fof(f_181_3,plain,
! [U_562,U_563] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_562),U_563),c_Groups_Ozero__class_Ozero(U_562)) = c_Groups_Ozero__class_Ozero(U_562)
| ~ class_RealVector_Oreal__normed__algebra(U_562) ),
inference(definitional_conversion,[status(esa)],[f_181_2]) ).
cnf(f_181_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_562),U_563),c_Groups_Ozero__class_Ozero(U_562)) = c_Groups_Ozero__class_Ozero(U_562)
| ~ class_RealVector_Oreal__normed__algebra(U_562) ),
inference(clausify,[status(thm)],[f_181_3]) ).
fof(f_182_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_182_2,plain,
! [U_565,U_564] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_564,U_565)) = c_RealVector_Onorm__class_Onorm(U_564,U_565)
| ~ class_RealVector_Oreal__normed__vector(U_564) ),
inference(variable_rename,[status(thm)],[f_182_1]) ).
fof(f_182_3,plain,
! [U_564,U_565] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_564,U_565)) = c_RealVector_Onorm__class_Onorm(U_564,U_565)
| ~ class_RealVector_Oreal__normed__vector(U_564) ),
inference(definitional_conversion,[status(esa)],[f_182_2]) ).
cnf(f_182_4,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_564,U_565)) = c_RealVector_Onorm__class_Onorm(U_564,U_565)
| ~ class_RealVector_Oreal__normed__vector(U_564) ),
inference(clausify,[status(thm)],[f_182_3]) ).
fof(f_183_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_183_2,plain,
! [U_568,U_567,U_566] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_568,U_566),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_568,U_567))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_566,U_567) ),
inference(variable_rename,[status(thm)],[f_183_1]) ).
fof(f_183_3,plain,
! [U_566,U_567,U_568] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_568,U_566),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_568,U_567))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_566,U_567) ),
inference(definitional_conversion,[status(esa)],[f_183_2]) ).
cnf(f_183_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_568,U_566),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_568,U_567))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_566,U_567) ),
inference(clausify,[status(thm)],[f_183_3]) ).
fof(f_184_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_184_2,plain,
! [U_570,U_569] :
( c_Orderings_Oord__class_Oless__eq(U_569,c_Groups_Ozero__class_Ozero(U_569),c_Groups_Oabs__class_Oabs(U_569,U_570))
| ~ class_Groups_Oordered__ab__group__add__abs(U_569) ),
inference(variable_rename,[status(thm)],[f_184_1]) ).
fof(f_184_3,plain,
! [U_569,U_570] :
( c_Orderings_Oord__class_Oless__eq(U_569,c_Groups_Ozero__class_Ozero(U_569),c_Groups_Oabs__class_Oabs(U_569,U_570))
| ~ class_Groups_Oordered__ab__group__add__abs(U_569) ),
inference(definitional_conversion,[status(esa)],[f_184_2]) ).
cnf(f_184_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_569,c_Groups_Ozero__class_Ozero(U_569),c_Groups_Oabs__class_Oabs(U_569,U_570))
| ~ class_Groups_Oordered__ab__group__add__abs(U_569) ),
inference(clausify,[status(thm)],[f_184_3]) ).
fof(f_185_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_185_2,plain,
! [U_572,U_571] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_571,c_Groups_Oabs__class_Oabs(U_571,U_572),c_Groups_Ozero__class_Ozero(U_571))
| U_572 != c_Groups_Ozero__class_Ozero(U_571) )
& ( U_572 = c_Groups_Ozero__class_Ozero(U_571)
| ~ c_Orderings_Oord__class_Oless__eq(U_571,c_Groups_Oabs__class_Oabs(U_571,U_572),c_Groups_Ozero__class_Ozero(U_571)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_571) ),
inference(variable_rename,[status(thm)],[f_185_1]) ).
fof(f_185_3,plain,
( ! [U_571,U_572] :
( c_Orderings_Oord__class_Oless__eq(U_571,c_Groups_Oabs__class_Oabs(U_571,U_572),c_Groups_Ozero__class_Ozero(U_571))
| U_572 != c_Groups_Ozero__class_Ozero(U_571)
| ~ sP54(U_571,U_572) )
& ! [U_571,U_572] :
( U_572 = c_Groups_Ozero__class_Ozero(U_571)
| ~ c_Orderings_Oord__class_Oless__eq(U_571,c_Groups_Oabs__class_Oabs(U_571,U_572),c_Groups_Ozero__class_Ozero(U_571))
| ~ sP54(U_571,U_572) )
& ! [U_571,U_572] :
( sP54(U_571,U_572)
| ~ class_Groups_Oordered__ab__group__add__abs(U_571) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_185_2]) ).
cnf(f_185_4,plain,
( sP54(U_571,U_572)
| ~ class_Groups_Oordered__ab__group__add__abs(U_571) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_5,plain,
( U_572 = c_Groups_Ozero__class_Ozero(U_571)
| ~ c_Orderings_Oord__class_Oless__eq(U_571,c_Groups_Oabs__class_Oabs(U_571,U_572),c_Groups_Ozero__class_Ozero(U_571))
| ~ sP54(U_571,U_572) ),
inference(clausify,[status(thm)],[f_185_3]) ).
cnf(f_185_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_571,c_Groups_Oabs__class_Oabs(U_571,U_572),c_Groups_Ozero__class_Ozero(U_571))
| U_572 != c_Groups_Ozero__class_Ozero(U_571)
| ~ sP54(U_571,U_572) ),
inference(clausify,[status(thm)],[f_185_3]) ).
fof(f_186_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_186_2,plain,
! [U_574,U_573] :
( c_Groups_Oabs__class_Oabs(U_573,U_574) = U_574
| ~ c_Orderings_Oord__class_Oless__eq(U_573,c_Groups_Ozero__class_Ozero(U_573),U_574)
| ~ class_Groups_Oordered__ab__group__add__abs(U_573) ),
inference(variable_rename,[status(thm)],[f_186_1]) ).
fof(f_186_3,plain,
! [U_573,U_574] :
( c_Groups_Oabs__class_Oabs(U_573,U_574) = U_574
| ~ c_Orderings_Oord__class_Oless__eq(U_573,c_Groups_Ozero__class_Ozero(U_573),U_574)
| ~ class_Groups_Oordered__ab__group__add__abs(U_573) ),
inference(definitional_conversion,[status(esa)],[f_186_2]) ).
cnf(f_186_4,plain,
( c_Groups_Oabs__class_Oabs(U_573,U_574) = U_574
| ~ c_Orderings_Oord__class_Oless__eq(U_573,c_Groups_Ozero__class_Ozero(U_573),U_574)
| ~ class_Groups_Oordered__ab__group__add__abs(U_573) ),
inference(clausify,[status(thm)],[f_186_3]) ).
fof(f_187_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_187_2,plain,
! [U_576,U_575] :
( ~ c_Orderings_Oord__class_Oless(U_575,c_Groups_Oabs__class_Oabs(U_575,U_576),c_Groups_Ozero__class_Ozero(U_575))
| ~ class_Groups_Oordered__ab__group__add__abs(U_575) ),
inference(variable_rename,[status(thm)],[f_187_1]) ).
fof(f_187_3,plain,
! [U_575,U_576] :
( ~ c_Orderings_Oord__class_Oless(U_575,c_Groups_Oabs__class_Oabs(U_575,U_576),c_Groups_Ozero__class_Ozero(U_575))
| ~ class_Groups_Oordered__ab__group__add__abs(U_575) ),
inference(definitional_conversion,[status(esa)],[f_187_2]) ).
cnf(f_187_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_575,c_Groups_Oabs__class_Oabs(U_575,U_576),c_Groups_Ozero__class_Ozero(U_575))
| ~ class_Groups_Oordered__ab__group__add__abs(U_575) ),
inference(clausify,[status(thm)],[f_187_3]) ).
fof(f_188_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_188_2,plain,
! [U_578,U_577] :
( ( ( c_Orderings_Oord__class_Oless(U_577,c_Groups_Ozero__class_Ozero(U_577),c_Groups_Oabs__class_Oabs(U_577,U_578))
| U_578 = c_Groups_Ozero__class_Ozero(U_577) )
& ( U_578 != c_Groups_Ozero__class_Ozero(U_577)
| ~ c_Orderings_Oord__class_Oless(U_577,c_Groups_Ozero__class_Ozero(U_577),c_Groups_Oabs__class_Oabs(U_577,U_578)) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_577) ),
inference(variable_rename,[status(thm)],[f_188_1]) ).
fof(f_188_3,plain,
( ! [U_577,U_578] :
( c_Orderings_Oord__class_Oless(U_577,c_Groups_Ozero__class_Ozero(U_577),c_Groups_Oabs__class_Oabs(U_577,U_578))
| U_578 = c_Groups_Ozero__class_Ozero(U_577)
| ~ sP55(U_577,U_578) )
& ! [U_577,U_578] :
( U_578 != c_Groups_Ozero__class_Ozero(U_577)
| ~ c_Orderings_Oord__class_Oless(U_577,c_Groups_Ozero__class_Ozero(U_577),c_Groups_Oabs__class_Oabs(U_577,U_578))
| ~ sP55(U_577,U_578) )
& ! [U_577,U_578] :
( sP55(U_577,U_578)
| ~ class_Groups_Oordered__ab__group__add__abs(U_577) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_188_2]) ).
cnf(f_188_4,plain,
( sP55(U_577,U_578)
| ~ class_Groups_Oordered__ab__group__add__abs(U_577) ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_5,plain,
( U_578 != c_Groups_Ozero__class_Ozero(U_577)
| ~ c_Orderings_Oord__class_Oless(U_577,c_Groups_Ozero__class_Ozero(U_577),c_Groups_Oabs__class_Oabs(U_577,U_578))
| ~ sP55(U_577,U_578) ),
inference(clausify,[status(thm)],[f_188_3]) ).
cnf(f_188_6,plain,
( c_Orderings_Oord__class_Oless(U_577,c_Groups_Ozero__class_Ozero(U_577),c_Groups_Oabs__class_Oabs(U_577,U_578))
| U_578 = c_Groups_Ozero__class_Ozero(U_577)
| ~ sP55(U_577,U_578) ),
inference(clausify,[status(thm)],[f_188_3]) ).
fof(f_189_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_189_2,plain,
! [U_580,U_579] :
( c_Groups_Oabs__class_Oabs(U_579,U_580) = U_580
| ~ c_Orderings_Oord__class_Oless(U_579,c_Groups_Ozero__class_Ozero(U_579),U_580)
| ~ class_Groups_Oordered__ab__group__add__abs(U_579) ),
inference(variable_rename,[status(thm)],[f_189_1]) ).
fof(f_189_3,plain,
! [U_580,U_579] :
( c_Groups_Oabs__class_Oabs(U_579,U_580) = U_580
| ~ c_Orderings_Oord__class_Oless(U_579,c_Groups_Ozero__class_Ozero(U_579),U_580)
| ~ class_Groups_Oordered__ab__group__add__abs(U_579) ),
inference(definitional_conversion,[status(esa)],[f_189_2]) ).
cnf(f_189_4,plain,
( c_Groups_Oabs__class_Oabs(U_579,U_580) = U_580
| ~ c_Orderings_Oord__class_Oless(U_579,c_Groups_Ozero__class_Ozero(U_579),U_580)
| ~ class_Groups_Oordered__ab__group__add__abs(U_579) ),
inference(clausify,[status(thm)],[f_189_3]) ).
fof(f_190_1,plain,
! [V_b_2,V_a_2,V_ca_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a_2),V_ca_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_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_ca_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_b_2),V_ca_2) ) )
| V_ca_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__right__cancel]) ).
fof(f_190_2,plain,
! [U_583,U_582,U_581] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_582),U_581) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_583),U_581)
| U_582 != U_583 )
& ( U_582 = U_583
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_582),U_581) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_583),U_581) ) )
| U_581 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_190_1]) ).
fof(f_190_3,plain,
( ! [U_581,U_582,U_583] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_582),U_581) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_583),U_581)
| U_582 != U_583
| ~ sP56(U_581,U_582,U_583) )
& ! [U_581,U_582,U_583] :
( U_582 = U_583
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_582),U_581) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_583),U_581)
| ~ sP56(U_581,U_582,U_583) )
& ! [U_581,U_582,U_583] :
( sP56(U_581,U_582,U_583)
| U_581 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_190_2]) ).
cnf(f_190_4,plain,
( sP56(U_581,U_582,U_583)
| U_581 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_190_3]) ).
cnf(f_190_5,plain,
( U_582 = U_583
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_582),U_581) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_583),U_581)
| ~ sP56(U_581,U_582,U_583) ),
inference(clausify,[status(thm)],[f_190_3]) ).
cnf(f_190_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_582),U_581) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_583),U_581)
| U_582 != U_583
| ~ sP56(U_581,U_582,U_583) ),
inference(clausify,[status(thm)],[f_190_3]) ).
fof(f_191_1,plain,
! [V_b_2,V_a_2,V_ca_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_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_ca_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_ca_2),V_b_2) ) )
| V_ca_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__left__cancel]) ).
fof(f_191_2,plain,
! [U_586,U_585,U_584] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_586)
| U_585 != U_586 )
& ( U_585 = U_586
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_585) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_586) ) )
| U_584 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(variable_rename,[status(thm)],[f_191_1]) ).
fof(f_191_3,plain,
( ! [U_586,U_585,U_584] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_586)
| U_585 != U_586
| ~ sP57(U_586,U_585,U_584) )
& ! [U_586,U_585,U_584] :
( U_585 = U_586
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_585) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_586)
| ~ sP57(U_586,U_585,U_584) )
& ! [U_586,U_585,U_584] :
( sP57(U_586,U_585,U_584)
| U_584 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57])],[f_191_2]) ).
cnf(f_191_4,plain,
( sP57(U_586,U_585,U_584)
| U_584 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_191_3]) ).
cnf(f_191_5,plain,
( U_585 = U_586
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_585) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_586)
| ~ sP57(U_586,U_585,U_584) ),
inference(clausify,[status(thm)],[f_191_3]) ).
cnf(f_191_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_585) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_584),U_586)
| U_585 != U_586
| ~ sP57(U_586,U_585,U_584) ),
inference(clausify,[status(thm)],[f_191_3]) ).
fof(f_192_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_192_2,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_192_1]) ).
cnf(f_192_3,plain,
c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) != c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_192_2]) ).
fof(f_193_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,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_193_2,plain,
! [U_588,U_587] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),c_Groups_Oplus__class_Oplus(U_587,U_588,U_588))
| ~ c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),U_588) )
& ( c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),U_588)
| ~ c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),c_Groups_Oplus__class_Oplus(U_587,U_588,U_588)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_587) ),
inference(variable_rename,[status(thm)],[f_193_1]) ).
fof(f_193_3,plain,
( ! [U_587,U_588] :
( c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),c_Groups_Oplus__class_Oplus(U_587,U_588,U_588))
| ~ c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),U_588)
| ~ sP58(U_587,U_588) )
& ! [U_587,U_588] :
( c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),U_588)
| ~ c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),c_Groups_Oplus__class_Oplus(U_587,U_588,U_588))
| ~ sP58(U_587,U_588) )
& ! [U_587,U_588] :
( sP58(U_587,U_588)
| ~ class_Groups_Olinordered__ab__group__add(U_587) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP58])],[f_193_2]) ).
cnf(f_193_4,plain,
( sP58(U_587,U_588)
| ~ class_Groups_Olinordered__ab__group__add(U_587) ),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_193_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),U_588)
| ~ c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),c_Groups_Oplus__class_Oplus(U_587,U_588,U_588))
| ~ sP58(U_587,U_588) ),
inference(clausify,[status(thm)],[f_193_3]) ).
cnf(f_193_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),c_Groups_Oplus__class_Oplus(U_587,U_588,U_588))
| ~ c_Orderings_Oord__class_Oless__eq(U_587,c_Groups_Ozero__class_Ozero(U_587),U_588)
| ~ sP58(U_587,U_588) ),
inference(clausify,[status(thm)],[f_193_3]) ).
fof(f_194_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_194_2,plain,
! [U_590,U_589] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_589,c_Groups_Oplus__class_Oplus(U_589,U_590,U_590),c_Groups_Ozero__class_Ozero(U_589))
| ~ c_Orderings_Oord__class_Oless__eq(U_589,U_590,c_Groups_Ozero__class_Ozero(U_589)) )
& ( c_Orderings_Oord__class_Oless__eq(U_589,U_590,c_Groups_Ozero__class_Ozero(U_589))
| ~ c_Orderings_Oord__class_Oless__eq(U_589,c_Groups_Oplus__class_Oplus(U_589,U_590,U_590),c_Groups_Ozero__class_Ozero(U_589)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_589) ),
inference(variable_rename,[status(thm)],[f_194_1]) ).
fof(f_194_3,plain,
( ! [U_590,U_589] :
( c_Orderings_Oord__class_Oless__eq(U_589,c_Groups_Oplus__class_Oplus(U_589,U_590,U_590),c_Groups_Ozero__class_Ozero(U_589))
| ~ c_Orderings_Oord__class_Oless__eq(U_589,U_590,c_Groups_Ozero__class_Ozero(U_589))
| ~ sP59(U_590,U_589) )
& ! [U_590,U_589] :
( c_Orderings_Oord__class_Oless__eq(U_589,U_590,c_Groups_Ozero__class_Ozero(U_589))
| ~ c_Orderings_Oord__class_Oless__eq(U_589,c_Groups_Oplus__class_Oplus(U_589,U_590,U_590),c_Groups_Ozero__class_Ozero(U_589))
| ~ sP59(U_590,U_589) )
& ! [U_590,U_589] :
( sP59(U_590,U_589)
| ~ class_Groups_Olinordered__ab__group__add(U_589) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_194_2]) ).
cnf(f_194_4,plain,
( sP59(U_590,U_589)
| ~ class_Groups_Olinordered__ab__group__add(U_589) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_589,U_590,c_Groups_Ozero__class_Ozero(U_589))
| ~ c_Orderings_Oord__class_Oless__eq(U_589,c_Groups_Oplus__class_Oplus(U_589,U_590,U_590),c_Groups_Ozero__class_Ozero(U_589))
| ~ sP59(U_590,U_589) ),
inference(clausify,[status(thm)],[f_194_3]) ).
cnf(f_194_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_589,c_Groups_Oplus__class_Oplus(U_589,U_590,U_590),c_Groups_Ozero__class_Ozero(U_589))
| ~ c_Orderings_Oord__class_Oless__eq(U_589,U_590,c_Groups_Ozero__class_Ozero(U_589))
| ~ sP59(U_590,U_589) ),
inference(clausify,[status(thm)],[f_194_3]) ).
fof(f_195_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_195_2,plain,
! [U_593,U_592,U_591] :
( c_Orderings_Oord__class_Oless__eq(U_591,c_Groups_Ozero__class_Ozero(U_591),c_Groups_Oplus__class_Oplus(U_591,U_592,U_593))
| ~ c_Orderings_Oord__class_Oless__eq(U_591,c_Groups_Ozero__class_Ozero(U_591),U_593)
| ~ c_Orderings_Oord__class_Oless__eq(U_591,c_Groups_Ozero__class_Ozero(U_591),U_592)
| ~ class_Groups_Oordered__comm__monoid__add(U_591) ),
inference(variable_rename,[status(thm)],[f_195_1]) ).
fof(f_195_3,plain,
! [U_593,U_592,U_591] :
( c_Orderings_Oord__class_Oless__eq(U_591,c_Groups_Ozero__class_Ozero(U_591),c_Groups_Oplus__class_Oplus(U_591,U_592,U_593))
| ~ c_Orderings_Oord__class_Oless__eq(U_591,c_Groups_Ozero__class_Ozero(U_591),U_593)
| ~ c_Orderings_Oord__class_Oless__eq(U_591,c_Groups_Ozero__class_Ozero(U_591),U_592)
| ~ class_Groups_Oordered__comm__monoid__add(U_591) ),
inference(definitional_conversion,[status(esa)],[f_195_2]) ).
cnf(f_195_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_591,c_Groups_Ozero__class_Ozero(U_591),c_Groups_Oplus__class_Oplus(U_591,U_592,U_593))
| ~ c_Orderings_Oord__class_Oless__eq(U_591,c_Groups_Ozero__class_Ozero(U_591),U_593)
| ~ c_Orderings_Oord__class_Oless__eq(U_591,c_Groups_Ozero__class_Ozero(U_591),U_592)
| ~ class_Groups_Oordered__comm__monoid__add(U_591) ),
inference(clausify,[status(thm)],[f_195_3]) ).
fof(f_196_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x_2)
| ~ class_Groups_Oordered__comm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__nonneg__eq__0__iff]) ).
fof(f_196_2,plain,
! [U_596,U_595,U_594] :
( ( ( c_Groups_Oplus__class_Oplus(U_594,U_595,U_596) = c_Groups_Ozero__class_Ozero(U_594)
| U_596 != c_Groups_Ozero__class_Ozero(U_594)
| U_595 != c_Groups_Ozero__class_Ozero(U_594) )
& ( ( U_596 = c_Groups_Ozero__class_Ozero(U_594)
& U_595 = c_Groups_Ozero__class_Ozero(U_594) )
| c_Groups_Oplus__class_Oplus(U_594,U_595,U_596) != c_Groups_Ozero__class_Ozero(U_594) ) )
| ~ c_Orderings_Oord__class_Oless__eq(U_594,c_Groups_Ozero__class_Ozero(U_594),U_596)
| ~ c_Orderings_Oord__class_Oless__eq(U_594,c_Groups_Ozero__class_Ozero(U_594),U_595)
| ~ class_Groups_Oordered__comm__monoid__add(U_594) ),
inference(variable_rename,[status(thm)],[f_196_1]) ).
fof(f_196_3,plain,
( ! [U_595,U_594,U_596] :
( U_596 = c_Groups_Ozero__class_Ozero(U_594)
| ~ sP60(U_595,U_594,U_596) )
& ! [U_595,U_594,U_596] :
( U_595 = c_Groups_Ozero__class_Ozero(U_594)
| ~ sP60(U_595,U_594,U_596) )
& ! [U_595,U_594,U_596] :
( c_Groups_Oplus__class_Oplus(U_594,U_595,U_596) = c_Groups_Ozero__class_Ozero(U_594)
| U_596 != c_Groups_Ozero__class_Ozero(U_594)
| U_595 != c_Groups_Ozero__class_Ozero(U_594)
| ~ sP61(U_595,U_594,U_596) )
& ! [U_595,U_594,U_596] :
( sP60(U_595,U_594,U_596)
| c_Groups_Oplus__class_Oplus(U_594,U_595,U_596) != c_Groups_Ozero__class_Ozero(U_594)
| ~ sP61(U_595,U_594,U_596) )
& ! [U_595,U_594,U_596] :
( sP61(U_595,U_594,U_596)
| ~ c_Orderings_Oord__class_Oless__eq(U_594,c_Groups_Ozero__class_Ozero(U_594),U_596)
| ~ c_Orderings_Oord__class_Oless__eq(U_594,c_Groups_Ozero__class_Ozero(U_594),U_595)
| ~ class_Groups_Oordered__comm__monoid__add(U_594) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60,sP61])],[f_196_2]) ).
cnf(f_196_4,plain,
( sP61(U_595,U_594,U_596)
| ~ c_Orderings_Oord__class_Oless__eq(U_594,c_Groups_Ozero__class_Ozero(U_594),U_596)
| ~ c_Orderings_Oord__class_Oless__eq(U_594,c_Groups_Ozero__class_Ozero(U_594),U_595)
| ~ class_Groups_Oordered__comm__monoid__add(U_594) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_5,plain,
( sP60(U_595,U_594,U_596)
| c_Groups_Oplus__class_Oplus(U_594,U_595,U_596) != c_Groups_Ozero__class_Ozero(U_594)
| ~ sP61(U_595,U_594,U_596) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_6,plain,
( c_Groups_Oplus__class_Oplus(U_594,U_595,U_596) = c_Groups_Ozero__class_Ozero(U_594)
| U_596 != c_Groups_Ozero__class_Ozero(U_594)
| U_595 != c_Groups_Ozero__class_Ozero(U_594)
| ~ sP61(U_595,U_594,U_596) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_7,plain,
( U_595 = c_Groups_Ozero__class_Ozero(U_594)
| ~ sP60(U_595,U_594,U_596) ),
inference(clausify,[status(thm)],[f_196_3]) ).
cnf(f_196_8,plain,
( U_596 = c_Groups_Ozero__class_Ozero(U_594)
| ~ sP60(U_595,U_594,U_596) ),
inference(clausify,[status(thm)],[f_196_3]) ).
fof(f_197_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_197_2,plain,
! [U_600,U_599,U_598,U_597] :
( c_Orderings_Oord__class_Oless__eq(U_597,U_599,c_Groups_Oplus__class_Oplus(U_597,U_598,U_600))
| ~ c_Orderings_Oord__class_Oless__eq(U_597,U_599,U_600)
| ~ c_Orderings_Oord__class_Oless__eq(U_597,c_Groups_Ozero__class_Ozero(U_597),U_598)
| ~ class_Groups_Oordered__comm__monoid__add(U_597) ),
inference(variable_rename,[status(thm)],[f_197_1]) ).
fof(f_197_3,plain,
! [U_599,U_600,U_598,U_597] :
( c_Orderings_Oord__class_Oless__eq(U_597,U_599,c_Groups_Oplus__class_Oplus(U_597,U_598,U_600))
| ~ c_Orderings_Oord__class_Oless__eq(U_597,U_599,U_600)
| ~ c_Orderings_Oord__class_Oless__eq(U_597,c_Groups_Ozero__class_Ozero(U_597),U_598)
| ~ class_Groups_Oordered__comm__monoid__add(U_597) ),
inference(definitional_conversion,[status(esa)],[f_197_2]) ).
cnf(f_197_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_597,U_599,c_Groups_Oplus__class_Oplus(U_597,U_598,U_600))
| ~ c_Orderings_Oord__class_Oless__eq(U_597,U_599,U_600)
| ~ c_Orderings_Oord__class_Oless__eq(U_597,c_Groups_Ozero__class_Ozero(U_597),U_598)
| ~ class_Groups_Oordered__comm__monoid__add(U_597) ),
inference(clausify,[status(thm)],[f_197_3]) ).
fof(f_198_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_198_2,plain,
! [U_604,U_603,U_602,U_601] :
( c_Orderings_Oord__class_Oless__eq(U_601,U_603,c_Groups_Oplus__class_Oplus(U_601,U_604,U_602))
| ~ c_Orderings_Oord__class_Oless__eq(U_601,U_603,U_604)
| ~ c_Orderings_Oord__class_Oless__eq(U_601,c_Groups_Ozero__class_Ozero(U_601),U_602)
| ~ class_Groups_Oordered__comm__monoid__add(U_601) ),
inference(variable_rename,[status(thm)],[f_198_1]) ).
fof(f_198_3,plain,
! [U_602,U_604,U_603,U_601] :
( c_Orderings_Oord__class_Oless__eq(U_601,U_603,c_Groups_Oplus__class_Oplus(U_601,U_604,U_602))
| ~ c_Orderings_Oord__class_Oless__eq(U_601,U_603,U_604)
| ~ c_Orderings_Oord__class_Oless__eq(U_601,c_Groups_Ozero__class_Ozero(U_601),U_602)
| ~ class_Groups_Oordered__comm__monoid__add(U_601) ),
inference(definitional_conversion,[status(esa)],[f_198_2]) ).
cnf(f_198_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_601,U_603,c_Groups_Oplus__class_Oplus(U_601,U_604,U_602))
| ~ c_Orderings_Oord__class_Oless__eq(U_601,U_603,U_604)
| ~ c_Orderings_Oord__class_Oless__eq(U_601,c_Groups_Ozero__class_Ozero(U_601),U_602)
| ~ class_Groups_Oordered__comm__monoid__add(U_601) ),
inference(clausify,[status(thm)],[f_198_3]) ).
fof(f_199_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_199_2,plain,
! [U_607,U_606,U_605] :
( c_Orderings_Oord__class_Oless__eq(U_605,c_Groups_Oplus__class_Oplus(U_605,U_606,U_607),c_Groups_Ozero__class_Ozero(U_605))
| ~ c_Orderings_Oord__class_Oless__eq(U_605,U_607,c_Groups_Ozero__class_Ozero(U_605))
| ~ c_Orderings_Oord__class_Oless__eq(U_605,U_606,c_Groups_Ozero__class_Ozero(U_605))
| ~ class_Groups_Oordered__comm__monoid__add(U_605) ),
inference(variable_rename,[status(thm)],[f_199_1]) ).
fof(f_199_3,plain,
! [U_607,U_605,U_606] :
( c_Orderings_Oord__class_Oless__eq(U_605,c_Groups_Oplus__class_Oplus(U_605,U_606,U_607),c_Groups_Ozero__class_Ozero(U_605))
| ~ c_Orderings_Oord__class_Oless__eq(U_605,U_607,c_Groups_Ozero__class_Ozero(U_605))
| ~ c_Orderings_Oord__class_Oless__eq(U_605,U_606,c_Groups_Ozero__class_Ozero(U_605))
| ~ class_Groups_Oordered__comm__monoid__add(U_605) ),
inference(definitional_conversion,[status(esa)],[f_199_2]) ).
cnf(f_199_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_605,c_Groups_Oplus__class_Oplus(U_605,U_606,U_607),c_Groups_Ozero__class_Ozero(U_605))
| ~ c_Orderings_Oord__class_Oless__eq(U_605,U_607,c_Groups_Ozero__class_Ozero(U_605))
| ~ c_Orderings_Oord__class_Oless__eq(U_605,U_606,c_Groups_Ozero__class_Ozero(U_605))
| ~ class_Groups_Oordered__comm__monoid__add(U_605) ),
inference(clausify,[status(thm)],[f_199_3]) ).
fof(f_200_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_200_2,plain,
! [U_609,U_608] :
( ( ( c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),c_Groups_Oplus__class_Oplus(U_608,U_609,U_609))
| ~ c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),U_609) )
& ( c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),U_609)
| ~ c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),c_Groups_Oplus__class_Oplus(U_608,U_609,U_609)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_608) ),
inference(variable_rename,[status(thm)],[f_200_1]) ).
fof(f_200_3,plain,
( ! [U_608,U_609] :
( c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),c_Groups_Oplus__class_Oplus(U_608,U_609,U_609))
| ~ c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),U_609)
| ~ sP62(U_608,U_609) )
& ! [U_608,U_609] :
( c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),U_609)
| ~ c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),c_Groups_Oplus__class_Oplus(U_608,U_609,U_609))
| ~ sP62(U_608,U_609) )
& ! [U_608,U_609] :
( sP62(U_608,U_609)
| ~ class_Groups_Olinordered__ab__group__add(U_608) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_200_2]) ).
cnf(f_200_4,plain,
( sP62(U_608,U_609)
| ~ class_Groups_Olinordered__ab__group__add(U_608) ),
inference(clausify,[status(thm)],[f_200_3]) ).
cnf(f_200_5,plain,
( c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),U_609)
| ~ c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),c_Groups_Oplus__class_Oplus(U_608,U_609,U_609))
| ~ sP62(U_608,U_609) ),
inference(clausify,[status(thm)],[f_200_3]) ).
cnf(f_200_6,plain,
( c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),c_Groups_Oplus__class_Oplus(U_608,U_609,U_609))
| ~ c_Orderings_Oord__class_Oless(U_608,c_Groups_Ozero__class_Ozero(U_608),U_609)
| ~ sP62(U_608,U_609) ),
inference(clausify,[status(thm)],[f_200_3]) ).
fof(f_201_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_201_2,plain,
! [U_611,U_610] :
( ( ( c_Orderings_Oord__class_Oless(U_610,c_Groups_Oplus__class_Oplus(U_610,U_611,U_611),c_Groups_Ozero__class_Ozero(U_610))
| ~ c_Orderings_Oord__class_Oless(U_610,U_611,c_Groups_Ozero__class_Ozero(U_610)) )
& ( c_Orderings_Oord__class_Oless(U_610,U_611,c_Groups_Ozero__class_Ozero(U_610))
| ~ c_Orderings_Oord__class_Oless(U_610,c_Groups_Oplus__class_Oplus(U_610,U_611,U_611),c_Groups_Ozero__class_Ozero(U_610)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_610) ),
inference(variable_rename,[status(thm)],[f_201_1]) ).
fof(f_201_3,plain,
( ! [U_611,U_610] :
( c_Orderings_Oord__class_Oless(U_610,c_Groups_Oplus__class_Oplus(U_610,U_611,U_611),c_Groups_Ozero__class_Ozero(U_610))
| ~ c_Orderings_Oord__class_Oless(U_610,U_611,c_Groups_Ozero__class_Ozero(U_610))
| ~ sP63(U_611,U_610) )
& ! [U_611,U_610] :
( c_Orderings_Oord__class_Oless(U_610,U_611,c_Groups_Ozero__class_Ozero(U_610))
| ~ c_Orderings_Oord__class_Oless(U_610,c_Groups_Oplus__class_Oplus(U_610,U_611,U_611),c_Groups_Ozero__class_Ozero(U_610))
| ~ sP63(U_611,U_610) )
& ! [U_611,U_610] :
( sP63(U_611,U_610)
| ~ class_Groups_Olinordered__ab__group__add(U_610) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_201_2]) ).
cnf(f_201_4,plain,
( sP63(U_611,U_610)
| ~ class_Groups_Olinordered__ab__group__add(U_610) ),
inference(clausify,[status(thm)],[f_201_3]) ).
cnf(f_201_5,plain,
( c_Orderings_Oord__class_Oless(U_610,U_611,c_Groups_Ozero__class_Ozero(U_610))
| ~ c_Orderings_Oord__class_Oless(U_610,c_Groups_Oplus__class_Oplus(U_610,U_611,U_611),c_Groups_Ozero__class_Ozero(U_610))
| ~ sP63(U_611,U_610) ),
inference(clausify,[status(thm)],[f_201_3]) ).
cnf(f_201_6,plain,
( c_Orderings_Oord__class_Oless(U_610,c_Groups_Oplus__class_Oplus(U_610,U_611,U_611),c_Groups_Ozero__class_Ozero(U_610))
| ~ c_Orderings_Oord__class_Oless(U_610,U_611,c_Groups_Ozero__class_Ozero(U_610))
| ~ sP63(U_611,U_610) ),
inference(clausify,[status(thm)],[f_201_3]) ).
fof(f_202_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_202_2,plain,
! [U_614,U_613,U_612] :
( c_Orderings_Oord__class_Oless(U_612,c_Groups_Ozero__class_Ozero(U_612),c_Groups_Oplus__class_Oplus(U_612,U_613,U_614))
| ~ c_Orderings_Oord__class_Oless(U_612,c_Groups_Ozero__class_Ozero(U_612),U_614)
| ~ c_Orderings_Oord__class_Oless(U_612,c_Groups_Ozero__class_Ozero(U_612),U_613)
| ~ class_Groups_Oordered__comm__monoid__add(U_612) ),
inference(variable_rename,[status(thm)],[f_202_1]) ).
fof(f_202_3,plain,
! [U_614,U_613,U_612] :
( c_Orderings_Oord__class_Oless(U_612,c_Groups_Ozero__class_Ozero(U_612),c_Groups_Oplus__class_Oplus(U_612,U_613,U_614))
| ~ c_Orderings_Oord__class_Oless(U_612,c_Groups_Ozero__class_Ozero(U_612),U_614)
| ~ c_Orderings_Oord__class_Oless(U_612,c_Groups_Ozero__class_Ozero(U_612),U_613)
| ~ class_Groups_Oordered__comm__monoid__add(U_612) ),
inference(definitional_conversion,[status(esa)],[f_202_2]) ).
cnf(f_202_4,plain,
( c_Orderings_Oord__class_Oless(U_612,c_Groups_Ozero__class_Ozero(U_612),c_Groups_Oplus__class_Oplus(U_612,U_613,U_614))
| ~ c_Orderings_Oord__class_Oless(U_612,c_Groups_Ozero__class_Ozero(U_612),U_614)
| ~ c_Orderings_Oord__class_Oless(U_612,c_Groups_Ozero__class_Ozero(U_612),U_613)
| ~ class_Groups_Oordered__comm__monoid__add(U_612) ),
inference(clausify,[status(thm)],[f_202_3]) ).
fof(f_203_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_203_2,plain,
! [U_618,U_617,U_616,U_615] :
( c_Orderings_Oord__class_Oless(U_615,U_617,c_Groups_Oplus__class_Oplus(U_615,U_616,U_618))
| ~ c_Orderings_Oord__class_Oless(U_615,U_617,U_618)
| ~ c_Orderings_Oord__class_Oless(U_615,c_Groups_Ozero__class_Ozero(U_615),U_616)
| ~ class_Rings_Olinordered__semidom(U_615) ),
inference(variable_rename,[status(thm)],[f_203_1]) ).
fof(f_203_3,plain,
! [U_615,U_616,U_617,U_618] :
( c_Orderings_Oord__class_Oless(U_615,U_617,c_Groups_Oplus__class_Oplus(U_615,U_616,U_618))
| ~ c_Orderings_Oord__class_Oless(U_615,U_617,U_618)
| ~ c_Orderings_Oord__class_Oless(U_615,c_Groups_Ozero__class_Ozero(U_615),U_616)
| ~ class_Rings_Olinordered__semidom(U_615) ),
inference(definitional_conversion,[status(esa)],[f_203_2]) ).
cnf(f_203_4,plain,
( c_Orderings_Oord__class_Oless(U_615,U_617,c_Groups_Oplus__class_Oplus(U_615,U_616,U_618))
| ~ c_Orderings_Oord__class_Oless(U_615,U_617,U_618)
| ~ c_Orderings_Oord__class_Oless(U_615,c_Groups_Ozero__class_Ozero(U_615),U_616)
| ~ class_Rings_Olinordered__semidom(U_615) ),
inference(clausify,[status(thm)],[f_203_3]) ).
fof(f_204_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_204_2,plain,
! [U_621,U_620,U_619] :
( c_Orderings_Oord__class_Oless(U_619,c_Groups_Oplus__class_Oplus(U_619,U_620,U_621),c_Groups_Ozero__class_Ozero(U_619))
| ~ c_Orderings_Oord__class_Oless(U_619,U_621,c_Groups_Ozero__class_Ozero(U_619))
| ~ c_Orderings_Oord__class_Oless(U_619,U_620,c_Groups_Ozero__class_Ozero(U_619))
| ~ class_Groups_Oordered__comm__monoid__add(U_619) ),
inference(variable_rename,[status(thm)],[f_204_1]) ).
fof(f_204_3,plain,
! [U_619,U_620,U_621] :
( c_Orderings_Oord__class_Oless(U_619,c_Groups_Oplus__class_Oplus(U_619,U_620,U_621),c_Groups_Ozero__class_Ozero(U_619))
| ~ c_Orderings_Oord__class_Oless(U_619,U_621,c_Groups_Ozero__class_Ozero(U_619))
| ~ c_Orderings_Oord__class_Oless(U_619,U_620,c_Groups_Ozero__class_Ozero(U_619))
| ~ class_Groups_Oordered__comm__monoid__add(U_619) ),
inference(definitional_conversion,[status(esa)],[f_204_2]) ).
cnf(f_204_4,plain,
( c_Orderings_Oord__class_Oless(U_619,c_Groups_Oplus__class_Oplus(U_619,U_620,U_621),c_Groups_Ozero__class_Ozero(U_619))
| ~ c_Orderings_Oord__class_Oless(U_619,U_621,c_Groups_Ozero__class_Ozero(U_619))
| ~ c_Orderings_Oord__class_Oless(U_619,U_620,c_Groups_Ozero__class_Ozero(U_619))
| ~ class_Groups_Oordered__comm__monoid__add(U_619) ),
inference(clausify,[status(thm)],[f_204_3]) ).
fof(f_205_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_205_2,plain,
! [U_626,U_625,U_624,U_623,U_622] :
( c_Orderings_Oord__class_Oless(U_622,c_Groups_Oplus__class_Oplus(U_622,U_623,U_625),c_Groups_Oplus__class_Oplus(U_622,U_624,U_626))
| ~ c_Orderings_Oord__class_Oless__eq(U_622,U_625,U_626)
| ~ c_Orderings_Oord__class_Oless(U_622,U_623,U_624)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_622) ),
inference(variable_rename,[status(thm)],[f_205_1]) ).
fof(f_205_3,plain,
! [U_623,U_622,U_624,U_625,U_626] :
( c_Orderings_Oord__class_Oless(U_622,c_Groups_Oplus__class_Oplus(U_622,U_623,U_625),c_Groups_Oplus__class_Oplus(U_622,U_624,U_626))
| ~ c_Orderings_Oord__class_Oless__eq(U_622,U_625,U_626)
| ~ c_Orderings_Oord__class_Oless(U_622,U_623,U_624)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_622) ),
inference(definitional_conversion,[status(esa)],[f_205_2]) ).
cnf(f_205_4,plain,
( c_Orderings_Oord__class_Oless(U_622,c_Groups_Oplus__class_Oplus(U_622,U_623,U_625),c_Groups_Oplus__class_Oplus(U_622,U_624,U_626))
| ~ c_Orderings_Oord__class_Oless__eq(U_622,U_625,U_626)
| ~ c_Orderings_Oord__class_Oless(U_622,U_623,U_624)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_622) ),
inference(clausify,[status(thm)],[f_205_3]) ).
fof(f_206_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_206_2,plain,
! [U_631,U_630,U_629,U_628,U_627] :
( c_Orderings_Oord__class_Oless(U_627,c_Groups_Oplus__class_Oplus(U_627,U_628,U_630),c_Groups_Oplus__class_Oplus(U_627,U_629,U_631))
| ~ c_Orderings_Oord__class_Oless(U_627,U_630,U_631)
| ~ c_Orderings_Oord__class_Oless__eq(U_627,U_628,U_629)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_627) ),
inference(variable_rename,[status(thm)],[f_206_1]) ).
fof(f_206_3,plain,
! [U_627,U_628,U_629,U_630,U_631] :
( c_Orderings_Oord__class_Oless(U_627,c_Groups_Oplus__class_Oplus(U_627,U_628,U_630),c_Groups_Oplus__class_Oplus(U_627,U_629,U_631))
| ~ c_Orderings_Oord__class_Oless(U_627,U_630,U_631)
| ~ c_Orderings_Oord__class_Oless__eq(U_627,U_628,U_629)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_627) ),
inference(definitional_conversion,[status(esa)],[f_206_2]) ).
cnf(f_206_4,plain,
( c_Orderings_Oord__class_Oless(U_627,c_Groups_Oplus__class_Oplus(U_627,U_628,U_630),c_Groups_Oplus__class_Oplus(U_627,U_629,U_631))
| ~ c_Orderings_Oord__class_Oless(U_627,U_630,U_631)
| ~ c_Orderings_Oord__class_Oless__eq(U_627,U_628,U_629)
| ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_627) ),
inference(clausify,[status(thm)],[f_206_3]) ).
fof(f_207_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_207_2,plain,
! [U_633,U_632] :
( c_Orderings_Oord__class_Oless__eq(U_632,c_Groups_Ozero__class_Ozero(U_632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_632),U_633),U_633))
| ~ class_Rings_Olinordered__ring(U_632) ),
inference(variable_rename,[status(thm)],[f_207_1]) ).
fof(f_207_3,plain,
! [U_632,U_633] :
( c_Orderings_Oord__class_Oless__eq(U_632,c_Groups_Ozero__class_Ozero(U_632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_632),U_633),U_633))
| ~ class_Rings_Olinordered__ring(U_632) ),
inference(definitional_conversion,[status(esa)],[f_207_2]) ).
cnf(f_207_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_632,c_Groups_Ozero__class_Ozero(U_632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_632),U_633),U_633))
| ~ class_Rings_Olinordered__ring(U_632) ),
inference(clausify,[status(thm)],[f_207_3]) ).
fof(f_208_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_208_2,plain,
! [U_636,U_635,U_634] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),U_636))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_634,U_636,c_Groups_Ozero__class_Ozero(U_634))
| ~ c_Orderings_Oord__class_Oless__eq(U_634,U_635,c_Groups_Ozero__class_Ozero(U_634)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_636)
| ~ 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,U_636,c_Groups_Ozero__class_Ozero(U_634))
& c_Orderings_Oord__class_Oless__eq(U_634,U_635,c_Groups_Ozero__class_Ozero(U_634)) )
| ( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_636)
& 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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),U_636)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_634) ),
inference(variable_rename,[status(thm)],[f_208_1]) ).
fof(f_208_3,plain,
( ! [U_635,U_636,U_634] :
( ~ c_Orderings_Oord__class_Oless__eq(U_634,U_636,c_Groups_Ozero__class_Ozero(U_634))
| ~ c_Orderings_Oord__class_Oless__eq(U_634,U_635,c_Groups_Ozero__class_Ozero(U_634))
| ~ sP66(U_635,U_636,U_634) )
& ! [U_635,U_636,U_634] :
( ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_636)
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635)
| ~ sP66(U_635,U_636,U_634) )
& ! [U_635,U_636,U_634] :
( c_Orderings_Oord__class_Oless__eq(U_634,U_636,c_Groups_Ozero__class_Ozero(U_634))
| ~ sP65(U_635,U_636,U_634) )
& ! [U_635,U_636,U_634] :
( c_Orderings_Oord__class_Oless__eq(U_634,U_635,c_Groups_Ozero__class_Ozero(U_634))
| ~ sP65(U_635,U_636,U_634) )
& ! [U_635,U_636,U_634] :
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_636)
| ~ sP64(U_635,U_636,U_634) )
& ! [U_635,U_636,U_634] :
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635)
| ~ sP64(U_635,U_636,U_634) )
& ! [U_635,U_636,U_634] :
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),U_636))
| sP66(U_635,U_636,U_634)
| ~ sP67(U_635,U_636,U_634) )
& ! [U_635,U_636,U_634] :
( sP65(U_635,U_636,U_634)
| sP64(U_635,U_636,U_634)
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),U_636))
| ~ sP67(U_635,U_636,U_634) )
& ! [U_635,U_636,U_634] :
( sP67(U_635,U_636,U_634)
| ~ class_Rings_Olinordered__ring__strict(U_634) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64,sP65,sP66,sP67])],[f_208_2]) ).
cnf(f_208_4,plain,
( sP67(U_635,U_636,U_634)
| ~ class_Rings_Olinordered__ring__strict(U_634) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_5,plain,
( sP65(U_635,U_636,U_634)
| sP64(U_635,U_636,U_634)
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),U_636))
| ~ sP67(U_635,U_636,U_634) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_634),U_635),U_636))
| sP66(U_635,U_636,U_634)
| ~ sP67(U_635,U_636,U_634) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635)
| ~ sP64(U_635,U_636,U_634) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_636)
| ~ sP64(U_635,U_636,U_634) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_634,U_635,c_Groups_Ozero__class_Ozero(U_634))
| ~ sP65(U_635,U_636,U_634) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_634,U_636,c_Groups_Ozero__class_Ozero(U_634))
| ~ sP65(U_635,U_636,U_634) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_11,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_636)
| ~ c_Orderings_Oord__class_Oless__eq(U_634,c_Groups_Ozero__class_Ozero(U_634),U_635)
| ~ sP66(U_635,U_636,U_634) ),
inference(clausify,[status(thm)],[f_208_3]) ).
cnf(f_208_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_634,U_636,c_Groups_Ozero__class_Ozero(U_634))
| ~ c_Orderings_Oord__class_Oless__eq(U_634,U_635,c_Groups_Ozero__class_Ozero(U_634))
| ~ sP66(U_635,U_636,U_634) ),
inference(clausify,[status(thm)],[f_208_3]) ).
fof(f_209_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_209_2,plain,
! [U_639,U_638,U_637] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_637),U_638),U_639),c_Groups_Ozero__class_Ozero(U_637))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_639)
| ~ c_Orderings_Oord__class_Oless__eq(U_637,U_638,c_Groups_Ozero__class_Ozero(U_637)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_637,U_639,c_Groups_Ozero__class_Ozero(U_637))
| ~ c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_638) ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_639)
& c_Orderings_Oord__class_Oless__eq(U_637,U_638,c_Groups_Ozero__class_Ozero(U_637)) )
| ( c_Orderings_Oord__class_Oless__eq(U_637,U_639,c_Groups_Ozero__class_Ozero(U_637))
& c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_638) )
| ~ c_Orderings_Oord__class_Oless__eq(U_637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_637),U_638),U_639),c_Groups_Ozero__class_Ozero(U_637)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_637) ),
inference(variable_rename,[status(thm)],[f_209_1]) ).
fof(f_209_3,plain,
( ! [U_638,U_639,U_637] :
( ~ c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_639)
| ~ c_Orderings_Oord__class_Oless__eq(U_637,U_638,c_Groups_Ozero__class_Ozero(U_637))
| ~ sP70(U_638,U_639,U_637) )
& ! [U_638,U_639,U_637] :
( ~ c_Orderings_Oord__class_Oless__eq(U_637,U_639,c_Groups_Ozero__class_Ozero(U_637))
| ~ c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_638)
| ~ sP70(U_638,U_639,U_637) )
& ! [U_638,U_639,U_637] :
( c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_639)
| ~ sP69(U_638,U_639,U_637) )
& ! [U_638,U_639,U_637] :
( c_Orderings_Oord__class_Oless__eq(U_637,U_638,c_Groups_Ozero__class_Ozero(U_637))
| ~ sP69(U_638,U_639,U_637) )
& ! [U_638,U_639,U_637] :
( c_Orderings_Oord__class_Oless__eq(U_637,U_639,c_Groups_Ozero__class_Ozero(U_637))
| ~ sP68(U_638,U_639,U_637) )
& ! [U_638,U_639,U_637] :
( c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_638)
| ~ sP68(U_638,U_639,U_637) )
& ! [U_638,U_639,U_637] :
( c_Orderings_Oord__class_Oless__eq(U_637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_637),U_638),U_639),c_Groups_Ozero__class_Ozero(U_637))
| sP70(U_638,U_639,U_637)
| ~ sP71(U_638,U_639,U_637) )
& ! [U_638,U_639,U_637] :
( sP69(U_638,U_639,U_637)
| sP68(U_638,U_639,U_637)
| ~ c_Orderings_Oord__class_Oless__eq(U_637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_637),U_638),U_639),c_Groups_Ozero__class_Ozero(U_637))
| ~ sP71(U_638,U_639,U_637) )
& ! [U_638,U_639,U_637] :
( sP71(U_638,U_639,U_637)
| ~ class_Rings_Olinordered__ring__strict(U_637) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68,sP69,sP70,sP71])],[f_209_2]) ).
cnf(f_209_4,plain,
( sP71(U_638,U_639,U_637)
| ~ class_Rings_Olinordered__ring__strict(U_637) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_5,plain,
( sP69(U_638,U_639,U_637)
| sP68(U_638,U_639,U_637)
| ~ c_Orderings_Oord__class_Oless__eq(U_637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_637),U_638),U_639),c_Groups_Ozero__class_Ozero(U_637))
| ~ sP71(U_638,U_639,U_637) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_637,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_637),U_638),U_639),c_Groups_Ozero__class_Ozero(U_637))
| sP70(U_638,U_639,U_637)
| ~ sP71(U_638,U_639,U_637) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_638)
| ~ sP68(U_638,U_639,U_637) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_637,U_639,c_Groups_Ozero__class_Ozero(U_637))
| ~ sP68(U_638,U_639,U_637) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_9,plain,
( c_Orderings_Oord__class_Oless__eq(U_637,U_638,c_Groups_Ozero__class_Ozero(U_637))
| ~ sP69(U_638,U_639,U_637) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_10,plain,
( c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_639)
| ~ sP69(U_638,U_639,U_637) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_11,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_637,U_639,c_Groups_Ozero__class_Ozero(U_637))
| ~ c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_638)
| ~ sP70(U_638,U_639,U_637) ),
inference(clausify,[status(thm)],[f_209_3]) ).
cnf(f_209_12,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_637,c_Groups_Ozero__class_Ozero(U_637),U_639)
| ~ c_Orderings_Oord__class_Oless__eq(U_637,U_638,c_Groups_Ozero__class_Ozero(U_637))
| ~ sP70(U_638,U_639,U_637) ),
inference(clausify,[status(thm)],[f_209_3]) ).
fof(f_210_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_210_2,plain,
! [U_642,U_641,U_640] :
( c_Orderings_Oord__class_Oless__eq(U_640,c_Groups_Ozero__class_Ozero(U_640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_640),U_641),U_642))
| ~ c_Orderings_Oord__class_Oless__eq(U_640,c_Groups_Ozero__class_Ozero(U_640),U_642)
| ~ c_Orderings_Oord__class_Oless__eq(U_640,c_Groups_Ozero__class_Ozero(U_640),U_641)
| ~ class_Rings_Oordered__cancel__semiring(U_640) ),
inference(variable_rename,[status(thm)],[f_210_1]) ).
fof(f_210_3,plain,
! [U_642,U_640,U_641] :
( c_Orderings_Oord__class_Oless__eq(U_640,c_Groups_Ozero__class_Ozero(U_640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_640),U_641),U_642))
| ~ c_Orderings_Oord__class_Oless__eq(U_640,c_Groups_Ozero__class_Ozero(U_640),U_642)
| ~ c_Orderings_Oord__class_Oless__eq(U_640,c_Groups_Ozero__class_Ozero(U_640),U_641)
| ~ class_Rings_Oordered__cancel__semiring(U_640) ),
inference(definitional_conversion,[status(esa)],[f_210_2]) ).
cnf(f_210_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_640,c_Groups_Ozero__class_Ozero(U_640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_640),U_641),U_642))
| ~ c_Orderings_Oord__class_Oless__eq(U_640,c_Groups_Ozero__class_Ozero(U_640),U_642)
| ~ c_Orderings_Oord__class_Oless__eq(U_640,c_Groups_Ozero__class_Ozero(U_640),U_641)
| ~ class_Rings_Oordered__cancel__semiring(U_640) ),
inference(clausify,[status(thm)],[f_210_3]) ).
fof(f_211_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_211_2,plain,
! [U_645,U_644,U_643] :
( c_Orderings_Oord__class_Oless__eq(U_643,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_643),U_644),U_645),c_Groups_Ozero__class_Ozero(U_643))
| ~ c_Orderings_Oord__class_Oless__eq(U_643,U_645,c_Groups_Ozero__class_Ozero(U_643))
| ~ c_Orderings_Oord__class_Oless__eq(U_643,c_Groups_Ozero__class_Ozero(U_643),U_644)
| ~ class_Rings_Oordered__cancel__semiring(U_643) ),
inference(variable_rename,[status(thm)],[f_211_1]) ).
fof(f_211_3,plain,
! [U_645,U_643,U_644] :
( c_Orderings_Oord__class_Oless__eq(U_643,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_643),U_644),U_645),c_Groups_Ozero__class_Ozero(U_643))
| ~ c_Orderings_Oord__class_Oless__eq(U_643,U_645,c_Groups_Ozero__class_Ozero(U_643))
| ~ c_Orderings_Oord__class_Oless__eq(U_643,c_Groups_Ozero__class_Ozero(U_643),U_644)
| ~ class_Rings_Oordered__cancel__semiring(U_643) ),
inference(definitional_conversion,[status(esa)],[f_211_2]) ).
cnf(f_211_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_643,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_643),U_644),U_645),c_Groups_Ozero__class_Ozero(U_643))
| ~ c_Orderings_Oord__class_Oless__eq(U_643,U_645,c_Groups_Ozero__class_Ozero(U_643))
| ~ c_Orderings_Oord__class_Oless__eq(U_643,c_Groups_Ozero__class_Ozero(U_643),U_644)
| ~ class_Rings_Oordered__cancel__semiring(U_643) ),
inference(clausify,[status(thm)],[f_211_3]) ).
fof(f_212_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_212_2,plain,
! [U_648,U_647,U_646] :
( c_Orderings_Oord__class_Oless__eq(U_646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_646),U_648),U_647),c_Groups_Ozero__class_Ozero(U_646))
| ~ c_Orderings_Oord__class_Oless__eq(U_646,U_648,c_Groups_Ozero__class_Ozero(U_646))
| ~ c_Orderings_Oord__class_Oless__eq(U_646,c_Groups_Ozero__class_Ozero(U_646),U_647)
| ~ class_Rings_Oordered__cancel__semiring(U_646) ),
inference(variable_rename,[status(thm)],[f_212_1]) ).
fof(f_212_3,plain,
! [U_646,U_647,U_648] :
( c_Orderings_Oord__class_Oless__eq(U_646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_646),U_648),U_647),c_Groups_Ozero__class_Ozero(U_646))
| ~ c_Orderings_Oord__class_Oless__eq(U_646,U_648,c_Groups_Ozero__class_Ozero(U_646))
| ~ c_Orderings_Oord__class_Oless__eq(U_646,c_Groups_Ozero__class_Ozero(U_646),U_647)
| ~ class_Rings_Oordered__cancel__semiring(U_646) ),
inference(definitional_conversion,[status(esa)],[f_212_2]) ).
cnf(f_212_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_646,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_646),U_648),U_647),c_Groups_Ozero__class_Ozero(U_646))
| ~ c_Orderings_Oord__class_Oless__eq(U_646,U_648,c_Groups_Ozero__class_Ozero(U_646))
| ~ c_Orderings_Oord__class_Oless__eq(U_646,c_Groups_Ozero__class_Ozero(U_646),U_647)
| ~ class_Rings_Oordered__cancel__semiring(U_646) ),
inference(clausify,[status(thm)],[f_212_3]) ).
fof(f_213_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_213_2,plain,
! [U_651,U_650,U_649] :
( c_Orderings_Oord__class_Oless__eq(U_649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_649),U_650),U_651),c_Groups_Ozero__class_Ozero(U_649))
| ~ c_Orderings_Oord__class_Oless__eq(U_649,c_Groups_Ozero__class_Ozero(U_649),U_651)
| ~ c_Orderings_Oord__class_Oless__eq(U_649,U_650,c_Groups_Ozero__class_Ozero(U_649))
| ~ class_Rings_Oordered__cancel__semiring(U_649) ),
inference(variable_rename,[status(thm)],[f_213_1]) ).
fof(f_213_3,plain,
! [U_649,U_650,U_651] :
( c_Orderings_Oord__class_Oless__eq(U_649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_649),U_650),U_651),c_Groups_Ozero__class_Ozero(U_649))
| ~ c_Orderings_Oord__class_Oless__eq(U_649,c_Groups_Ozero__class_Ozero(U_649),U_651)
| ~ c_Orderings_Oord__class_Oless__eq(U_649,U_650,c_Groups_Ozero__class_Ozero(U_649))
| ~ class_Rings_Oordered__cancel__semiring(U_649) ),
inference(definitional_conversion,[status(esa)],[f_213_2]) ).
cnf(f_213_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_649),U_650),U_651),c_Groups_Ozero__class_Ozero(U_649))
| ~ c_Orderings_Oord__class_Oless__eq(U_649,c_Groups_Ozero__class_Ozero(U_649),U_651)
| ~ c_Orderings_Oord__class_Oless__eq(U_649,U_650,c_Groups_Ozero__class_Ozero(U_649))
| ~ class_Rings_Oordered__cancel__semiring(U_649) ),
inference(clausify,[status(thm)],[f_213_3]) ).
fof(f_214_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_214_2,plain,
! [U_654,U_653,U_652] :
( c_Orderings_Oord__class_Oless__eq(U_652,c_Groups_Ozero__class_Ozero(U_652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_652),U_653),U_654))
| ~ 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_Rings_Oordered__ring(U_652) ),
inference(variable_rename,[status(thm)],[f_214_1]) ).
fof(f_214_3,plain,
! [U_652,U_653,U_654] :
( c_Orderings_Oord__class_Oless__eq(U_652,c_Groups_Ozero__class_Ozero(U_652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_652),U_653),U_654))
| ~ 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_Rings_Oordered__ring(U_652) ),
inference(definitional_conversion,[status(esa)],[f_214_2]) ).
cnf(f_214_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_652,c_Groups_Ozero__class_Ozero(U_652),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_652),U_653),U_654))
| ~ 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_Rings_Oordered__ring(U_652) ),
inference(clausify,[status(thm)],[f_214_3]) ).
fof(f_215_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_215_2,plain,
! [U_658,U_657,U_656,U_655] :
( c_Orderings_Oord__class_Oless__eq(U_655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),U_658),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_657),U_658))
| ~ c_Orderings_Oord__class_Oless__eq(U_655,c_Groups_Ozero__class_Ozero(U_655),U_658)
| ~ c_Orderings_Oord__class_Oless__eq(U_655,U_656,U_657)
| ~ class_Rings_Oordered__semiring(U_655) ),
inference(variable_rename,[status(thm)],[f_215_1]) ).
fof(f_215_3,plain,
! [U_655,U_656,U_657,U_658] :
( c_Orderings_Oord__class_Oless__eq(U_655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),U_658),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_657),U_658))
| ~ c_Orderings_Oord__class_Oless__eq(U_655,c_Groups_Ozero__class_Ozero(U_655),U_658)
| ~ c_Orderings_Oord__class_Oless__eq(U_655,U_656,U_657)
| ~ class_Rings_Oordered__semiring(U_655) ),
inference(definitional_conversion,[status(esa)],[f_215_2]) ).
cnf(f_215_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_656),U_658),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_655),U_657),U_658))
| ~ c_Orderings_Oord__class_Oless__eq(U_655,c_Groups_Ozero__class_Ozero(U_655),U_658)
| ~ c_Orderings_Oord__class_Oless__eq(U_655,U_656,U_657)
| ~ class_Rings_Oordered__semiring(U_655) ),
inference(clausify,[status(thm)],[f_215_3]) ).
fof(f_216_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_216_2,plain,
! [U_662,U_661,U_660,U_659] :
( c_Orderings_Oord__class_Oless__eq(U_659,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_662),U_660),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_662),U_661))
| ~ c_Orderings_Oord__class_Oless__eq(U_659,c_Groups_Ozero__class_Ozero(U_659),U_662)
| ~ c_Orderings_Oord__class_Oless__eq(U_659,U_660,U_661)
| ~ class_Rings_Oordered__semiring(U_659) ),
inference(variable_rename,[status(thm)],[f_216_1]) ).
fof(f_216_3,plain,
! [U_659,U_660,U_661,U_662] :
( c_Orderings_Oord__class_Oless__eq(U_659,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_662),U_660),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_662),U_661))
| ~ c_Orderings_Oord__class_Oless__eq(U_659,c_Groups_Ozero__class_Ozero(U_659),U_662)
| ~ c_Orderings_Oord__class_Oless__eq(U_659,U_660,U_661)
| ~ class_Rings_Oordered__semiring(U_659) ),
inference(definitional_conversion,[status(esa)],[f_216_2]) ).
cnf(f_216_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_659,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_662),U_660),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_659),U_662),U_661))
| ~ c_Orderings_Oord__class_Oless__eq(U_659,c_Groups_Ozero__class_Ozero(U_659),U_662)
| ~ c_Orderings_Oord__class_Oless__eq(U_659,U_660,U_661)
| ~ class_Rings_Oordered__semiring(U_659) ),
inference(clausify,[status(thm)],[f_216_3]) ).
fof(f_217_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_217_2,plain,
! [U_666,U_665,U_664,U_663] :
( c_Orderings_Oord__class_Oless__eq(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_664),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665))
| ~ c_Orderings_Oord__class_Oless__eq(U_663,c_Groups_Ozero__class_Ozero(U_663),U_666)
| ~ c_Orderings_Oord__class_Oless__eq(U_663,U_664,U_665)
| ~ class_Rings_Oordered__comm__semiring(U_663) ),
inference(variable_rename,[status(thm)],[f_217_1]) ).
fof(f_217_3,plain,
! [U_663,U_664,U_665,U_666] :
( c_Orderings_Oord__class_Oless__eq(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_664),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665))
| ~ c_Orderings_Oord__class_Oless__eq(U_663,c_Groups_Ozero__class_Ozero(U_663),U_666)
| ~ c_Orderings_Oord__class_Oless__eq(U_663,U_664,U_665)
| ~ class_Rings_Oordered__comm__semiring(U_663) ),
inference(definitional_conversion,[status(esa)],[f_217_2]) ).
cnf(f_217_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_663,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_664),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_663),U_666),U_665))
| ~ c_Orderings_Oord__class_Oless__eq(U_663,c_Groups_Ozero__class_Ozero(U_663),U_666)
| ~ c_Orderings_Oord__class_Oless__eq(U_663,U_664,U_665)
| ~ class_Rings_Oordered__comm__semiring(U_663) ),
inference(clausify,[status(thm)],[f_217_3]) ).
fof(f_218_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_218_2,plain,
! [U_670,U_669,U_668,U_667] :
( c_Orderings_Oord__class_Oless__eq(U_667,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_669),U_670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_668),U_670))
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_670,c_Groups_Ozero__class_Ozero(U_667))
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_668,U_669)
| ~ class_Rings_Oordered__ring(U_667) ),
inference(variable_rename,[status(thm)],[f_218_1]) ).
fof(f_218_3,plain,
! [U_667,U_668,U_669,U_670] :
( c_Orderings_Oord__class_Oless__eq(U_667,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_669),U_670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_668),U_670))
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_670,c_Groups_Ozero__class_Ozero(U_667))
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_668,U_669)
| ~ class_Rings_Oordered__ring(U_667) ),
inference(definitional_conversion,[status(esa)],[f_218_2]) ).
cnf(f_218_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_667,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_669),U_670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_667),U_668),U_670))
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_670,c_Groups_Ozero__class_Ozero(U_667))
| ~ c_Orderings_Oord__class_Oless__eq(U_667,U_668,U_669)
| ~ class_Rings_Oordered__ring(U_667) ),
inference(clausify,[status(thm)],[f_218_3]) ).
fof(f_219_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_219_2,plain,
! [U_674,U_673,U_672,U_671] :
( c_Orderings_Oord__class_Oless__eq(U_671,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_672))
| ~ c_Orderings_Oord__class_Oless__eq(U_671,U_674,c_Groups_Ozero__class_Ozero(U_671))
| ~ c_Orderings_Oord__class_Oless__eq(U_671,U_672,U_673)
| ~ class_Rings_Oordered__ring(U_671) ),
inference(variable_rename,[status(thm)],[f_219_1]) ).
fof(f_219_3,plain,
! [U_671,U_672,U_673,U_674] :
( c_Orderings_Oord__class_Oless__eq(U_671,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_672))
| ~ c_Orderings_Oord__class_Oless__eq(U_671,U_674,c_Groups_Ozero__class_Ozero(U_671))
| ~ c_Orderings_Oord__class_Oless__eq(U_671,U_672,U_673)
| ~ class_Rings_Oordered__ring(U_671) ),
inference(definitional_conversion,[status(esa)],[f_219_2]) ).
cnf(f_219_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_671,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_671),U_674),U_672))
| ~ c_Orderings_Oord__class_Oless__eq(U_671,U_674,c_Groups_Ozero__class_Ozero(U_671))
| ~ c_Orderings_Oord__class_Oless__eq(U_671,U_672,U_673)
| ~ class_Rings_Oordered__ring(U_671) ),
inference(clausify,[status(thm)],[f_219_3]) ).
fof(f_220_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_220_2,plain,
! [U_679,U_678,U_677,U_676,U_675] :
( c_Orderings_Oord__class_Oless__eq(U_675,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_675),U_676),U_678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_675),U_677),U_679))
| ~ c_Orderings_Oord__class_Oless__eq(U_675,c_Groups_Ozero__class_Ozero(U_675),U_678)
| ~ c_Orderings_Oord__class_Oless__eq(U_675,c_Groups_Ozero__class_Ozero(U_675),U_676)
| ~ c_Orderings_Oord__class_Oless__eq(U_675,U_678,U_679)
| ~ c_Orderings_Oord__class_Oless__eq(U_675,U_676,U_677)
| ~ class_Rings_Oordered__semiring(U_675) ),
inference(variable_rename,[status(thm)],[f_220_1]) ).
fof(f_220_3,plain,
! [U_675,U_676,U_677,U_678,U_679] :
( c_Orderings_Oord__class_Oless__eq(U_675,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_675),U_676),U_678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_675),U_677),U_679))
| ~ c_Orderings_Oord__class_Oless__eq(U_675,c_Groups_Ozero__class_Ozero(U_675),U_678)
| ~ c_Orderings_Oord__class_Oless__eq(U_675,c_Groups_Ozero__class_Ozero(U_675),U_676)
| ~ c_Orderings_Oord__class_Oless__eq(U_675,U_678,U_679)
| ~ c_Orderings_Oord__class_Oless__eq(U_675,U_676,U_677)
| ~ class_Rings_Oordered__semiring(U_675) ),
inference(definitional_conversion,[status(esa)],[f_220_2]) ).
cnf(f_220_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_675,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_675),U_676),U_678),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_675),U_677),U_679))
| ~ c_Orderings_Oord__class_Oless__eq(U_675,c_Groups_Ozero__class_Ozero(U_675),U_678)
| ~ c_Orderings_Oord__class_Oless__eq(U_675,c_Groups_Ozero__class_Ozero(U_675),U_676)
| ~ c_Orderings_Oord__class_Oless__eq(U_675,U_678,U_679)
| ~ c_Orderings_Oord__class_Oless__eq(U_675,U_676,U_677)
| ~ class_Rings_Oordered__semiring(U_675) ),
inference(clausify,[status(thm)],[f_220_3]) ).
fof(f_221_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_221_2,plain,
! [U_684,U_683,U_682,U_681,U_680] :
( c_Orderings_Oord__class_Oless__eq(U_680,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_682),U_684))
| ~ c_Orderings_Oord__class_Oless__eq(U_680,c_Groups_Ozero__class_Ozero(U_680),U_683)
| ~ c_Orderings_Oord__class_Oless__eq(U_680,c_Groups_Ozero__class_Ozero(U_680),U_682)
| ~ c_Orderings_Oord__class_Oless__eq(U_680,U_683,U_684)
| ~ c_Orderings_Oord__class_Oless__eq(U_680,U_681,U_682)
| ~ class_Rings_Oordered__semiring(U_680) ),
inference(variable_rename,[status(thm)],[f_221_1]) ).
fof(f_221_3,plain,
! [U_680,U_683,U_681,U_682,U_684] :
( c_Orderings_Oord__class_Oless__eq(U_680,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_682),U_684))
| ~ c_Orderings_Oord__class_Oless__eq(U_680,c_Groups_Ozero__class_Ozero(U_680),U_683)
| ~ c_Orderings_Oord__class_Oless__eq(U_680,c_Groups_Ozero__class_Ozero(U_680),U_682)
| ~ c_Orderings_Oord__class_Oless__eq(U_680,U_683,U_684)
| ~ c_Orderings_Oord__class_Oless__eq(U_680,U_681,U_682)
| ~ class_Rings_Oordered__semiring(U_680) ),
inference(definitional_conversion,[status(esa)],[f_221_2]) ).
cnf(f_221_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_680,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_682),U_684))
| ~ c_Orderings_Oord__class_Oless__eq(U_680,c_Groups_Ozero__class_Ozero(U_680),U_683)
| ~ c_Orderings_Oord__class_Oless__eq(U_680,c_Groups_Ozero__class_Ozero(U_680),U_682)
| ~ c_Orderings_Oord__class_Oless__eq(U_680,U_683,U_684)
| ~ c_Orderings_Oord__class_Oless__eq(U_680,U_681,U_682)
| ~ class_Rings_Oordered__semiring(U_680) ),
inference(clausify,[status(thm)],[f_221_3]) ).
fof(f_222_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_222_2,plain,
! [U_687,U_686,U_685] :
( c_Orderings_Oord__class_Oless__eq(U_685,c_Groups_Ozero__class_Ozero(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_685,U_687,c_Groups_Ozero__class_Ozero(U_685))
| ~ c_Orderings_Oord__class_Oless__eq(U_685,U_686,c_Groups_Ozero__class_Ozero(U_685)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_685,c_Groups_Ozero__class_Ozero(U_685),U_687)
| ~ c_Orderings_Oord__class_Oless__eq(U_685,c_Groups_Ozero__class_Ozero(U_685),U_686) ) )
| ~ class_Rings_Oordered__ring(U_685) ),
inference(variable_rename,[status(thm)],[f_222_1]) ).
fof(f_222_3,plain,
( ! [U_687,U_686,U_685] :
( ~ c_Orderings_Oord__class_Oless__eq(U_685,U_687,c_Groups_Ozero__class_Ozero(U_685))
| ~ c_Orderings_Oord__class_Oless__eq(U_685,U_686,c_Groups_Ozero__class_Ozero(U_685))
| ~ sP72(U_687,U_686,U_685) )
& ! [U_687,U_686,U_685] :
( ~ c_Orderings_Oord__class_Oless__eq(U_685,c_Groups_Ozero__class_Ozero(U_685),U_687)
| ~ c_Orderings_Oord__class_Oless__eq(U_685,c_Groups_Ozero__class_Ozero(U_685),U_686)
| ~ sP72(U_687,U_686,U_685) )
& ! [U_687,U_686,U_685] :
( c_Orderings_Oord__class_Oless__eq(U_685,c_Groups_Ozero__class_Ozero(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687))
| sP72(U_687,U_686,U_685)
| ~ class_Rings_Oordered__ring(U_685) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_222_2]) ).
cnf(f_222_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_685,c_Groups_Ozero__class_Ozero(U_685),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_685),U_686),U_687))
| sP72(U_687,U_686,U_685)
| ~ class_Rings_Oordered__ring(U_685) ),
inference(clausify,[status(thm)],[f_222_3]) ).
cnf(f_222_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_685,c_Groups_Ozero__class_Ozero(U_685),U_687)
| ~ c_Orderings_Oord__class_Oless__eq(U_685,c_Groups_Ozero__class_Ozero(U_685),U_686)
| ~ sP72(U_687,U_686,U_685) ),
inference(clausify,[status(thm)],[f_222_3]) ).
cnf(f_222_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_685,U_687,c_Groups_Ozero__class_Ozero(U_685))
| ~ c_Orderings_Oord__class_Oless__eq(U_685,U_686,c_Groups_Ozero__class_Ozero(U_685))
| ~ sP72(U_687,U_686,U_685) ),
inference(clausify,[status(thm)],[f_222_3]) ).
fof(f_223_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_223_2,plain,
! [U_690,U_689,U_688] :
( c_Orderings_Oord__class_Oless__eq(U_688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_688),U_689),U_690),c_Groups_Ozero__class_Ozero(U_688))
| ( ( ~ c_Orderings_Oord__class_Oless__eq(U_688,c_Groups_Ozero__class_Ozero(U_688),U_690)
| ~ c_Orderings_Oord__class_Oless__eq(U_688,U_689,c_Groups_Ozero__class_Ozero(U_688)) )
& ( ~ c_Orderings_Oord__class_Oless__eq(U_688,U_690,c_Groups_Ozero__class_Ozero(U_688))
| ~ c_Orderings_Oord__class_Oless__eq(U_688,c_Groups_Ozero__class_Ozero(U_688),U_689) ) )
| ~ class_Rings_Oordered__cancel__semiring(U_688) ),
inference(variable_rename,[status(thm)],[f_223_1]) ).
fof(f_223_3,plain,
( ! [U_689,U_690,U_688] :
( ~ c_Orderings_Oord__class_Oless__eq(U_688,c_Groups_Ozero__class_Ozero(U_688),U_690)
| ~ c_Orderings_Oord__class_Oless__eq(U_688,U_689,c_Groups_Ozero__class_Ozero(U_688))
| ~ sP73(U_689,U_690,U_688) )
& ! [U_689,U_690,U_688] :
( ~ c_Orderings_Oord__class_Oless__eq(U_688,U_690,c_Groups_Ozero__class_Ozero(U_688))
| ~ c_Orderings_Oord__class_Oless__eq(U_688,c_Groups_Ozero__class_Ozero(U_688),U_689)
| ~ sP73(U_689,U_690,U_688) )
& ! [U_689,U_690,U_688] :
( c_Orderings_Oord__class_Oless__eq(U_688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_688),U_689),U_690),c_Groups_Ozero__class_Ozero(U_688))
| sP73(U_689,U_690,U_688)
| ~ class_Rings_Oordered__cancel__semiring(U_688) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_223_2]) ).
cnf(f_223_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_688,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_688),U_689),U_690),c_Groups_Ozero__class_Ozero(U_688))
| sP73(U_689,U_690,U_688)
| ~ class_Rings_Oordered__cancel__semiring(U_688) ),
inference(clausify,[status(thm)],[f_223_3]) ).
cnf(f_223_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_688,U_690,c_Groups_Ozero__class_Ozero(U_688))
| ~ c_Orderings_Oord__class_Oless__eq(U_688,c_Groups_Ozero__class_Ozero(U_688),U_689)
| ~ sP73(U_689,U_690,U_688) ),
inference(clausify,[status(thm)],[f_223_3]) ).
cnf(f_223_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_688,c_Groups_Ozero__class_Ozero(U_688),U_690)
| ~ c_Orderings_Oord__class_Oless__eq(U_688,U_689,c_Groups_Ozero__class_Ozero(U_688))
| ~ sP73(U_689,U_690,U_688) ),
inference(clausify,[status(thm)],[f_223_3]) ).
fof(f_224_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_224_2,plain,
! [U_692,U_691] :
( ~ c_Orderings_Oord__class_Oless(U_691,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_691),U_692),U_692),c_Groups_Ozero__class_Ozero(U_691))
| ~ class_Rings_Olinordered__ring(U_691) ),
inference(variable_rename,[status(thm)],[f_224_1]) ).
fof(f_224_3,plain,
! [U_692,U_691] :
( ~ c_Orderings_Oord__class_Oless(U_691,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_691),U_692),U_692),c_Groups_Ozero__class_Ozero(U_691))
| ~ class_Rings_Olinordered__ring(U_691) ),
inference(definitional_conversion,[status(esa)],[f_224_2]) ).
cnf(f_224_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_691,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_691),U_692),U_692),c_Groups_Ozero__class_Ozero(U_691))
| ~ class_Rings_Olinordered__ring(U_691) ),
inference(clausify,[status(thm)],[f_224_3]) ).
fof(f_225_1,plain,
! [V_b_2,V_ca_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_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
| ( ( ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__right__disj]) ).
fof(f_225_2,plain,
! [U_696,U_695,U_694,U_693] :
( ( ( c_Orderings_Oord__class_Oless(U_693,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_696),U_695))
| ( ( ~ c_Orderings_Oord__class_Oless(U_693,U_696,U_694)
| ~ c_Orderings_Oord__class_Oless(U_693,U_695,c_Groups_Ozero__class_Ozero(U_693)) )
& ( ~ c_Orderings_Oord__class_Oless(U_693,U_694,U_696)
| ~ c_Orderings_Oord__class_Oless(U_693,c_Groups_Ozero__class_Ozero(U_693),U_695) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_693,U_696,U_694)
& c_Orderings_Oord__class_Oless(U_693,U_695,c_Groups_Ozero__class_Ozero(U_693)) )
| ( c_Orderings_Oord__class_Oless(U_693,U_694,U_696)
& c_Orderings_Oord__class_Oless(U_693,c_Groups_Ozero__class_Ozero(U_693),U_695) )
| ~ c_Orderings_Oord__class_Oless(U_693,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_696),U_695)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_693) ),
inference(variable_rename,[status(thm)],[f_225_1]) ).
fof(f_225_3,plain,
( ! [U_693,U_694,U_695,U_696] :
( ~ c_Orderings_Oord__class_Oless(U_693,U_696,U_694)
| ~ c_Orderings_Oord__class_Oless(U_693,U_695,c_Groups_Ozero__class_Ozero(U_693))
| ~ sP76(U_693,U_694,U_695,U_696) )
& ! [U_693,U_694,U_695,U_696] :
( ~ c_Orderings_Oord__class_Oless(U_693,U_694,U_696)
| ~ c_Orderings_Oord__class_Oless(U_693,c_Groups_Ozero__class_Ozero(U_693),U_695)
| ~ sP76(U_693,U_694,U_695,U_696) )
& ! [U_693,U_694,U_695,U_696] :
( c_Orderings_Oord__class_Oless(U_693,U_696,U_694)
| ~ sP75(U_693,U_694,U_695,U_696) )
& ! [U_693,U_694,U_695,U_696] :
( c_Orderings_Oord__class_Oless(U_693,U_695,c_Groups_Ozero__class_Ozero(U_693))
| ~ sP75(U_693,U_694,U_695,U_696) )
& ! [U_693,U_694,U_695,U_696] :
( c_Orderings_Oord__class_Oless(U_693,U_694,U_696)
| ~ sP74(U_693,U_694,U_695,U_696) )
& ! [U_693,U_694,U_695,U_696] :
( c_Orderings_Oord__class_Oless(U_693,c_Groups_Ozero__class_Ozero(U_693),U_695)
| ~ sP74(U_693,U_694,U_695,U_696) )
& ! [U_693,U_694,U_695,U_696] :
( c_Orderings_Oord__class_Oless(U_693,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_696),U_695))
| sP76(U_693,U_694,U_695,U_696)
| ~ sP77(U_693,U_694,U_695,U_696) )
& ! [U_693,U_694,U_695,U_696] :
( sP75(U_693,U_694,U_695,U_696)
| sP74(U_693,U_694,U_695,U_696)
| ~ c_Orderings_Oord__class_Oless(U_693,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_696),U_695))
| ~ sP77(U_693,U_694,U_695,U_696) )
& ! [U_693,U_694,U_695,U_696] :
( sP77(U_693,U_694,U_695,U_696)
| ~ class_Rings_Olinordered__ring__strict(U_693) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74,sP75,sP76,sP77])],[f_225_2]) ).
cnf(f_225_4,plain,
( sP77(U_693,U_694,U_695,U_696)
| ~ class_Rings_Olinordered__ring__strict(U_693) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_5,plain,
( sP75(U_693,U_694,U_695,U_696)
| sP74(U_693,U_694,U_695,U_696)
| ~ c_Orderings_Oord__class_Oless(U_693,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_696),U_695))
| ~ sP77(U_693,U_694,U_695,U_696) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_6,plain,
( c_Orderings_Oord__class_Oless(U_693,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_694),U_695),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_696),U_695))
| sP76(U_693,U_694,U_695,U_696)
| ~ sP77(U_693,U_694,U_695,U_696) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_7,plain,
( c_Orderings_Oord__class_Oless(U_693,c_Groups_Ozero__class_Ozero(U_693),U_695)
| ~ sP74(U_693,U_694,U_695,U_696) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_8,plain,
( c_Orderings_Oord__class_Oless(U_693,U_694,U_696)
| ~ sP74(U_693,U_694,U_695,U_696) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_9,plain,
( c_Orderings_Oord__class_Oless(U_693,U_695,c_Groups_Ozero__class_Ozero(U_693))
| ~ sP75(U_693,U_694,U_695,U_696) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_10,plain,
( c_Orderings_Oord__class_Oless(U_693,U_696,U_694)
| ~ sP75(U_693,U_694,U_695,U_696) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_693,U_694,U_696)
| ~ c_Orderings_Oord__class_Oless(U_693,c_Groups_Ozero__class_Ozero(U_693),U_695)
| ~ sP76(U_693,U_694,U_695,U_696) ),
inference(clausify,[status(thm)],[f_225_3]) ).
cnf(f_225_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_693,U_696,U_694)
| ~ c_Orderings_Oord__class_Oless(U_693,U_695,c_Groups_Ozero__class_Ozero(U_693))
| ~ sP76(U_693,U_694,U_695,U_696) ),
inference(clausify,[status(thm)],[f_225_3]) ).
fof(f_226_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_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_ca_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_ca_2) ) ) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_b_2,V_a_2)
& c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__disj]) ).
fof(f_226_2,plain,
! [U_700,U_699,U_698,U_697] :
( ( ( c_Orderings_Oord__class_Oless(U_697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_700))
| ( ( ~ c_Orderings_Oord__class_Oless(U_697,U_700,U_699)
| ~ c_Orderings_Oord__class_Oless(U_697,U_698,c_Groups_Ozero__class_Ozero(U_697)) )
& ( ~ c_Orderings_Oord__class_Oless(U_697,U_699,U_700)
| ~ c_Orderings_Oord__class_Oless(U_697,c_Groups_Ozero__class_Ozero(U_697),U_698) ) ) )
& ( ( c_Orderings_Oord__class_Oless(U_697,U_700,U_699)
& c_Orderings_Oord__class_Oless(U_697,U_698,c_Groups_Ozero__class_Ozero(U_697)) )
| ( c_Orderings_Oord__class_Oless(U_697,U_699,U_700)
& c_Orderings_Oord__class_Oless(U_697,c_Groups_Ozero__class_Ozero(U_697),U_698) )
| ~ c_Orderings_Oord__class_Oless(U_697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_700)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_697) ),
inference(variable_rename,[status(thm)],[f_226_1]) ).
fof(f_226_3,plain,
( ! [U_698,U_700,U_697,U_699] :
( ~ c_Orderings_Oord__class_Oless(U_697,U_700,U_699)
| ~ c_Orderings_Oord__class_Oless(U_697,U_698,c_Groups_Ozero__class_Ozero(U_697))
| ~ sP80(U_698,U_700,U_697,U_699) )
& ! [U_698,U_700,U_697,U_699] :
( ~ c_Orderings_Oord__class_Oless(U_697,U_699,U_700)
| ~ c_Orderings_Oord__class_Oless(U_697,c_Groups_Ozero__class_Ozero(U_697),U_698)
| ~ sP80(U_698,U_700,U_697,U_699) )
& ! [U_698,U_700,U_697,U_699] :
( c_Orderings_Oord__class_Oless(U_697,U_700,U_699)
| ~ sP79(U_698,U_700,U_697,U_699) )
& ! [U_698,U_700,U_697,U_699] :
( c_Orderings_Oord__class_Oless(U_697,U_698,c_Groups_Ozero__class_Ozero(U_697))
| ~ sP79(U_698,U_700,U_697,U_699) )
& ! [U_698,U_700,U_697,U_699] :
( c_Orderings_Oord__class_Oless(U_697,U_699,U_700)
| ~ sP78(U_698,U_700,U_697,U_699) )
& ! [U_698,U_700,U_697,U_699] :
( c_Orderings_Oord__class_Oless(U_697,c_Groups_Ozero__class_Ozero(U_697),U_698)
| ~ sP78(U_698,U_700,U_697,U_699) )
& ! [U_698,U_700,U_697,U_699] :
( c_Orderings_Oord__class_Oless(U_697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_700))
| sP80(U_698,U_700,U_697,U_699)
| ~ sP81(U_698,U_700,U_697,U_699) )
& ! [U_698,U_700,U_697,U_699] :
( sP79(U_698,U_700,U_697,U_699)
| sP78(U_698,U_700,U_697,U_699)
| ~ c_Orderings_Oord__class_Oless(U_697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_700))
| ~ sP81(U_698,U_700,U_697,U_699) )
& ! [U_698,U_700,U_697,U_699] :
( sP81(U_698,U_700,U_697,U_699)
| ~ class_Rings_Olinordered__ring__strict(U_697) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78,sP79,sP80,sP81])],[f_226_2]) ).
cnf(f_226_4,plain,
( sP81(U_698,U_700,U_697,U_699)
| ~ class_Rings_Olinordered__ring__strict(U_697) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_5,plain,
( sP79(U_698,U_700,U_697,U_699)
| sP78(U_698,U_700,U_697,U_699)
| ~ c_Orderings_Oord__class_Oless(U_697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_700))
| ~ sP81(U_698,U_700,U_697,U_699) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_6,plain,
( c_Orderings_Oord__class_Oless(U_697,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_697),U_698),U_700))
| sP80(U_698,U_700,U_697,U_699)
| ~ sP81(U_698,U_700,U_697,U_699) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_7,plain,
( c_Orderings_Oord__class_Oless(U_697,c_Groups_Ozero__class_Ozero(U_697),U_698)
| ~ sP78(U_698,U_700,U_697,U_699) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_8,plain,
( c_Orderings_Oord__class_Oless(U_697,U_699,U_700)
| ~ sP78(U_698,U_700,U_697,U_699) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_9,plain,
( c_Orderings_Oord__class_Oless(U_697,U_698,c_Groups_Ozero__class_Ozero(U_697))
| ~ sP79(U_698,U_700,U_697,U_699) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_10,plain,
( c_Orderings_Oord__class_Oless(U_697,U_700,U_699)
| ~ sP79(U_698,U_700,U_697,U_699) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_11,plain,
( ~ c_Orderings_Oord__class_Oless(U_697,U_699,U_700)
| ~ c_Orderings_Oord__class_Oless(U_697,c_Groups_Ozero__class_Ozero(U_697),U_698)
| ~ sP80(U_698,U_700,U_697,U_699) ),
inference(clausify,[status(thm)],[f_226_3]) ).
cnf(f_226_12,plain,
( ~ c_Orderings_Oord__class_Oless(U_697,U_700,U_699)
| ~ c_Orderings_Oord__class_Oless(U_697,U_698,c_Groups_Ozero__class_Ozero(U_697))
| ~ sP80(U_698,U_700,U_697,U_699) ),
inference(clausify,[status(thm)],[f_226_3]) ).
fof(f_227_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_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_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__less__cancel__left__pos]) ).
fof(f_227_2,plain,
! [U_704,U_703,U_702,U_701] :
( ( ( c_Orderings_Oord__class_Oless(U_701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_704))
| ~ c_Orderings_Oord__class_Oless(U_701,U_703,U_704) )
& ( c_Orderings_Oord__class_Oless(U_701,U_703,U_704)
| ~ c_Orderings_Oord__class_Oless(U_701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_704)) ) )
| ~ c_Orderings_Oord__class_Oless(U_701,c_Groups_Ozero__class_Ozero(U_701),U_702)
| ~ class_Rings_Olinordered__ring__strict(U_701) ),
inference(variable_rename,[status(thm)],[f_227_1]) ).
fof(f_227_3,plain,
( ! [U_704,U_703,U_702,U_701] :
( c_Orderings_Oord__class_Oless(U_701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_704))
| ~ c_Orderings_Oord__class_Oless(U_701,U_703,U_704)
| ~ sP82(U_704,U_703,U_702,U_701) )
& ! [U_704,U_703,U_702,U_701] :
( c_Orderings_Oord__class_Oless(U_701,U_703,U_704)
| ~ c_Orderings_Oord__class_Oless(U_701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_704))
| ~ sP82(U_704,U_703,U_702,U_701) )
& ! [U_704,U_703,U_702,U_701] :
( sP82(U_704,U_703,U_702,U_701)
| ~ c_Orderings_Oord__class_Oless(U_701,c_Groups_Ozero__class_Ozero(U_701),U_702)
| ~ class_Rings_Olinordered__ring__strict(U_701) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_227_2]) ).
cnf(f_227_4,plain,
( sP82(U_704,U_703,U_702,U_701)
| ~ c_Orderings_Oord__class_Oless(U_701,c_Groups_Ozero__class_Ozero(U_701),U_702)
| ~ class_Rings_Olinordered__ring__strict(U_701) ),
inference(clausify,[status(thm)],[f_227_3]) ).
cnf(f_227_5,plain,
( c_Orderings_Oord__class_Oless(U_701,U_703,U_704)
| ~ c_Orderings_Oord__class_Oless(U_701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_704))
| ~ sP82(U_704,U_703,U_702,U_701) ),
inference(clausify,[status(thm)],[f_227_3]) ).
cnf(f_227_6,plain,
( c_Orderings_Oord__class_Oless(U_701,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_703),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_701),U_702),U_704))
| ~ c_Orderings_Oord__class_Oless(U_701,U_703,U_704)
| ~ sP82(U_704,U_703,U_702,U_701) ),
inference(clausify,[status(thm)],[f_227_3]) ).
fof(f_228_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_228_2,plain,
! [U_707,U_706,U_705] :
( c_Orderings_Oord__class_Oless(U_705,c_Groups_Ozero__class_Ozero(U_705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_705),U_706),U_707))
| ~ c_Orderings_Oord__class_Oless(U_705,c_Groups_Ozero__class_Ozero(U_705),U_707)
| ~ c_Orderings_Oord__class_Oless(U_705,c_Groups_Ozero__class_Ozero(U_705),U_706)
| ~ class_Rings_Olinordered__semiring__strict(U_705) ),
inference(variable_rename,[status(thm)],[f_228_1]) ).
fof(f_228_3,plain,
! [U_706,U_705,U_707] :
( c_Orderings_Oord__class_Oless(U_705,c_Groups_Ozero__class_Ozero(U_705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_705),U_706),U_707))
| ~ c_Orderings_Oord__class_Oless(U_705,c_Groups_Ozero__class_Ozero(U_705),U_707)
| ~ c_Orderings_Oord__class_Oless(U_705,c_Groups_Ozero__class_Ozero(U_705),U_706)
| ~ class_Rings_Olinordered__semiring__strict(U_705) ),
inference(definitional_conversion,[status(esa)],[f_228_2]) ).
cnf(f_228_4,plain,
( c_Orderings_Oord__class_Oless(U_705,c_Groups_Ozero__class_Ozero(U_705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_705),U_706),U_707))
| ~ c_Orderings_Oord__class_Oless(U_705,c_Groups_Ozero__class_Ozero(U_705),U_707)
| ~ c_Orderings_Oord__class_Oless(U_705,c_Groups_Ozero__class_Ozero(U_705),U_706)
| ~ class_Rings_Olinordered__semiring__strict(U_705) ),
inference(clausify,[status(thm)],[f_228_3]) ).
fof(f_229_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_229_2,plain,
! [U_710,U_709,U_708] :
( c_Orderings_Oord__class_Oless(U_708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_708),U_709),U_710),c_Groups_Ozero__class_Ozero(U_708))
| ~ c_Orderings_Oord__class_Oless(U_708,U_710,c_Groups_Ozero__class_Ozero(U_708))
| ~ c_Orderings_Oord__class_Oless(U_708,c_Groups_Ozero__class_Ozero(U_708),U_709)
| ~ class_Rings_Olinordered__semiring__strict(U_708) ),
inference(variable_rename,[status(thm)],[f_229_1]) ).
fof(f_229_3,plain,
! [U_710,U_708,U_709] :
( c_Orderings_Oord__class_Oless(U_708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_708),U_709),U_710),c_Groups_Ozero__class_Ozero(U_708))
| ~ c_Orderings_Oord__class_Oless(U_708,U_710,c_Groups_Ozero__class_Ozero(U_708))
| ~ c_Orderings_Oord__class_Oless(U_708,c_Groups_Ozero__class_Ozero(U_708),U_709)
| ~ class_Rings_Olinordered__semiring__strict(U_708) ),
inference(definitional_conversion,[status(esa)],[f_229_2]) ).
cnf(f_229_4,plain,
( c_Orderings_Oord__class_Oless(U_708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_708),U_709),U_710),c_Groups_Ozero__class_Ozero(U_708))
| ~ c_Orderings_Oord__class_Oless(U_708,U_710,c_Groups_Ozero__class_Ozero(U_708))
| ~ c_Orderings_Oord__class_Oless(U_708,c_Groups_Ozero__class_Ozero(U_708),U_709)
| ~ class_Rings_Olinordered__semiring__strict(U_708) ),
inference(clausify,[status(thm)],[f_229_3]) ).
fof(f_230_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_230_2,plain,
! [U_713,U_712,U_711] :
( c_Orderings_Oord__class_Oless(U_711,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_711),U_713),U_712),c_Groups_Ozero__class_Ozero(U_711))
| ~ c_Orderings_Oord__class_Oless(U_711,U_713,c_Groups_Ozero__class_Ozero(U_711))
| ~ c_Orderings_Oord__class_Oless(U_711,c_Groups_Ozero__class_Ozero(U_711),U_712)
| ~ class_Rings_Olinordered__semiring__strict(U_711) ),
inference(variable_rename,[status(thm)],[f_230_1]) ).
fof(f_230_3,plain,
! [U_711,U_712,U_713] :
( c_Orderings_Oord__class_Oless(U_711,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_711),U_713),U_712),c_Groups_Ozero__class_Ozero(U_711))
| ~ c_Orderings_Oord__class_Oless(U_711,U_713,c_Groups_Ozero__class_Ozero(U_711))
| ~ c_Orderings_Oord__class_Oless(U_711,c_Groups_Ozero__class_Ozero(U_711),U_712)
| ~ class_Rings_Olinordered__semiring__strict(U_711) ),
inference(definitional_conversion,[status(esa)],[f_230_2]) ).
cnf(f_230_4,plain,
( c_Orderings_Oord__class_Oless(U_711,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_711),U_713),U_712),c_Groups_Ozero__class_Ozero(U_711))
| ~ c_Orderings_Oord__class_Oless(U_711,U_713,c_Groups_Ozero__class_Ozero(U_711))
| ~ c_Orderings_Oord__class_Oless(U_711,c_Groups_Ozero__class_Ozero(U_711),U_712)
| ~ class_Rings_Olinordered__semiring__strict(U_711) ),
inference(clausify,[status(thm)],[f_230_3]) ).
fof(f_231_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_231_2,plain,
! [U_716,U_715,U_714] :
( c_Orderings_Oord__class_Oless(U_714,c_Groups_Ozero__class_Ozero(U_714),U_716)
| ~ c_Orderings_Oord__class_Oless(U_714,c_Groups_Ozero__class_Ozero(U_714),U_715)
| ~ c_Orderings_Oord__class_Oless(U_714,c_Groups_Ozero__class_Ozero(U_714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_714),U_715),U_716))
| ~ class_Rings_Olinordered__semiring__strict(U_714) ),
inference(variable_rename,[status(thm)],[f_231_1]) ).
fof(f_231_3,plain,
! [U_714,U_715,U_716] :
( c_Orderings_Oord__class_Oless(U_714,c_Groups_Ozero__class_Ozero(U_714),U_716)
| ~ c_Orderings_Oord__class_Oless(U_714,c_Groups_Ozero__class_Ozero(U_714),U_715)
| ~ c_Orderings_Oord__class_Oless(U_714,c_Groups_Ozero__class_Ozero(U_714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_714),U_715),U_716))
| ~ class_Rings_Olinordered__semiring__strict(U_714) ),
inference(definitional_conversion,[status(esa)],[f_231_2]) ).
cnf(f_231_4,plain,
( c_Orderings_Oord__class_Oless(U_714,c_Groups_Ozero__class_Ozero(U_714),U_716)
| ~ c_Orderings_Oord__class_Oless(U_714,c_Groups_Ozero__class_Ozero(U_714),U_715)
| ~ c_Orderings_Oord__class_Oless(U_714,c_Groups_Ozero__class_Ozero(U_714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_714),U_715),U_716))
| ~ class_Rings_Olinordered__semiring__strict(U_714) ),
inference(clausify,[status(thm)],[f_231_3]) ).
fof(f_232_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_232_2,plain,
! [U_719,U_718,U_717] :
( c_Orderings_Oord__class_Oless(U_717,c_Groups_Ozero__class_Ozero(U_717),U_718)
| ~ c_Orderings_Oord__class_Oless(U_717,c_Groups_Ozero__class_Ozero(U_717),U_719)
| ~ c_Orderings_Oord__class_Oless(U_717,c_Groups_Ozero__class_Ozero(U_717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_717),U_718),U_719))
| ~ class_Rings_Olinordered__semiring__strict(U_717) ),
inference(variable_rename,[status(thm)],[f_232_1]) ).
fof(f_232_3,plain,
! [U_717,U_718,U_719] :
( c_Orderings_Oord__class_Oless(U_717,c_Groups_Ozero__class_Ozero(U_717),U_718)
| ~ c_Orderings_Oord__class_Oless(U_717,c_Groups_Ozero__class_Ozero(U_717),U_719)
| ~ c_Orderings_Oord__class_Oless(U_717,c_Groups_Ozero__class_Ozero(U_717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_717),U_718),U_719))
| ~ class_Rings_Olinordered__semiring__strict(U_717) ),
inference(definitional_conversion,[status(esa)],[f_232_2]) ).
cnf(f_232_4,plain,
( c_Orderings_Oord__class_Oless(U_717,c_Groups_Ozero__class_Ozero(U_717),U_718)
| ~ c_Orderings_Oord__class_Oless(U_717,c_Groups_Ozero__class_Ozero(U_717),U_719)
| ~ c_Orderings_Oord__class_Oless(U_717,c_Groups_Ozero__class_Ozero(U_717),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_717),U_718),U_719))
| ~ class_Rings_Olinordered__semiring__strict(U_717) ),
inference(clausify,[status(thm)],[f_232_3]) ).
fof(f_233_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_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_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_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_233_2,plain,
! [U_723,U_722,U_721,U_720] :
( ( ( c_Orderings_Oord__class_Oless(U_720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_723))
| ~ c_Orderings_Oord__class_Oless(U_720,U_723,U_722) )
& ( c_Orderings_Oord__class_Oless(U_720,U_723,U_722)
| ~ c_Orderings_Oord__class_Oless(U_720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_723)) ) )
| ~ c_Orderings_Oord__class_Oless(U_720,U_721,c_Groups_Ozero__class_Ozero(U_720))
| ~ class_Rings_Olinordered__ring__strict(U_720) ),
inference(variable_rename,[status(thm)],[f_233_1]) ).
fof(f_233_3,plain,
( ! [U_720,U_721,U_722,U_723] :
( c_Orderings_Oord__class_Oless(U_720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_723))
| ~ c_Orderings_Oord__class_Oless(U_720,U_723,U_722)
| ~ sP83(U_720,U_721,U_722,U_723) )
& ! [U_720,U_721,U_722,U_723] :
( c_Orderings_Oord__class_Oless(U_720,U_723,U_722)
| ~ c_Orderings_Oord__class_Oless(U_720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_723))
| ~ sP83(U_720,U_721,U_722,U_723) )
& ! [U_720,U_721,U_722,U_723] :
( sP83(U_720,U_721,U_722,U_723)
| ~ c_Orderings_Oord__class_Oless(U_720,U_721,c_Groups_Ozero__class_Ozero(U_720))
| ~ class_Rings_Olinordered__ring__strict(U_720) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_233_2]) ).
cnf(f_233_4,plain,
( sP83(U_720,U_721,U_722,U_723)
| ~ c_Orderings_Oord__class_Oless(U_720,U_721,c_Groups_Ozero__class_Ozero(U_720))
| ~ class_Rings_Olinordered__ring__strict(U_720) ),
inference(clausify,[status(thm)],[f_233_3]) ).
cnf(f_233_5,plain,
( c_Orderings_Oord__class_Oless(U_720,U_723,U_722)
| ~ c_Orderings_Oord__class_Oless(U_720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_723))
| ~ sP83(U_720,U_721,U_722,U_723) ),
inference(clausify,[status(thm)],[f_233_3]) ).
cnf(f_233_6,plain,
( c_Orderings_Oord__class_Oless(U_720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_720),U_721),U_723))
| ~ c_Orderings_Oord__class_Oless(U_720,U_723,U_722)
| ~ sP83(U_720,U_721,U_722,U_723) ),
inference(clausify,[status(thm)],[f_233_3]) ).
fof(f_234_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_234_2,plain,
! [U_726,U_725,U_724] :
( c_Orderings_Oord__class_Oless(U_724,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_724),U_725),U_726),c_Groups_Ozero__class_Ozero(U_724))
| ~ c_Orderings_Oord__class_Oless(U_724,c_Groups_Ozero__class_Ozero(U_724),U_726)
| ~ c_Orderings_Oord__class_Oless(U_724,U_725,c_Groups_Ozero__class_Ozero(U_724))
| ~ class_Rings_Olinordered__semiring__strict(U_724) ),
inference(variable_rename,[status(thm)],[f_234_1]) ).
fof(f_234_3,plain,
! [U_726,U_724,U_725] :
( c_Orderings_Oord__class_Oless(U_724,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_724),U_725),U_726),c_Groups_Ozero__class_Ozero(U_724))
| ~ c_Orderings_Oord__class_Oless(U_724,c_Groups_Ozero__class_Ozero(U_724),U_726)
| ~ c_Orderings_Oord__class_Oless(U_724,U_725,c_Groups_Ozero__class_Ozero(U_724))
| ~ class_Rings_Olinordered__semiring__strict(U_724) ),
inference(definitional_conversion,[status(esa)],[f_234_2]) ).
cnf(f_234_4,plain,
( c_Orderings_Oord__class_Oless(U_724,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_724),U_725),U_726),c_Groups_Ozero__class_Ozero(U_724))
| ~ c_Orderings_Oord__class_Oless(U_724,c_Groups_Ozero__class_Ozero(U_724),U_726)
| ~ c_Orderings_Oord__class_Oless(U_724,U_725,c_Groups_Ozero__class_Ozero(U_724))
| ~ class_Rings_Olinordered__semiring__strict(U_724) ),
inference(clausify,[status(thm)],[f_234_3]) ).
fof(f_235_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_235_2,plain,
! [U_729,U_728,U_727] :
( c_Orderings_Oord__class_Oless(U_727,c_Groups_Ozero__class_Ozero(U_727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_727),U_728),U_729))
| ~ c_Orderings_Oord__class_Oless(U_727,U_729,c_Groups_Ozero__class_Ozero(U_727))
| ~ c_Orderings_Oord__class_Oless(U_727,U_728,c_Groups_Ozero__class_Ozero(U_727))
| ~ class_Rings_Olinordered__ring__strict(U_727) ),
inference(variable_rename,[status(thm)],[f_235_1]) ).
fof(f_235_3,plain,
! [U_727,U_728,U_729] :
( c_Orderings_Oord__class_Oless(U_727,c_Groups_Ozero__class_Ozero(U_727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_727),U_728),U_729))
| ~ c_Orderings_Oord__class_Oless(U_727,U_729,c_Groups_Ozero__class_Ozero(U_727))
| ~ c_Orderings_Oord__class_Oless(U_727,U_728,c_Groups_Ozero__class_Ozero(U_727))
| ~ class_Rings_Olinordered__ring__strict(U_727) ),
inference(definitional_conversion,[status(esa)],[f_235_2]) ).
cnf(f_235_4,plain,
( c_Orderings_Oord__class_Oless(U_727,c_Groups_Ozero__class_Ozero(U_727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_727),U_728),U_729))
| ~ c_Orderings_Oord__class_Oless(U_727,U_729,c_Groups_Ozero__class_Ozero(U_727))
| ~ c_Orderings_Oord__class_Oless(U_727,U_728,c_Groups_Ozero__class_Ozero(U_727))
| ~ class_Rings_Olinordered__ring__strict(U_727) ),
inference(clausify,[status(thm)],[f_235_3]) ).
fof(f_236_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_236_2,plain,
! [U_733,U_732,U_731,U_730] :
( c_Orderings_Oord__class_Oless(U_730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_731),U_733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_732),U_733))
| ~ c_Orderings_Oord__class_Oless(U_730,c_Groups_Ozero__class_Ozero(U_730),U_733)
| ~ c_Orderings_Oord__class_Oless(U_730,U_731,U_732)
| ~ class_Rings_Olinordered__semiring__strict(U_730) ),
inference(variable_rename,[status(thm)],[f_236_1]) ).
fof(f_236_3,plain,
! [U_730,U_731,U_732,U_733] :
( c_Orderings_Oord__class_Oless(U_730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_731),U_733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_732),U_733))
| ~ c_Orderings_Oord__class_Oless(U_730,c_Groups_Ozero__class_Ozero(U_730),U_733)
| ~ c_Orderings_Oord__class_Oless(U_730,U_731,U_732)
| ~ class_Rings_Olinordered__semiring__strict(U_730) ),
inference(definitional_conversion,[status(esa)],[f_236_2]) ).
cnf(f_236_4,plain,
( c_Orderings_Oord__class_Oless(U_730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_731),U_733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_730),U_732),U_733))
| ~ c_Orderings_Oord__class_Oless(U_730,c_Groups_Ozero__class_Ozero(U_730),U_733)
| ~ c_Orderings_Oord__class_Oless(U_730,U_731,U_732)
| ~ class_Rings_Olinordered__semiring__strict(U_730) ),
inference(clausify,[status(thm)],[f_236_3]) ).
fof(f_237_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_237_2,plain,
! [U_737,U_736,U_735,U_734] :
( c_Orderings_Oord__class_Oless(U_734,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_737),U_735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_737),U_736))
| ~ c_Orderings_Oord__class_Oless(U_734,c_Groups_Ozero__class_Ozero(U_734),U_737)
| ~ c_Orderings_Oord__class_Oless(U_734,U_735,U_736)
| ~ class_Rings_Olinordered__semiring__strict(U_734) ),
inference(variable_rename,[status(thm)],[f_237_1]) ).
fof(f_237_3,plain,
! [U_734,U_735,U_736,U_737] :
( c_Orderings_Oord__class_Oless(U_734,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_737),U_735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_737),U_736))
| ~ c_Orderings_Oord__class_Oless(U_734,c_Groups_Ozero__class_Ozero(U_734),U_737)
| ~ c_Orderings_Oord__class_Oless(U_734,U_735,U_736)
| ~ class_Rings_Olinordered__semiring__strict(U_734) ),
inference(definitional_conversion,[status(esa)],[f_237_2]) ).
cnf(f_237_4,plain,
( c_Orderings_Oord__class_Oless(U_734,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_737),U_735),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_734),U_737),U_736))
| ~ c_Orderings_Oord__class_Oless(U_734,c_Groups_Ozero__class_Ozero(U_734),U_737)
| ~ c_Orderings_Oord__class_Oless(U_734,U_735,U_736)
| ~ class_Rings_Olinordered__semiring__strict(U_734) ),
inference(clausify,[status(thm)],[f_237_3]) ).
fof(f_238_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_238_2,plain,
! [U_741,U_740,U_739,U_738] :
( c_Orderings_Oord__class_Oless(U_738,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_740))
| ~ c_Orderings_Oord__class_Oless(U_738,c_Groups_Ozero__class_Ozero(U_738),U_741)
| ~ c_Orderings_Oord__class_Oless(U_738,U_739,U_740)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_738) ),
inference(variable_rename,[status(thm)],[f_238_1]) ).
fof(f_238_3,plain,
! [U_738,U_739,U_740,U_741] :
( c_Orderings_Oord__class_Oless(U_738,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_740))
| ~ c_Orderings_Oord__class_Oless(U_738,c_Groups_Ozero__class_Ozero(U_738),U_741)
| ~ c_Orderings_Oord__class_Oless(U_738,U_739,U_740)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_738) ),
inference(definitional_conversion,[status(esa)],[f_238_2]) ).
cnf(f_238_4,plain,
( c_Orderings_Oord__class_Oless(U_738,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_739),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_738),U_741),U_740))
| ~ c_Orderings_Oord__class_Oless(U_738,c_Groups_Ozero__class_Ozero(U_738),U_741)
| ~ c_Orderings_Oord__class_Oless(U_738,U_739,U_740)
| ~ class_Rings_Olinordered__comm__semiring__strict(U_738) ),
inference(clausify,[status(thm)],[f_238_3]) ).
fof(f_239_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_239_2,plain,
! [U_745,U_744,U_743,U_742] :
( c_Orderings_Oord__class_Oless(U_742,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_742),U_744),U_745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_742),U_743),U_745))
| ~ c_Orderings_Oord__class_Oless(U_742,U_745,c_Groups_Ozero__class_Ozero(U_742))
| ~ c_Orderings_Oord__class_Oless(U_742,U_743,U_744)
| ~ class_Rings_Olinordered__ring__strict(U_742) ),
inference(variable_rename,[status(thm)],[f_239_1]) ).
fof(f_239_3,plain,
! [U_742,U_743,U_744,U_745] :
( c_Orderings_Oord__class_Oless(U_742,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_742),U_744),U_745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_742),U_743),U_745))
| ~ c_Orderings_Oord__class_Oless(U_742,U_745,c_Groups_Ozero__class_Ozero(U_742))
| ~ c_Orderings_Oord__class_Oless(U_742,U_743,U_744)
| ~ class_Rings_Olinordered__ring__strict(U_742) ),
inference(definitional_conversion,[status(esa)],[f_239_2]) ).
cnf(f_239_4,plain,
( c_Orderings_Oord__class_Oless(U_742,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_742),U_744),U_745),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_742),U_743),U_745))
| ~ c_Orderings_Oord__class_Oless(U_742,U_745,c_Groups_Ozero__class_Ozero(U_742))
| ~ c_Orderings_Oord__class_Oless(U_742,U_743,U_744)
| ~ class_Rings_Olinordered__ring__strict(U_742) ),
inference(clausify,[status(thm)],[f_239_3]) ).
fof(f_240_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_240_2,plain,
! [U_749,U_748,U_747,U_746] :
( c_Orderings_Oord__class_Oless(U_746,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_746),U_749),U_748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_746),U_749),U_747))
| ~ c_Orderings_Oord__class_Oless(U_746,U_749,c_Groups_Ozero__class_Ozero(U_746))
| ~ c_Orderings_Oord__class_Oless(U_746,U_747,U_748)
| ~ class_Rings_Olinordered__ring__strict(U_746) ),
inference(variable_rename,[status(thm)],[f_240_1]) ).
fof(f_240_3,plain,
! [U_746,U_747,U_748,U_749] :
( c_Orderings_Oord__class_Oless(U_746,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_746),U_749),U_748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_746),U_749),U_747))
| ~ c_Orderings_Oord__class_Oless(U_746,U_749,c_Groups_Ozero__class_Ozero(U_746))
| ~ c_Orderings_Oord__class_Oless(U_746,U_747,U_748)
| ~ class_Rings_Olinordered__ring__strict(U_746) ),
inference(definitional_conversion,[status(esa)],[f_240_2]) ).
cnf(f_240_4,plain,
( c_Orderings_Oord__class_Oless(U_746,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_746),U_749),U_748),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_746),U_749),U_747))
| ~ c_Orderings_Oord__class_Oless(U_746,U_749,c_Groups_Ozero__class_Ozero(U_746))
| ~ c_Orderings_Oord__class_Oless(U_746,U_747,U_748)
| ~ class_Rings_Olinordered__ring__strict(U_746) ),
inference(clausify,[status(thm)],[f_240_3]) ).
fof(f_241_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_241_2,plain,
! [U_750] :
( ~ c_Orderings_Oord__class_Oless__eq(U_750,c_Groups_Oone__class_Oone(U_750),c_Groups_Ozero__class_Ozero(U_750))
| ~ class_Rings_Olinordered__semidom(U_750) ),
inference(variable_rename,[status(thm)],[f_241_1]) ).
fof(f_241_3,plain,
! [U_750] :
( ~ c_Orderings_Oord__class_Oless__eq(U_750,c_Groups_Oone__class_Oone(U_750),c_Groups_Ozero__class_Ozero(U_750))
| ~ class_Rings_Olinordered__semidom(U_750) ),
inference(definitional_conversion,[status(esa)],[f_241_2]) ).
cnf(f_241_4,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_750,c_Groups_Oone__class_Oone(U_750),c_Groups_Ozero__class_Ozero(U_750))
| ~ class_Rings_Olinordered__semidom(U_750) ),
inference(clausify,[status(thm)],[f_241_3]) ).
fof(f_242_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_242_2,plain,
! [U_751] :
( c_Orderings_Oord__class_Oless__eq(U_751,c_Groups_Ozero__class_Ozero(U_751),c_Groups_Oone__class_Oone(U_751))
| ~ class_Rings_Olinordered__semidom(U_751) ),
inference(variable_rename,[status(thm)],[f_242_1]) ).
fof(f_242_3,plain,
! [U_751] :
( c_Orderings_Oord__class_Oless__eq(U_751,c_Groups_Ozero__class_Ozero(U_751),c_Groups_Oone__class_Oone(U_751))
| ~ class_Rings_Olinordered__semidom(U_751) ),
inference(definitional_conversion,[status(esa)],[f_242_2]) ).
cnf(f_242_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_751,c_Groups_Ozero__class_Ozero(U_751),c_Groups_Oone__class_Oone(U_751))
| ~ class_Rings_Olinordered__semidom(U_751) ),
inference(clausify,[status(thm)],[f_242_3]) ).
fof(f_243_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_243_2,plain,
! [U_752] :
( ~ c_Orderings_Oord__class_Oless(U_752,c_Groups_Oone__class_Oone(U_752),c_Groups_Ozero__class_Ozero(U_752))
| ~ class_Rings_Olinordered__semidom(U_752) ),
inference(variable_rename,[status(thm)],[f_243_1]) ).
fof(f_243_3,plain,
! [U_752] :
( ~ c_Orderings_Oord__class_Oless(U_752,c_Groups_Oone__class_Oone(U_752),c_Groups_Ozero__class_Ozero(U_752))
| ~ class_Rings_Olinordered__semidom(U_752) ),
inference(definitional_conversion,[status(esa)],[f_243_2]) ).
cnf(f_243_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_752,c_Groups_Oone__class_Oone(U_752),c_Groups_Ozero__class_Ozero(U_752))
| ~ class_Rings_Olinordered__semidom(U_752) ),
inference(clausify,[status(thm)],[f_243_3]) ).
fof(f_244_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_244_2,plain,
! [U_753] :
( c_Orderings_Oord__class_Oless(U_753,c_Groups_Ozero__class_Ozero(U_753),c_Groups_Oone__class_Oone(U_753))
| ~ class_Rings_Olinordered__semidom(U_753) ),
inference(variable_rename,[status(thm)],[f_244_1]) ).
fof(f_244_3,plain,
! [U_753] :
( c_Orderings_Oord__class_Oless(U_753,c_Groups_Ozero__class_Ozero(U_753),c_Groups_Oone__class_Oone(U_753))
| ~ class_Rings_Olinordered__semidom(U_753) ),
inference(definitional_conversion,[status(esa)],[f_244_2]) ).
cnf(f_244_4,plain,
( c_Orderings_Oord__class_Oless(U_753,c_Groups_Ozero__class_Ozero(U_753),c_Groups_Oone__class_Oone(U_753))
| ~ class_Rings_Olinordered__semidom(U_753) ),
inference(clausify,[status(thm)],[f_244_3]) ).
fof(f_245_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_245_2,plain,
! [U_756,U_755,U_754] :
( c_Orderings_Oord__class_Oless(U_754,c_Groups_Ozero__class_Ozero(U_754),c_Groups_Oplus__class_Oplus(U_754,U_755,U_756))
| ~ c_Orderings_Oord__class_Oless__eq(U_754,c_Groups_Ozero__class_Ozero(U_754),U_756)
| ~ c_Orderings_Oord__class_Oless(U_754,c_Groups_Ozero__class_Ozero(U_754),U_755)
| ~ class_Groups_Oordered__comm__monoid__add(U_754) ),
inference(variable_rename,[status(thm)],[f_245_1]) ).
fof(f_245_3,plain,
! [U_754,U_755,U_756] :
( c_Orderings_Oord__class_Oless(U_754,c_Groups_Ozero__class_Ozero(U_754),c_Groups_Oplus__class_Oplus(U_754,U_755,U_756))
| ~ c_Orderings_Oord__class_Oless__eq(U_754,c_Groups_Ozero__class_Ozero(U_754),U_756)
| ~ c_Orderings_Oord__class_Oless(U_754,c_Groups_Ozero__class_Ozero(U_754),U_755)
| ~ class_Groups_Oordered__comm__monoid__add(U_754) ),
inference(definitional_conversion,[status(esa)],[f_245_2]) ).
cnf(f_245_4,plain,
( c_Orderings_Oord__class_Oless(U_754,c_Groups_Ozero__class_Ozero(U_754),c_Groups_Oplus__class_Oplus(U_754,U_755,U_756))
| ~ c_Orderings_Oord__class_Oless__eq(U_754,c_Groups_Ozero__class_Ozero(U_754),U_756)
| ~ c_Orderings_Oord__class_Oless(U_754,c_Groups_Ozero__class_Ozero(U_754),U_755)
| ~ class_Groups_Oordered__comm__monoid__add(U_754) ),
inference(clausify,[status(thm)],[f_245_3]) ).
fof(f_246_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_246_2,plain,
! [U_759,U_758,U_757] :
( c_Orderings_Oord__class_Oless(U_757,c_Groups_Ozero__class_Ozero(U_757),c_Groups_Oplus__class_Oplus(U_757,U_758,U_759))
| ~ c_Orderings_Oord__class_Oless(U_757,c_Groups_Ozero__class_Ozero(U_757),U_759)
| ~ c_Orderings_Oord__class_Oless__eq(U_757,c_Groups_Ozero__class_Ozero(U_757),U_758)
| ~ class_Groups_Oordered__comm__monoid__add(U_757) ),
inference(variable_rename,[status(thm)],[f_246_1]) ).
fof(f_246_3,plain,
! [U_757,U_758,U_759] :
( c_Orderings_Oord__class_Oless(U_757,c_Groups_Ozero__class_Ozero(U_757),c_Groups_Oplus__class_Oplus(U_757,U_758,U_759))
| ~ c_Orderings_Oord__class_Oless(U_757,c_Groups_Ozero__class_Ozero(U_757),U_759)
| ~ c_Orderings_Oord__class_Oless__eq(U_757,c_Groups_Ozero__class_Ozero(U_757),U_758)
| ~ class_Groups_Oordered__comm__monoid__add(U_757) ),
inference(definitional_conversion,[status(esa)],[f_246_2]) ).
cnf(f_246_4,plain,
( c_Orderings_Oord__class_Oless(U_757,c_Groups_Ozero__class_Ozero(U_757),c_Groups_Oplus__class_Oplus(U_757,U_758,U_759))
| ~ c_Orderings_Oord__class_Oless(U_757,c_Groups_Ozero__class_Ozero(U_757),U_759)
| ~ c_Orderings_Oord__class_Oless__eq(U_757,c_Groups_Ozero__class_Ozero(U_757),U_758)
| ~ class_Groups_Oordered__comm__monoid__add(U_757) ),
inference(clausify,[status(thm)],[f_246_3]) ).
fof(f_247_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_247_2,plain,
! [U_763,U_762,U_761,U_760] :
( c_Orderings_Oord__class_Oless(U_760,U_762,c_Groups_Oplus__class_Oplus(U_760,U_761,U_763))
| ~ c_Orderings_Oord__class_Oless__eq(U_760,U_762,U_763)
| ~ c_Orderings_Oord__class_Oless(U_760,c_Groups_Ozero__class_Ozero(U_760),U_761)
| ~ class_Groups_Oordered__comm__monoid__add(U_760) ),
inference(variable_rename,[status(thm)],[f_247_1]) ).
fof(f_247_3,plain,
! [U_762,U_763,U_761,U_760] :
( c_Orderings_Oord__class_Oless(U_760,U_762,c_Groups_Oplus__class_Oplus(U_760,U_761,U_763))
| ~ c_Orderings_Oord__class_Oless__eq(U_760,U_762,U_763)
| ~ c_Orderings_Oord__class_Oless(U_760,c_Groups_Ozero__class_Ozero(U_760),U_761)
| ~ class_Groups_Oordered__comm__monoid__add(U_760) ),
inference(definitional_conversion,[status(esa)],[f_247_2]) ).
cnf(f_247_4,plain,
( c_Orderings_Oord__class_Oless(U_760,U_762,c_Groups_Oplus__class_Oplus(U_760,U_761,U_763))
| ~ c_Orderings_Oord__class_Oless__eq(U_760,U_762,U_763)
| ~ c_Orderings_Oord__class_Oless(U_760,c_Groups_Ozero__class_Ozero(U_760),U_761)
| ~ class_Groups_Oordered__comm__monoid__add(U_760) ),
inference(clausify,[status(thm)],[f_247_3]) ).
fof(f_248_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_248_2,plain,
! [U_767,U_766,U_765,U_764] :
( c_Orderings_Oord__class_Oless(U_764,U_766,c_Groups_Oplus__class_Oplus(U_764,U_765,U_767))
| ~ c_Orderings_Oord__class_Oless(U_764,U_766,U_767)
| ~ c_Orderings_Oord__class_Oless__eq(U_764,c_Groups_Ozero__class_Ozero(U_764),U_765)
| ~ class_Groups_Oordered__comm__monoid__add(U_764) ),
inference(variable_rename,[status(thm)],[f_248_1]) ).
fof(f_248_3,plain,
! [U_766,U_767,U_765,U_764] :
( c_Orderings_Oord__class_Oless(U_764,U_766,c_Groups_Oplus__class_Oplus(U_764,U_765,U_767))
| ~ c_Orderings_Oord__class_Oless(U_764,U_766,U_767)
| ~ c_Orderings_Oord__class_Oless__eq(U_764,c_Groups_Ozero__class_Ozero(U_764),U_765)
| ~ class_Groups_Oordered__comm__monoid__add(U_764) ),
inference(definitional_conversion,[status(esa)],[f_248_2]) ).
cnf(f_248_4,plain,
( c_Orderings_Oord__class_Oless(U_764,U_766,c_Groups_Oplus__class_Oplus(U_764,U_765,U_767))
| ~ c_Orderings_Oord__class_Oless(U_764,U_766,U_767)
| ~ c_Orderings_Oord__class_Oless__eq(U_764,c_Groups_Ozero__class_Ozero(U_764),U_765)
| ~ class_Groups_Oordered__comm__monoid__add(U_764) ),
inference(clausify,[status(thm)],[f_248_3]) ).
fof(f_249_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_249_2,plain,
! [U_770,U_769,U_768] :
( c_Orderings_Oord__class_Oless(U_768,c_Groups_Oplus__class_Oplus(U_768,U_769,U_770),c_Groups_Ozero__class_Ozero(U_768))
| ~ c_Orderings_Oord__class_Oless__eq(U_768,U_770,c_Groups_Ozero__class_Ozero(U_768))
| ~ c_Orderings_Oord__class_Oless(U_768,U_769,c_Groups_Ozero__class_Ozero(U_768))
| ~ class_Groups_Oordered__comm__monoid__add(U_768) ),
inference(variable_rename,[status(thm)],[f_249_1]) ).
fof(f_249_3,plain,
! [U_769,U_768,U_770] :
( c_Orderings_Oord__class_Oless(U_768,c_Groups_Oplus__class_Oplus(U_768,U_769,U_770),c_Groups_Ozero__class_Ozero(U_768))
| ~ c_Orderings_Oord__class_Oless__eq(U_768,U_770,c_Groups_Ozero__class_Ozero(U_768))
| ~ c_Orderings_Oord__class_Oless(U_768,U_769,c_Groups_Ozero__class_Ozero(U_768))
| ~ class_Groups_Oordered__comm__monoid__add(U_768) ),
inference(definitional_conversion,[status(esa)],[f_249_2]) ).
cnf(f_249_4,plain,
( c_Orderings_Oord__class_Oless(U_768,c_Groups_Oplus__class_Oplus(U_768,U_769,U_770),c_Groups_Ozero__class_Ozero(U_768))
| ~ c_Orderings_Oord__class_Oless__eq(U_768,U_770,c_Groups_Ozero__class_Ozero(U_768))
| ~ c_Orderings_Oord__class_Oless(U_768,U_769,c_Groups_Ozero__class_Ozero(U_768))
| ~ class_Groups_Oordered__comm__monoid__add(U_768) ),
inference(clausify,[status(thm)],[f_249_3]) ).
fof(f_250_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_250_2,plain,
! [U_773,U_772,U_771] :
( c_Orderings_Oord__class_Oless(U_771,c_Groups_Oplus__class_Oplus(U_771,U_772,U_773),c_Groups_Ozero__class_Ozero(U_771))
| ~ c_Orderings_Oord__class_Oless(U_771,U_773,c_Groups_Ozero__class_Ozero(U_771))
| ~ c_Orderings_Oord__class_Oless__eq(U_771,U_772,c_Groups_Ozero__class_Ozero(U_771))
| ~ class_Groups_Oordered__comm__monoid__add(U_771) ),
inference(variable_rename,[status(thm)],[f_250_1]) ).
fof(f_250_3,plain,
! [U_771,U_772,U_773] :
( c_Orderings_Oord__class_Oless(U_771,c_Groups_Oplus__class_Oplus(U_771,U_772,U_773),c_Groups_Ozero__class_Ozero(U_771))
| ~ c_Orderings_Oord__class_Oless(U_771,U_773,c_Groups_Ozero__class_Ozero(U_771))
| ~ c_Orderings_Oord__class_Oless__eq(U_771,U_772,c_Groups_Ozero__class_Ozero(U_771))
| ~ class_Groups_Oordered__comm__monoid__add(U_771) ),
inference(definitional_conversion,[status(esa)],[f_250_2]) ).
cnf(f_250_4,plain,
( c_Orderings_Oord__class_Oless(U_771,c_Groups_Oplus__class_Oplus(U_771,U_772,U_773),c_Groups_Ozero__class_Ozero(U_771))
| ~ c_Orderings_Oord__class_Oless(U_771,U_773,c_Groups_Ozero__class_Ozero(U_771))
| ~ c_Orderings_Oord__class_Oless__eq(U_771,U_772,c_Groups_Ozero__class_Ozero(U_771))
| ~ class_Groups_Oordered__comm__monoid__add(U_771) ),
inference(clausify,[status(thm)],[f_250_3]) ).
fof(f_251_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_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_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_ca_2)
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel__left__pos]) ).
fof(f_251_2,plain,
! [U_777,U_776,U_775,U_774] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_774,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_777))
| ~ c_Orderings_Oord__class_Oless__eq(U_774,U_776,U_777) )
& ( c_Orderings_Oord__class_Oless__eq(U_774,U_776,U_777)
| ~ c_Orderings_Oord__class_Oless__eq(U_774,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_777)) ) )
| ~ c_Orderings_Oord__class_Oless(U_774,c_Groups_Ozero__class_Ozero(U_774),U_775)
| ~ class_Rings_Olinordered__ring__strict(U_774) ),
inference(variable_rename,[status(thm)],[f_251_1]) ).
fof(f_251_3,plain,
( ! [U_774,U_775,U_776,U_777] :
( c_Orderings_Oord__class_Oless__eq(U_774,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_777))
| ~ c_Orderings_Oord__class_Oless__eq(U_774,U_776,U_777)
| ~ sP84(U_774,U_775,U_776,U_777) )
& ! [U_774,U_775,U_776,U_777] :
( c_Orderings_Oord__class_Oless__eq(U_774,U_776,U_777)
| ~ c_Orderings_Oord__class_Oless__eq(U_774,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_777))
| ~ sP84(U_774,U_775,U_776,U_777) )
& ! [U_774,U_775,U_776,U_777] :
( sP84(U_774,U_775,U_776,U_777)
| ~ c_Orderings_Oord__class_Oless(U_774,c_Groups_Ozero__class_Ozero(U_774),U_775)
| ~ class_Rings_Olinordered__ring__strict(U_774) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_251_2]) ).
cnf(f_251_4,plain,
( sP84(U_774,U_775,U_776,U_777)
| ~ c_Orderings_Oord__class_Oless(U_774,c_Groups_Ozero__class_Ozero(U_774),U_775)
| ~ class_Rings_Olinordered__ring__strict(U_774) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_774,U_776,U_777)
| ~ c_Orderings_Oord__class_Oless__eq(U_774,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_777))
| ~ sP84(U_774,U_775,U_776,U_777) ),
inference(clausify,[status(thm)],[f_251_3]) ).
cnf(f_251_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_774,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_774),U_775),U_777))
| ~ c_Orderings_Oord__class_Oless__eq(U_774,U_776,U_777)
| ~ sP84(U_774,U_775,U_776,U_777) ),
inference(clausify,[status(thm)],[f_251_3]) ).
fof(f_252_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_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_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,V_ca_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_252_2,plain,
! [U_781,U_780,U_779,U_778] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_781))
| ~ c_Orderings_Oord__class_Oless__eq(U_778,U_781,U_780) )
& ( c_Orderings_Oord__class_Oless__eq(U_778,U_781,U_780)
| ~ c_Orderings_Oord__class_Oless__eq(U_778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_781)) ) )
| ~ c_Orderings_Oord__class_Oless(U_778,U_779,c_Groups_Ozero__class_Ozero(U_778))
| ~ class_Rings_Olinordered__ring__strict(U_778) ),
inference(variable_rename,[status(thm)],[f_252_1]) ).
fof(f_252_3,plain,
( ! [U_781,U_778,U_780,U_779] :
( c_Orderings_Oord__class_Oless__eq(U_778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_781))
| ~ c_Orderings_Oord__class_Oless__eq(U_778,U_781,U_780)
| ~ sP85(U_781,U_778,U_780,U_779) )
& ! [U_781,U_778,U_780,U_779] :
( c_Orderings_Oord__class_Oless__eq(U_778,U_781,U_780)
| ~ c_Orderings_Oord__class_Oless__eq(U_778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_781))
| ~ sP85(U_781,U_778,U_780,U_779) )
& ! [U_781,U_778,U_780,U_779] :
( sP85(U_781,U_778,U_780,U_779)
| ~ c_Orderings_Oord__class_Oless(U_778,U_779,c_Groups_Ozero__class_Ozero(U_778))
| ~ class_Rings_Olinordered__ring__strict(U_778) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_252_2]) ).
cnf(f_252_4,plain,
( sP85(U_781,U_778,U_780,U_779)
| ~ c_Orderings_Oord__class_Oless(U_778,U_779,c_Groups_Ozero__class_Ozero(U_778))
| ~ class_Rings_Olinordered__ring__strict(U_778) ),
inference(clausify,[status(thm)],[f_252_3]) ).
cnf(f_252_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_778,U_781,U_780)
| ~ c_Orderings_Oord__class_Oless__eq(U_778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_781))
| ~ sP85(U_781,U_778,U_780,U_779) ),
inference(clausify,[status(thm)],[f_252_3]) ).
cnf(f_252_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_778,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_780),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_778),U_779),U_781))
| ~ c_Orderings_Oord__class_Oless__eq(U_778,U_781,U_780)
| ~ sP85(U_781,U_778,U_780,U_779) ),
inference(clausify,[status(thm)],[f_252_3]) ).
fof(f_253_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_253_2,plain,
! [U_786,U_785,U_784,U_783,U_782] :
( c_Orderings_Oord__class_Oless(U_782,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_782),U_783),U_785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_782),U_784),U_786))
| ~ c_Orderings_Oord__class_Oless__eq(U_782,c_Groups_Ozero__class_Ozero(U_782),U_785)
| ~ c_Orderings_Oord__class_Oless(U_782,c_Groups_Ozero__class_Ozero(U_782),U_784)
| ~ c_Orderings_Oord__class_Oless(U_782,U_785,U_786)
| ~ c_Orderings_Oord__class_Oless(U_782,U_783,U_784)
| ~ class_Rings_Olinordered__semiring__strict(U_782) ),
inference(variable_rename,[status(thm)],[f_253_1]) ).
fof(f_253_3,plain,
! [U_782,U_784,U_785,U_786,U_783] :
( c_Orderings_Oord__class_Oless(U_782,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_782),U_783),U_785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_782),U_784),U_786))
| ~ c_Orderings_Oord__class_Oless__eq(U_782,c_Groups_Ozero__class_Ozero(U_782),U_785)
| ~ c_Orderings_Oord__class_Oless(U_782,c_Groups_Ozero__class_Ozero(U_782),U_784)
| ~ c_Orderings_Oord__class_Oless(U_782,U_785,U_786)
| ~ c_Orderings_Oord__class_Oless(U_782,U_783,U_784)
| ~ class_Rings_Olinordered__semiring__strict(U_782) ),
inference(definitional_conversion,[status(esa)],[f_253_2]) ).
cnf(f_253_4,plain,
( c_Orderings_Oord__class_Oless(U_782,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_782),U_783),U_785),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_782),U_784),U_786))
| ~ c_Orderings_Oord__class_Oless__eq(U_782,c_Groups_Ozero__class_Ozero(U_782),U_785)
| ~ c_Orderings_Oord__class_Oless(U_782,c_Groups_Ozero__class_Ozero(U_782),U_784)
| ~ c_Orderings_Oord__class_Oless(U_782,U_785,U_786)
| ~ c_Orderings_Oord__class_Oless(U_782,U_783,U_784)
| ~ class_Rings_Olinordered__semiring__strict(U_782) ),
inference(clausify,[status(thm)],[f_253_3]) ).
fof(f_254_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_254_2,plain,
! [U_791,U_790,U_789,U_788,U_787] :
( c_Orderings_Oord__class_Oless(U_787,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_787),U_788),U_790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_787),U_789),U_791))
| ~ c_Orderings_Oord__class_Oless__eq(U_787,c_Groups_Ozero__class_Ozero(U_787),U_790)
| ~ c_Orderings_Oord__class_Oless__eq(U_787,c_Groups_Ozero__class_Ozero(U_787),U_788)
| ~ c_Orderings_Oord__class_Oless(U_787,U_790,U_791)
| ~ c_Orderings_Oord__class_Oless(U_787,U_788,U_789)
| ~ class_Rings_Olinordered__semiring__strict(U_787) ),
inference(variable_rename,[status(thm)],[f_254_1]) ).
fof(f_254_3,plain,
! [U_789,U_791,U_790,U_788,U_787] :
( c_Orderings_Oord__class_Oless(U_787,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_787),U_788),U_790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_787),U_789),U_791))
| ~ c_Orderings_Oord__class_Oless__eq(U_787,c_Groups_Ozero__class_Ozero(U_787),U_790)
| ~ c_Orderings_Oord__class_Oless__eq(U_787,c_Groups_Ozero__class_Ozero(U_787),U_788)
| ~ c_Orderings_Oord__class_Oless(U_787,U_790,U_791)
| ~ c_Orderings_Oord__class_Oless(U_787,U_788,U_789)
| ~ class_Rings_Olinordered__semiring__strict(U_787) ),
inference(definitional_conversion,[status(esa)],[f_254_2]) ).
cnf(f_254_4,plain,
( c_Orderings_Oord__class_Oless(U_787,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_787),U_788),U_790),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_787),U_789),U_791))
| ~ c_Orderings_Oord__class_Oless__eq(U_787,c_Groups_Ozero__class_Ozero(U_787),U_790)
| ~ c_Orderings_Oord__class_Oless__eq(U_787,c_Groups_Ozero__class_Ozero(U_787),U_788)
| ~ c_Orderings_Oord__class_Oless(U_787,U_790,U_791)
| ~ c_Orderings_Oord__class_Oless(U_787,U_788,U_789)
| ~ class_Rings_Olinordered__semiring__strict(U_787) ),
inference(clausify,[status(thm)],[f_254_3]) ).
fof(f_255_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_255_2,plain,
! [U_796,U_795,U_794,U_793,U_792] :
( c_Orderings_Oord__class_Oless(U_792,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_792),U_793),U_795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_792),U_794),U_796))
| ~ c_Orderings_Oord__class_Oless(U_792,c_Groups_Ozero__class_Ozero(U_792),U_795)
| ~ c_Orderings_Oord__class_Oless__eq(U_792,c_Groups_Ozero__class_Ozero(U_792),U_793)
| ~ c_Orderings_Oord__class_Oless__eq(U_792,U_795,U_796)
| ~ c_Orderings_Oord__class_Oless(U_792,U_793,U_794)
| ~ class_Rings_Olinordered__semiring__strict(U_792) ),
inference(variable_rename,[status(thm)],[f_255_1]) ).
fof(f_255_3,plain,
! [U_793,U_792,U_796,U_795,U_794] :
( c_Orderings_Oord__class_Oless(U_792,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_792),U_793),U_795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_792),U_794),U_796))
| ~ c_Orderings_Oord__class_Oless(U_792,c_Groups_Ozero__class_Ozero(U_792),U_795)
| ~ c_Orderings_Oord__class_Oless__eq(U_792,c_Groups_Ozero__class_Ozero(U_792),U_793)
| ~ c_Orderings_Oord__class_Oless__eq(U_792,U_795,U_796)
| ~ c_Orderings_Oord__class_Oless(U_792,U_793,U_794)
| ~ class_Rings_Olinordered__semiring__strict(U_792) ),
inference(definitional_conversion,[status(esa)],[f_255_2]) ).
cnf(f_255_4,plain,
( c_Orderings_Oord__class_Oless(U_792,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_792),U_793),U_795),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_792),U_794),U_796))
| ~ c_Orderings_Oord__class_Oless(U_792,c_Groups_Ozero__class_Ozero(U_792),U_795)
| ~ c_Orderings_Oord__class_Oless__eq(U_792,c_Groups_Ozero__class_Ozero(U_792),U_793)
| ~ c_Orderings_Oord__class_Oless__eq(U_792,U_795,U_796)
| ~ c_Orderings_Oord__class_Oless(U_792,U_793,U_794)
| ~ class_Rings_Olinordered__semiring__strict(U_792) ),
inference(clausify,[status(thm)],[f_255_3]) ).
fof(f_256_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_256_2,plain,
! [U_801,U_800,U_799,U_798,U_797] :
( c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_799),U_801))
| ~ c_Orderings_Oord__class_Oless__eq(U_797,c_Groups_Ozero__class_Ozero(U_797),U_800)
| ~ c_Orderings_Oord__class_Oless(U_797,c_Groups_Ozero__class_Ozero(U_797),U_798)
| ~ c_Orderings_Oord__class_Oless(U_797,U_800,U_801)
| ~ c_Orderings_Oord__class_Oless__eq(U_797,U_798,U_799)
| ~ class_Rings_Olinordered__semiring__strict(U_797) ),
inference(variable_rename,[status(thm)],[f_256_1]) ).
fof(f_256_3,plain,
! [U_797,U_798,U_799,U_800,U_801] :
( c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_799),U_801))
| ~ c_Orderings_Oord__class_Oless__eq(U_797,c_Groups_Ozero__class_Ozero(U_797),U_800)
| ~ c_Orderings_Oord__class_Oless(U_797,c_Groups_Ozero__class_Ozero(U_797),U_798)
| ~ c_Orderings_Oord__class_Oless(U_797,U_800,U_801)
| ~ c_Orderings_Oord__class_Oless__eq(U_797,U_798,U_799)
| ~ class_Rings_Olinordered__semiring__strict(U_797) ),
inference(definitional_conversion,[status(esa)],[f_256_2]) ).
cnf(f_256_4,plain,
( c_Orderings_Oord__class_Oless(U_797,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_798),U_800),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_797),U_799),U_801))
| ~ c_Orderings_Oord__class_Oless__eq(U_797,c_Groups_Ozero__class_Ozero(U_797),U_800)
| ~ c_Orderings_Oord__class_Oless(U_797,c_Groups_Ozero__class_Ozero(U_797),U_798)
| ~ c_Orderings_Oord__class_Oless(U_797,U_800,U_801)
| ~ c_Orderings_Oord__class_Oless__eq(U_797,U_798,U_799)
| ~ class_Rings_Olinordered__semiring__strict(U_797) ),
inference(clausify,[status(thm)],[f_256_3]) ).
fof(f_257_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_257_2,plain,
! [U_805,U_804,U_803,U_802] :
( c_Orderings_Oord__class_Oless(U_802,U_803,U_805)
| ~ c_Orderings_Oord__class_Oless__eq(U_802,c_Groups_Ozero__class_Ozero(U_802),U_804)
| ~ c_Orderings_Oord__class_Oless(U_802,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_802),U_803),U_804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_802),U_805),U_804))
| ~ class_Rings_Olinordered__semiring(U_802) ),
inference(variable_rename,[status(thm)],[f_257_1]) ).
fof(f_257_3,plain,
! [U_802,U_803,U_804,U_805] :
( c_Orderings_Oord__class_Oless(U_802,U_803,U_805)
| ~ c_Orderings_Oord__class_Oless__eq(U_802,c_Groups_Ozero__class_Ozero(U_802),U_804)
| ~ c_Orderings_Oord__class_Oless(U_802,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_802),U_803),U_804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_802),U_805),U_804))
| ~ class_Rings_Olinordered__semiring(U_802) ),
inference(definitional_conversion,[status(esa)],[f_257_2]) ).
cnf(f_257_4,plain,
( c_Orderings_Oord__class_Oless(U_802,U_803,U_805)
| ~ c_Orderings_Oord__class_Oless__eq(U_802,c_Groups_Ozero__class_Ozero(U_802),U_804)
| ~ c_Orderings_Oord__class_Oless(U_802,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_802),U_803),U_804),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_802),U_805),U_804))
| ~ class_Rings_Olinordered__semiring(U_802) ),
inference(clausify,[status(thm)],[f_257_3]) ).
fof(f_258_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_258_2,plain,
! [U_809,U_808,U_807,U_806] :
( c_Orderings_Oord__class_Oless(U_806,U_807,U_809)
| ~ c_Orderings_Oord__class_Oless__eq(U_806,c_Groups_Ozero__class_Ozero(U_806),U_808)
| ~ c_Orderings_Oord__class_Oless(U_806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_809),U_808))
| ~ class_Rings_Olinordered__semiring__strict(U_806) ),
inference(variable_rename,[status(thm)],[f_258_1]) ).
fof(f_258_3,plain,
! [U_809,U_807,U_808,U_806] :
( c_Orderings_Oord__class_Oless(U_806,U_807,U_809)
| ~ c_Orderings_Oord__class_Oless__eq(U_806,c_Groups_Ozero__class_Ozero(U_806),U_808)
| ~ c_Orderings_Oord__class_Oless(U_806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_809),U_808))
| ~ class_Rings_Olinordered__semiring__strict(U_806) ),
inference(definitional_conversion,[status(esa)],[f_258_2]) ).
cnf(f_258_4,plain,
( c_Orderings_Oord__class_Oless(U_806,U_807,U_809)
| ~ c_Orderings_Oord__class_Oless__eq(U_806,c_Groups_Ozero__class_Ozero(U_806),U_808)
| ~ c_Orderings_Oord__class_Oless(U_806,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_807),U_808),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_806),U_809),U_808))
| ~ class_Rings_Olinordered__semiring__strict(U_806) ),
inference(clausify,[status(thm)],[f_258_3]) ).
fof(f_259_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_259_2,plain,
! [U_813,U_812,U_811,U_810] :
( c_Orderings_Oord__class_Oless(U_810,U_812,U_813)
| ~ c_Orderings_Oord__class_Oless__eq(U_810,c_Groups_Ozero__class_Ozero(U_810),U_811)
| ~ c_Orderings_Oord__class_Oless(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_812),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_813))
| ~ class_Rings_Olinordered__semiring(U_810) ),
inference(variable_rename,[status(thm)],[f_259_1]) ).
fof(f_259_3,plain,
! [U_813,U_811,U_810,U_812] :
( c_Orderings_Oord__class_Oless(U_810,U_812,U_813)
| ~ c_Orderings_Oord__class_Oless__eq(U_810,c_Groups_Ozero__class_Ozero(U_810),U_811)
| ~ c_Orderings_Oord__class_Oless(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_812),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_813))
| ~ class_Rings_Olinordered__semiring(U_810) ),
inference(definitional_conversion,[status(esa)],[f_259_2]) ).
cnf(f_259_4,plain,
( c_Orderings_Oord__class_Oless(U_810,U_812,U_813)
| ~ c_Orderings_Oord__class_Oless__eq(U_810,c_Groups_Ozero__class_Ozero(U_810),U_811)
| ~ c_Orderings_Oord__class_Oless(U_810,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_812),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_810),U_811),U_813))
| ~ class_Rings_Olinordered__semiring(U_810) ),
inference(clausify,[status(thm)],[f_259_3]) ).
fof(f_260_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_260_2,plain,
! [U_817,U_816,U_815,U_814] :
( c_Orderings_Oord__class_Oless(U_814,U_816,U_817)
| ~ c_Orderings_Oord__class_Oless__eq(U_814,c_Groups_Ozero__class_Ozero(U_814),U_815)
| ~ c_Orderings_Oord__class_Oless(U_814,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_814),U_815),U_816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_814),U_815),U_817))
| ~ class_Rings_Olinordered__semiring__strict(U_814) ),
inference(variable_rename,[status(thm)],[f_260_1]) ).
fof(f_260_3,plain,
! [U_815,U_816,U_817,U_814] :
( c_Orderings_Oord__class_Oless(U_814,U_816,U_817)
| ~ c_Orderings_Oord__class_Oless__eq(U_814,c_Groups_Ozero__class_Ozero(U_814),U_815)
| ~ c_Orderings_Oord__class_Oless(U_814,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_814),U_815),U_816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_814),U_815),U_817))
| ~ class_Rings_Olinordered__semiring__strict(U_814) ),
inference(definitional_conversion,[status(esa)],[f_260_2]) ).
cnf(f_260_4,plain,
( c_Orderings_Oord__class_Oless(U_814,U_816,U_817)
| ~ c_Orderings_Oord__class_Oless__eq(U_814,c_Groups_Ozero__class_Ozero(U_814),U_815)
| ~ c_Orderings_Oord__class_Oless(U_814,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_814),U_815),U_816),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_814),U_815),U_817))
| ~ class_Rings_Olinordered__semiring__strict(U_814) ),
inference(clausify,[status(thm)],[f_260_3]) ).
fof(f_261_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_261_2,plain,
! [U_821,U_820,U_819,U_818] :
( c_Orderings_Oord__class_Oless__eq(U_818,U_819,U_821)
| ~ c_Orderings_Oord__class_Oless(U_818,c_Groups_Ozero__class_Ozero(U_818),U_820)
| ~ c_Orderings_Oord__class_Oless__eq(U_818,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_818),U_819),U_820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_818),U_821),U_820))
| ~ class_Rings_Olinordered__semiring__strict(U_818) ),
inference(variable_rename,[status(thm)],[f_261_1]) ).
fof(f_261_3,plain,
! [U_818,U_819,U_820,U_821] :
( c_Orderings_Oord__class_Oless__eq(U_818,U_819,U_821)
| ~ c_Orderings_Oord__class_Oless(U_818,c_Groups_Ozero__class_Ozero(U_818),U_820)
| ~ c_Orderings_Oord__class_Oless__eq(U_818,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_818),U_819),U_820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_818),U_821),U_820))
| ~ class_Rings_Olinordered__semiring__strict(U_818) ),
inference(definitional_conversion,[status(esa)],[f_261_2]) ).
cnf(f_261_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_818,U_819,U_821)
| ~ c_Orderings_Oord__class_Oless(U_818,c_Groups_Ozero__class_Ozero(U_818),U_820)
| ~ c_Orderings_Oord__class_Oless__eq(U_818,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_818),U_819),U_820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_818),U_821),U_820))
| ~ class_Rings_Olinordered__semiring__strict(U_818) ),
inference(clausify,[status(thm)],[f_261_3]) ).
fof(f_262_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_262_2,plain,
! [U_825,U_824,U_823,U_822] :
( c_Orderings_Oord__class_Oless__eq(U_822,U_824,U_825)
| ~ c_Orderings_Oord__class_Oless(U_822,c_Groups_Ozero__class_Ozero(U_822),U_823)
| ~ c_Orderings_Oord__class_Oless__eq(U_822,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_822),U_823),U_824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_822),U_823),U_825))
| ~ class_Rings_Olinordered__semiring__strict(U_822) ),
inference(variable_rename,[status(thm)],[f_262_1]) ).
fof(f_262_3,plain,
! [U_822,U_823,U_824,U_825] :
( c_Orderings_Oord__class_Oless__eq(U_822,U_824,U_825)
| ~ c_Orderings_Oord__class_Oless(U_822,c_Groups_Ozero__class_Ozero(U_822),U_823)
| ~ c_Orderings_Oord__class_Oless__eq(U_822,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_822),U_823),U_824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_822),U_823),U_825))
| ~ class_Rings_Olinordered__semiring__strict(U_822) ),
inference(definitional_conversion,[status(esa)],[f_262_2]) ).
cnf(f_262_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_822,U_824,U_825)
| ~ c_Orderings_Oord__class_Oless(U_822,c_Groups_Ozero__class_Ozero(U_822),U_823)
| ~ c_Orderings_Oord__class_Oless__eq(U_822,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_822),U_823),U_824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_822),U_823),U_825))
| ~ class_Rings_Olinordered__semiring__strict(U_822) ),
inference(clausify,[status(thm)],[f_262_3]) ).
fof(f_263_1,plain,
! [T_a] :
( ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_not__pos__poly__0]) ).
fof(f_263_2,plain,
! [U_826] :
( ~ c_Polynomial_Opos__poly(U_826,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_826)))
| ~ class_Rings_Olinordered__idom(U_826) ),
inference(variable_rename,[status(thm)],[f_263_1]) ).
fof(f_263_3,plain,
! [U_826] :
( ~ c_Polynomial_Opos__poly(U_826,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_826)))
| ~ class_Rings_Olinordered__idom(U_826) ),
inference(definitional_conversion,[status(esa)],[f_263_2]) ).
cnf(f_263_4,plain,
( ~ c_Polynomial_Opos__poly(U_826,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_826)))
| ~ class_Rings_Olinordered__idom(U_826) ),
inference(clausify,[status(thm)],[f_263_3]) ).
fof(f_264_1,plain,
! [V_y_2,V_x_2,V_z_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__less__iff1]) ).
fof(f_264_2,plain,
! [U_829,U_828,U_827] :
( ( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_828),U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_829),U_827))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_828,U_829) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_828,U_829)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_828),U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_829),U_827)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_827) ),
inference(variable_rename,[status(thm)],[f_264_1]) ).
fof(f_264_3,plain,
( ! [U_829,U_828,U_827] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_828),U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_829),U_827))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_828,U_829)
| ~ sP86(U_829,U_828,U_827) )
& ! [U_829,U_828,U_827] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_828,U_829)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_828),U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_829),U_827))
| ~ sP86(U_829,U_828,U_827) )
& ! [U_829,U_828,U_827] :
( sP86(U_829,U_828,U_827)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_827) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_264_2]) ).
cnf(f_264_4,plain,
( sP86(U_829,U_828,U_827)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_827) ),
inference(clausify,[status(thm)],[f_264_3]) ).
cnf(f_264_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_828,U_829)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_828),U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_829),U_827))
| ~ sP86(U_829,U_828,U_827) ),
inference(clausify,[status(thm)],[f_264_3]) ).
cnf(f_264_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_828),U_827),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_829),U_827))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_828,U_829)
| ~ sP86(U_829,U_828,U_827) ),
inference(clausify,[status(thm)],[f_264_3]) ).
fof(f_265_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_265_2,plain,
! [U_831,U_830] :
( 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_830),U_831))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_831)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_830) ),
inference(variable_rename,[status(thm)],[f_265_1]) ).
fof(f_265_3,plain,
! [U_830,U_831] :
( 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_830),U_831))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_831)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_830) ),
inference(definitional_conversion,[status(esa)],[f_265_2]) ).
cnf(f_265_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_830),U_831))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_831)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_830) ),
inference(clausify,[status(thm)],[f_265_3]) ).
fof(f_266_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_266_2,plain,
! [U_834,U_833,U_832] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_832),U_833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_832),U_834))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_833,U_834)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_832) ),
inference(variable_rename,[status(thm)],[f_266_1]) ).
fof(f_266_3,plain,
! [U_832,U_834,U_833] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_832),U_833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_832),U_834))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_833,U_834)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_832) ),
inference(definitional_conversion,[status(esa)],[f_266_2]) ).
cnf(f_266_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_832),U_833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_832),U_834))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_833,U_834)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_832) ),
inference(clausify,[status(thm)],[f_266_3]) ).
fof(f_267_1,plain,
! [V_c,T_a] :
( c_Polynomial_Osynthetic__div(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_c) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_synthetic__div__0]) ).
fof(f_267_2,plain,
! [U_836,U_835] :
( c_Polynomial_Osynthetic__div(U_835,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_835)),U_836) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_835))
| ~ class_Rings_Ocomm__semiring__0(U_835) ),
inference(variable_rename,[status(thm)],[f_267_1]) ).
fof(f_267_3,plain,
! [U_836,U_835] :
( c_Polynomial_Osynthetic__div(U_835,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_835)),U_836) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_835))
| ~ class_Rings_Ocomm__semiring__0(U_835) ),
inference(definitional_conversion,[status(esa)],[f_267_2]) ).
cnf(f_267_4,plain,
( c_Polynomial_Osynthetic__div(U_835,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_835)),U_836) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_835))
| ~ class_Rings_Ocomm__semiring__0(U_835) ),
inference(clausify,[status(thm)],[f_267_3]) ).
fof(f_268_1,plain,
! [V_y_2,V_x_2,V_z_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_y_2),V_z_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff1]) ).
fof(f_268_2,plain,
! [U_839,U_838,U_837] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_838),U_837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_837))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_838,U_839) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_838,U_839)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_838),U_837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_837)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_837) ),
inference(variable_rename,[status(thm)],[f_268_1]) ).
fof(f_268_3,plain,
( ! [U_838,U_837,U_839] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_838),U_837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_837))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_838,U_839)
| ~ sP87(U_838,U_837,U_839) )
& ! [U_838,U_837,U_839] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_838,U_839)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_838),U_837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_837))
| ~ sP87(U_838,U_837,U_839) )
& ! [U_838,U_837,U_839] :
( sP87(U_838,U_837,U_839)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_837) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_268_2]) ).
cnf(f_268_4,plain,
( sP87(U_838,U_837,U_839)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_837) ),
inference(clausify,[status(thm)],[f_268_3]) ).
cnf(f_268_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_838,U_839)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_838),U_837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_837))
| ~ sP87(U_838,U_837,U_839) ),
inference(clausify,[status(thm)],[f_268_3]) ).
cnf(f_268_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_838),U_837),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_839),U_837))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_838,U_839)
| ~ sP87(U_838,U_837,U_839) ),
inference(clausify,[status(thm)],[f_268_3]) ).
fof(f_269_1,plain,
! [V_y_2,V_x_2,V_z_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_z_2),V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_z_2) ),
inference(fof_nnf,[status(thm)],[fact_real__mult__le__cancel__iff2]) ).
fof(f_269_2,plain,
! [U_842,U_841,U_840] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_842))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_841,U_842) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_841,U_842)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_842)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_840) ),
inference(variable_rename,[status(thm)],[f_269_1]) ).
fof(f_269_3,plain,
( ! [U_842,U_840,U_841] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_842))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_841,U_842)
| ~ sP88(U_842,U_840,U_841) )
& ! [U_842,U_840,U_841] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_841,U_842)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_842))
| ~ sP88(U_842,U_840,U_841) )
& ! [U_842,U_840,U_841] :
( sP88(U_842,U_840,U_841)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_840) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_269_2]) ).
cnf(f_269_4,plain,
( sP88(U_842,U_840,U_841)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_840) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_841,U_842)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_842))
| ~ sP88(U_842,U_840,U_841) ),
inference(clausify,[status(thm)],[f_269_3]) ).
cnf(f_269_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_841),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_840),U_842))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_841,U_842)
| ~ sP88(U_842,U_840,U_841) ),
inference(clausify,[status(thm)],[f_269_3]) ).
fof(f_270_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_270_2,plain,
! [U_846,U_845,U_844,U_843] :
( U_845 = c_Groups_Ozero__class_Ozero(U_843)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_843,U_845),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_844),c_RealVector_Onorm__class_Onorm(U_843,U_846)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_844,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_843) ),
inference(variable_rename,[status(thm)],[f_270_1]) ).
fof(f_270_3,plain,
! [U_845,U_846,U_844,U_843] :
( U_845 = c_Groups_Ozero__class_Ozero(U_843)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_843,U_845),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_844),c_RealVector_Onorm__class_Onorm(U_843,U_846)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_844,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_843) ),
inference(definitional_conversion,[status(esa)],[f_270_2]) ).
cnf(f_270_4,plain,
( U_845 = c_Groups_Ozero__class_Ozero(U_843)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_843,U_845),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_844),c_RealVector_Onorm__class_Onorm(U_843,U_846)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_844,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ class_RealVector_Oreal__normed__vector(U_843) ),
inference(clausify,[status(thm)],[f_270_3]) ).
fof(f_271_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_271_2,plain,
! [U_849,U_848,U_847] :
( U_848 = 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_848),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_847),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_849)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_847,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_271_1]) ).
fof(f_271_3,plain,
! [U_849,U_848,U_847] :
( U_848 = 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_848),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_847),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_849)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_847,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(definitional_conversion,[status(esa)],[f_271_2]) ).
cnf(f_271_4,plain,
( U_848 = 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_848),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_847),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_849)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_847,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_271_3]) ).
fof(f_272_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_272_2,plain,
! [U_852,U_851,U_850] :
( ~ c_Orderings_Oord__class_Oless(U_850,c_Groups_Oplus__class_Oplus(U_850,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_851),U_851),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_852),U_852)),c_Groups_Ozero__class_Ozero(U_850))
| ~ class_Rings_Olinordered__ring(U_850) ),
inference(variable_rename,[status(thm)],[f_272_1]) ).
fof(f_272_3,plain,
! [U_850,U_851,U_852] :
( ~ c_Orderings_Oord__class_Oless(U_850,c_Groups_Oplus__class_Oplus(U_850,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_851),U_851),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_852),U_852)),c_Groups_Ozero__class_Ozero(U_850))
| ~ class_Rings_Olinordered__ring(U_850) ),
inference(definitional_conversion,[status(esa)],[f_272_2]) ).
cnf(f_272_4,plain,
( ~ c_Orderings_Oord__class_Oless(U_850,c_Groups_Oplus__class_Oplus(U_850,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_851),U_851),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_850),U_852),U_852)),c_Groups_Ozero__class_Ozero(U_850))
| ~ class_Rings_Olinordered__ring(U_850) ),
inference(clausify,[status(thm)],[f_272_3]) ).
fof(f_273_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)))
| ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) )
& ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2))) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__gt__zero__iff]) ).
fof(f_273_2,plain,
! [U_855,U_854,U_853] :
( ( ( c_Orderings_Oord__class_Oless(U_853,c_Groups_Ozero__class_Ozero(U_853),c_Groups_Oplus__class_Oplus(U_853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_854),U_854),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_855),U_855)))
| ( U_855 = c_Groups_Ozero__class_Ozero(U_853)
& U_854 = c_Groups_Ozero__class_Ozero(U_853) ) )
& ( U_855 != c_Groups_Ozero__class_Ozero(U_853)
| U_854 != c_Groups_Ozero__class_Ozero(U_853)
| ~ c_Orderings_Oord__class_Oless(U_853,c_Groups_Ozero__class_Ozero(U_853),c_Groups_Oplus__class_Oplus(U_853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_854),U_854),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_855),U_855))) ) )
| ~ class_Rings_Olinordered__ring__strict(U_853) ),
inference(variable_rename,[status(thm)],[f_273_1]) ).
fof(f_273_3,plain,
( ! [U_854,U_853,U_855] :
( U_855 = c_Groups_Ozero__class_Ozero(U_853)
| ~ sP89(U_854,U_853,U_855) )
& ! [U_854,U_853,U_855] :
( U_854 = c_Groups_Ozero__class_Ozero(U_853)
| ~ sP89(U_854,U_853,U_855) )
& ! [U_854,U_853,U_855] :
( c_Orderings_Oord__class_Oless(U_853,c_Groups_Ozero__class_Ozero(U_853),c_Groups_Oplus__class_Oplus(U_853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_854),U_854),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_855),U_855)))
| sP89(U_854,U_853,U_855)
| ~ sP90(U_854,U_853,U_855) )
& ! [U_854,U_853,U_855] :
( U_855 != c_Groups_Ozero__class_Ozero(U_853)
| U_854 != c_Groups_Ozero__class_Ozero(U_853)
| ~ c_Orderings_Oord__class_Oless(U_853,c_Groups_Ozero__class_Ozero(U_853),c_Groups_Oplus__class_Oplus(U_853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_854),U_854),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_855),U_855)))
| ~ sP90(U_854,U_853,U_855) )
& ! [U_854,U_853,U_855] :
( sP90(U_854,U_853,U_855)
| ~ class_Rings_Olinordered__ring__strict(U_853) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89,sP90])],[f_273_2]) ).
cnf(f_273_4,plain,
( sP90(U_854,U_853,U_855)
| ~ class_Rings_Olinordered__ring__strict(U_853) ),
inference(clausify,[status(thm)],[f_273_3]) ).
cnf(f_273_5,plain,
( U_855 != c_Groups_Ozero__class_Ozero(U_853)
| U_854 != c_Groups_Ozero__class_Ozero(U_853)
| ~ c_Orderings_Oord__class_Oless(U_853,c_Groups_Ozero__class_Ozero(U_853),c_Groups_Oplus__class_Oplus(U_853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_854),U_854),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_855),U_855)))
| ~ sP90(U_854,U_853,U_855) ),
inference(clausify,[status(thm)],[f_273_3]) ).
cnf(f_273_6,plain,
( c_Orderings_Oord__class_Oless(U_853,c_Groups_Ozero__class_Ozero(U_853),c_Groups_Oplus__class_Oplus(U_853,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_854),U_854),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_853),U_855),U_855)))
| sP89(U_854,U_853,U_855)
| ~ sP90(U_854,U_853,U_855) ),
inference(clausify,[status(thm)],[f_273_3]) ).
cnf(f_273_7,plain,
( U_854 = c_Groups_Ozero__class_Ozero(U_853)
| ~ sP89(U_854,U_853,U_855) ),
inference(clausify,[status(thm)],[f_273_3]) ).
cnf(f_273_8,plain,
( U_855 = c_Groups_Ozero__class_Ozero(U_853)
| ~ sP89(U_854,U_853,U_855) ),
inference(clausify,[status(thm)],[f_273_3]) ).
fof(f_274_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_274_2,plain,
! [U_858,U_857,U_856] :
( c_Orderings_Oord__class_Oless__eq(U_856,c_Groups_Ozero__class_Ozero(U_856),c_Groups_Oplus__class_Oplus(U_856,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_856),U_857),U_857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_856),U_858),U_858)))
| ~ class_Rings_Olinordered__ring(U_856) ),
inference(variable_rename,[status(thm)],[f_274_1]) ).
fof(f_274_3,plain,
! [U_858,U_857,U_856] :
( c_Orderings_Oord__class_Oless__eq(U_856,c_Groups_Ozero__class_Ozero(U_856),c_Groups_Oplus__class_Oplus(U_856,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_856),U_857),U_857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_856),U_858),U_858)))
| ~ class_Rings_Olinordered__ring(U_856) ),
inference(definitional_conversion,[status(esa)],[f_274_2]) ).
cnf(f_274_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_856,c_Groups_Ozero__class_Ozero(U_856),c_Groups_Oplus__class_Oplus(U_856,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_856),U_857),U_857),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_856),U_858),U_858)))
| ~ class_Rings_Olinordered__ring(U_856) ),
inference(clausify,[status(thm)],[f_274_3]) ).
fof(f_275_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a))
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__le__zero__iff]) ).
fof(f_275_2,plain,
! [U_861,U_860,U_859] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_859,c_Groups_Oplus__class_Oplus(U_859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_860),U_860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_861),U_861)),c_Groups_Ozero__class_Ozero(U_859))
| U_861 != c_Groups_Ozero__class_Ozero(U_859)
| U_860 != c_Groups_Ozero__class_Ozero(U_859) )
& ( ( U_861 = c_Groups_Ozero__class_Ozero(U_859)
& U_860 = c_Groups_Ozero__class_Ozero(U_859) )
| ~ c_Orderings_Oord__class_Oless__eq(U_859,c_Groups_Oplus__class_Oplus(U_859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_860),U_860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_861),U_861)),c_Groups_Ozero__class_Ozero(U_859)) ) )
| ~ class_Rings_Olinordered__ring__strict(U_859) ),
inference(variable_rename,[status(thm)],[f_275_1]) ).
fof(f_275_3,plain,
( ! [U_860,U_859,U_861] :
( U_861 = c_Groups_Ozero__class_Ozero(U_859)
| ~ sP91(U_860,U_859,U_861) )
& ! [U_860,U_859,U_861] :
( U_860 = c_Groups_Ozero__class_Ozero(U_859)
| ~ sP91(U_860,U_859,U_861) )
& ! [U_860,U_859,U_861] :
( c_Orderings_Oord__class_Oless__eq(U_859,c_Groups_Oplus__class_Oplus(U_859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_860),U_860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_861),U_861)),c_Groups_Ozero__class_Ozero(U_859))
| U_861 != c_Groups_Ozero__class_Ozero(U_859)
| U_860 != c_Groups_Ozero__class_Ozero(U_859)
| ~ sP92(U_860,U_859,U_861) )
& ! [U_860,U_859,U_861] :
( sP91(U_860,U_859,U_861)
| ~ c_Orderings_Oord__class_Oless__eq(U_859,c_Groups_Oplus__class_Oplus(U_859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_860),U_860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_861),U_861)),c_Groups_Ozero__class_Ozero(U_859))
| ~ sP92(U_860,U_859,U_861) )
& ! [U_860,U_859,U_861] :
( sP92(U_860,U_859,U_861)
| ~ class_Rings_Olinordered__ring__strict(U_859) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91,sP92])],[f_275_2]) ).
cnf(f_275_4,plain,
( sP92(U_860,U_859,U_861)
| ~ class_Rings_Olinordered__ring__strict(U_859) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_5,plain,
( sP91(U_860,U_859,U_861)
| ~ c_Orderings_Oord__class_Oless__eq(U_859,c_Groups_Oplus__class_Oplus(U_859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_860),U_860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_861),U_861)),c_Groups_Ozero__class_Ozero(U_859))
| ~ sP92(U_860,U_859,U_861) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_859,c_Groups_Oplus__class_Oplus(U_859,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_860),U_860),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_859),U_861),U_861)),c_Groups_Ozero__class_Ozero(U_859))
| U_861 != c_Groups_Ozero__class_Ozero(U_859)
| U_860 != c_Groups_Ozero__class_Ozero(U_859)
| ~ sP92(U_860,U_859,U_861) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_7,plain,
( U_860 = c_Groups_Ozero__class_Ozero(U_859)
| ~ sP91(U_860,U_859,U_861) ),
inference(clausify,[status(thm)],[f_275_3]) ).
cnf(f_275_8,plain,
( U_861 = c_Groups_Ozero__class_Ozero(U_859)
| ~ sP91(U_860,U_859,U_861) ),
inference(clausify,[status(thm)],[f_275_3]) ).
fof(f_276_1,plain,
! [V_x_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_x_2),V_x_2))
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x_2),V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_not__real__square__gt__zero]) ).
fof(f_276_2,plain,
! [U_862] :
( ( ~ 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_862),U_862))
| U_862 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( U_862 = 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_862),U_862)) ) ),
inference(variable_rename,[status(thm)],[f_276_1]) ).
fof(f_276_3,plain,
( ! [U_864] :
( ~ 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_864),U_864))
| U_864 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_863] :
( U_863 = 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_863),U_863)) ) ),
inference(miniscope,[status(thm)],[f_276_2]) ).
fof(f_276_4,plain,
( ! [U_864] :
( ~ 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_864),U_864))
| U_864 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_863] :
( U_863 = 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_863),U_863)) ) ),
inference(definitional_conversion,[status(esa)],[f_276_3]) ).
cnf(f_276_5,plain,
( U_863 = 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_863),U_863)) ),
inference(clausify,[status(thm)],[f_276_4]) ).
cnf(f_276_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_864),U_864))
| U_864 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_276_4]) ).
fof(f_277_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_277_2,plain,
! [U_867,U_866,U_865] :
( c_Groups_Oplus__class_Oplus(U_865,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_865),U_866),U_867),U_867) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_865),c_Groups_Oplus__class_Oplus(U_865,U_866,c_Groups_Oone__class_Oone(U_865))),U_867)
| ~ class_Rings_Ocomm__semiring__1(U_865) ),
inference(variable_rename,[status(thm)],[f_277_1]) ).
fof(f_277_3,plain,
! [U_866,U_867,U_865] :
( c_Groups_Oplus__class_Oplus(U_865,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_865),U_866),U_867),U_867) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_865),c_Groups_Oplus__class_Oplus(U_865,U_866,c_Groups_Oone__class_Oone(U_865))),U_867)
| ~ class_Rings_Ocomm__semiring__1(U_865) ),
inference(definitional_conversion,[status(esa)],[f_277_2]) ).
cnf(f_277_4,plain,
( c_Groups_Oplus__class_Oplus(U_865,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_865),U_866),U_867),U_867) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_865),c_Groups_Oplus__class_Oplus(U_865,U_866,c_Groups_Oone__class_Oone(U_865))),U_867)
| ~ class_Rings_Ocomm__semiring__1(U_865) ),
inference(clausify,[status(thm)],[f_277_3]) ).
fof(f_278_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_278_2,plain,
! [U_870,U_869,U_868] :
( c_Groups_Oplus__class_Oplus(U_868,U_869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_868),U_870),U_869)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_868),c_Groups_Oplus__class_Oplus(U_868,U_870,c_Groups_Oone__class_Oone(U_868))),U_869)
| ~ class_Rings_Ocomm__semiring__1(U_868) ),
inference(variable_rename,[status(thm)],[f_278_1]) ).
fof(f_278_3,plain,
! [U_868,U_869,U_870] :
( c_Groups_Oplus__class_Oplus(U_868,U_869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_868),U_870),U_869)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_868),c_Groups_Oplus__class_Oplus(U_868,U_870,c_Groups_Oone__class_Oone(U_868))),U_869)
| ~ class_Rings_Ocomm__semiring__1(U_868) ),
inference(definitional_conversion,[status(esa)],[f_278_2]) ).
cnf(f_278_4,plain,
( c_Groups_Oplus__class_Oplus(U_868,U_869,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_868),U_870),U_869)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_868),c_Groups_Oplus__class_Oplus(U_868,U_870,c_Groups_Oone__class_Oone(U_868))),U_869)
| ~ class_Rings_Ocomm__semiring__1(U_868) ),
inference(clausify,[status(thm)],[f_278_3]) ).
fof(f_279_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_279_2,plain,
! [U_872,U_871] :
( c_Groups_Oplus__class_Oplus(U_871,U_872,U_872) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_871),c_Groups_Oplus__class_Oplus(U_871,c_Groups_Oone__class_Oone(U_871),c_Groups_Oone__class_Oone(U_871))),U_872)
| ~ class_Rings_Ocomm__semiring__1(U_871) ),
inference(variable_rename,[status(thm)],[f_279_1]) ).
fof(f_279_3,plain,
! [U_871,U_872] :
( c_Groups_Oplus__class_Oplus(U_871,U_872,U_872) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_871),c_Groups_Oplus__class_Oplus(U_871,c_Groups_Oone__class_Oone(U_871),c_Groups_Oone__class_Oone(U_871))),U_872)
| ~ class_Rings_Ocomm__semiring__1(U_871) ),
inference(definitional_conversion,[status(esa)],[f_279_2]) ).
cnf(f_279_4,plain,
( c_Groups_Oplus__class_Oplus(U_871,U_872,U_872) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_871),c_Groups_Oplus__class_Oplus(U_871,c_Groups_Oone__class_Oone(U_871),c_Groups_Oone__class_Oone(U_871))),U_872)
| ~ class_Rings_Ocomm__semiring__1(U_871) ),
inference(clausify,[status(thm)],[f_279_3]) ).
fof(f_280_1,plain,
! [V_r,V_q,V_p,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_r) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),V_r))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__poly__add__left]) ).
fof(f_280_2,plain,
! [U_876,U_875,U_874,U_873] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_873)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_873),U_874,U_875)),U_876) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_873)),U_874),U_876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_873)),U_875),U_876))
| ~ class_Rings_Ocomm__semiring__0(U_873) ),
inference(variable_rename,[status(thm)],[f_280_1]) ).
fof(f_280_3,plain,
! [U_873,U_874,U_875,U_876] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_873)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_873),U_874,U_875)),U_876) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_873)),U_874),U_876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_873)),U_875),U_876))
| ~ class_Rings_Ocomm__semiring__0(U_873) ),
inference(definitional_conversion,[status(esa)],[f_280_2]) ).
cnf(f_280_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_873)),c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_873),U_874,U_875)),U_876) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_873)),U_874),U_876),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_873)),U_875),U_876))
| ~ class_Rings_Ocomm__semiring__0(U_873) ),
inference(clausify,[status(thm)],[f_280_3]) ).
fof(f_281_1,plain,
! [V_q,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = V_q
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__poly__code_I1_J]) ).
fof(f_281_2,plain,
! [U_878,U_877] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_877),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_877)),U_878) = U_878
| ~ class_Groups_Ocomm__monoid__add(U_877) ),
inference(variable_rename,[status(thm)],[f_281_1]) ).
fof(f_281_3,plain,
! [U_878,U_877] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_877),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_877)),U_878) = U_878
| ~ class_Groups_Ocomm__monoid__add(U_877) ),
inference(definitional_conversion,[status(esa)],[f_281_2]) ).
cnf(f_281_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_877),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_877)),U_878) = U_878
| ~ class_Groups_Ocomm__monoid__add(U_877) ),
inference(clausify,[status(thm)],[f_281_3]) ).
fof(f_282_1,plain,
! [V_p,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
| ~ class_Groups_Ocomm__monoid__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__poly__code_I2_J]) ).
fof(f_282_2,plain,
! [U_880,U_879] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_879),U_880,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_879))) = U_880
| ~ class_Groups_Ocomm__monoid__add(U_879) ),
inference(variable_rename,[status(thm)],[f_282_1]) ).
fof(f_282_3,plain,
! [U_879,U_880] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_879),U_880,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_879))) = U_880
| ~ class_Groups_Ocomm__monoid__add(U_879) ),
inference(definitional_conversion,[status(esa)],[f_282_2]) ).
cnf(f_282_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_879),U_880,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_879))) = U_880
| ~ class_Groups_Ocomm__monoid__add(U_879) ),
inference(clausify,[status(thm)],[f_282_3]) ).
fof(f_283_1,plain,
! [V_q,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__poly__0__left]) ).
fof(f_283_2,plain,
! [U_882,U_881] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_881)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_881))),U_882) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_881))
| ~ class_Rings_Ocomm__semiring__0(U_881) ),
inference(variable_rename,[status(thm)],[f_283_1]) ).
fof(f_283_3,plain,
! [U_881,U_882] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_881)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_881))),U_882) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_881))
| ~ class_Rings_Ocomm__semiring__0(U_881) ),
inference(definitional_conversion,[status(esa)],[f_283_2]) ).
cnf(f_283_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_881)),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_881))),U_882) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_881))
| ~ class_Rings_Ocomm__semiring__0(U_881) ),
inference(clausify,[status(thm)],[f_283_3]) ).
fof(f_284_1,plain,
! [V_p,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__poly__0__right]) ).
fof(f_284_2,plain,
! [U_884,U_883] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_883)),U_884),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_883))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_883))
| ~ class_Rings_Ocomm__semiring__0(U_883) ),
inference(variable_rename,[status(thm)],[f_284_1]) ).
fof(f_284_3,plain,
! [U_883,U_884] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_883)),U_884),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_883))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_883))
| ~ class_Rings_Ocomm__semiring__0(U_883) ),
inference(definitional_conversion,[status(esa)],[f_284_2]) ).
cnf(f_284_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_883)),U_884),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_883))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_883))
| ~ class_Rings_Ocomm__semiring__0(U_883) ),
inference(clausify,[status(thm)],[f_284_3]) ).
fof(f_285_1,plain,
! [V_q,V_p,T_a] :
( c_Polynomial_Opos__poly(T_a,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),V_p,V_q))
| ~ c_Polynomial_Opos__poly(T_a,V_q)
| ~ c_Polynomial_Opos__poly(T_a,V_p)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__add]) ).
fof(f_285_2,plain,
! [U_887,U_886,U_885] :
( c_Polynomial_Opos__poly(U_885,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_885),U_886,U_887))
| ~ c_Polynomial_Opos__poly(U_885,U_887)
| ~ c_Polynomial_Opos__poly(U_885,U_886)
| ~ class_Rings_Olinordered__idom(U_885) ),
inference(variable_rename,[status(thm)],[f_285_1]) ).
fof(f_285_3,plain,
! [U_885,U_886,U_887] :
( c_Polynomial_Opos__poly(U_885,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_885),U_886,U_887))
| ~ c_Polynomial_Opos__poly(U_885,U_887)
| ~ c_Polynomial_Opos__poly(U_885,U_886)
| ~ class_Rings_Olinordered__idom(U_885) ),
inference(definitional_conversion,[status(esa)],[f_285_2]) ).
cnf(f_285_4,plain,
( c_Polynomial_Opos__poly(U_885,c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_885),U_886,U_887))
| ~ c_Polynomial_Opos__poly(U_885,U_887)
| ~ c_Polynomial_Opos__poly(U_885,U_886)
| ~ class_Rings_Olinordered__idom(U_885) ),
inference(clausify,[status(thm)],[f_285_3]) ).
fof(f_286_1,plain,
! [V_q,V_p,T_a] :
( c_Polynomial_Opos__poly(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_p),V_q))
| ~ c_Polynomial_Opos__poly(T_a,V_q)
| ~ c_Polynomial_Opos__poly(T_a,V_p)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__mult]) ).
fof(f_286_2,plain,
! [U_890,U_889,U_888] :
( c_Polynomial_Opos__poly(U_888,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_888)),U_889),U_890))
| ~ c_Polynomial_Opos__poly(U_888,U_890)
| ~ c_Polynomial_Opos__poly(U_888,U_889)
| ~ class_Rings_Olinordered__idom(U_888) ),
inference(variable_rename,[status(thm)],[f_286_1]) ).
fof(f_286_3,plain,
! [U_888,U_889,U_890] :
( c_Polynomial_Opos__poly(U_888,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_888)),U_889),U_890))
| ~ c_Polynomial_Opos__poly(U_888,U_890)
| ~ c_Polynomial_Opos__poly(U_888,U_889)
| ~ class_Rings_Olinordered__idom(U_888) ),
inference(definitional_conversion,[status(esa)],[f_286_2]) ).
cnf(f_286_4,plain,
( c_Polynomial_Opos__poly(U_888,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_888)),U_889),U_890))
| ~ c_Polynomial_Opos__poly(U_888,U_890)
| ~ c_Polynomial_Opos__poly(U_888,U_889)
| ~ class_Rings_Olinordered__idom(U_888) ),
inference(clausify,[status(thm)],[f_286_3]) ).
fof(f_287_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_287_2,plain,
! [U_893,U_892,U_891] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_892),U_893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_893),U_892)
| ~ class_Rings_Ocomm__semiring__1(U_891) ),
inference(variable_rename,[status(thm)],[f_287_1]) ).
fof(f_287_3,plain,
! [U_893,U_892,U_891] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_892),U_893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_893),U_892)
| ~ class_Rings_Ocomm__semiring__1(U_891) ),
inference(definitional_conversion,[status(esa)],[f_287_2]) ).
cnf(f_287_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_892),U_893) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_891),U_893),U_892)
| ~ class_Rings_Ocomm__semiring__1(U_891) ),
inference(clausify,[status(thm)],[f_287_3]) ).
fof(f_288_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_288_2,plain,
! [U_897,U_896,U_895,U_894] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_896),U_897)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_895),U_897))
| ~ class_Rings_Ocomm__semiring__1(U_894) ),
inference(variable_rename,[status(thm)],[f_288_1]) ).
fof(f_288_3,plain,
! [U_894,U_895,U_896,U_897] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_896),U_897)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_895),U_897))
| ~ class_Rings_Ocomm__semiring__1(U_894) ),
inference(definitional_conversion,[status(esa)],[f_288_2]) ).
cnf(f_288_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_895),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_896),U_897)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_896),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_894),U_895),U_897))
| ~ class_Rings_Ocomm__semiring__1(U_894) ),
inference(clausify,[status(thm)],[f_288_3]) ).
fof(f_289_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_289_2,plain,
! [U_901,U_900,U_899,U_898] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),U_899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),U_900),U_901)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),U_899),U_900)),U_901)
| ~ class_Rings_Ocomm__semiring__1(U_898) ),
inference(variable_rename,[status(thm)],[f_289_1]) ).
fof(f_289_3,plain,
! [U_898,U_899,U_900,U_901] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),U_899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),U_900),U_901)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),U_899),U_900)),U_901)
| ~ class_Rings_Ocomm__semiring__1(U_898) ),
inference(definitional_conversion,[status(esa)],[f_289_2]) ).
cnf(f_289_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),U_899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),U_900),U_901)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_898),U_899),U_900)),U_901)
| ~ class_Rings_Ocomm__semiring__1(U_898) ),
inference(clausify,[status(thm)],[f_289_3]) ).
fof(f_290_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_290_2,plain,
! [U_905,U_904,U_903,U_902] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_903),U_904)),U_905) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_904),U_905))
| ~ class_Rings_Ocomm__semiring__1(U_902) ),
inference(variable_rename,[status(thm)],[f_290_1]) ).
fof(f_290_3,plain,
! [U_903,U_904,U_905,U_902] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_903),U_904)),U_905) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_904),U_905))
| ~ class_Rings_Ocomm__semiring__1(U_902) ),
inference(definitional_conversion,[status(esa)],[f_290_2]) ).
cnf(f_290_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_903),U_904)),U_905) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_902),U_904),U_905))
| ~ class_Rings_Ocomm__semiring__1(U_902) ),
inference(clausify,[status(thm)],[f_290_3]) ).
fof(f_291_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_291_2,plain,
! [U_909,U_908,U_907,U_906] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_907),U_908)),U_909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_907),U_909)),U_908)
| ~ class_Rings_Ocomm__semiring__1(U_906) ),
inference(variable_rename,[status(thm)],[f_291_1]) ).
fof(f_291_3,plain,
! [U_906,U_907,U_908,U_909] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_907),U_908)),U_909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_907),U_909)),U_908)
| ~ class_Rings_Ocomm__semiring__1(U_906) ),
inference(definitional_conversion,[status(esa)],[f_291_2]) ).
cnf(f_291_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_907),U_908)),U_909) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_906),U_907),U_909)),U_908)
| ~ class_Rings_Ocomm__semiring__1(U_906) ),
inference(clausify,[status(thm)],[f_291_3]) ).
fof(f_292_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_292_2,plain,
! [U_914,U_913,U_912,U_911,U_910] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_911),U_912)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_913),U_914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_913),U_914)))
| ~ class_Rings_Ocomm__semiring__1(U_910) ),
inference(variable_rename,[status(thm)],[f_292_1]) ).
fof(f_292_3,plain,
! [U_910,U_911,U_912,U_913,U_914] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_911),U_912)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_913),U_914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_913),U_914)))
| ~ class_Rings_Ocomm__semiring__1(U_910) ),
inference(definitional_conversion,[status(esa)],[f_292_2]) ).
cnf(f_292_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_911),U_912)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_913),U_914)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_911),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_910),U_913),U_914)))
| ~ class_Rings_Ocomm__semiring__1(U_910) ),
inference(clausify,[status(thm)],[f_292_3]) ).
fof(f_293_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_293_2,plain,
! [U_919,U_918,U_917,U_916,U_915] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_916),U_917)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_918),U_919)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_916),U_917)),U_919))
| ~ class_Rings_Ocomm__semiring__1(U_915) ),
inference(variable_rename,[status(thm)],[f_293_1]) ).
fof(f_293_3,plain,
! [U_915,U_916,U_917,U_918,U_919] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_916),U_917)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_918),U_919)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_916),U_917)),U_919))
| ~ class_Rings_Ocomm__semiring__1(U_915) ),
inference(definitional_conversion,[status(esa)],[f_293_2]) ).
cnf(f_293_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_916),U_917)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_918),U_919)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_918),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_915),U_916),U_917)),U_919))
| ~ class_Rings_Ocomm__semiring__1(U_915) ),
inference(clausify,[status(thm)],[f_293_3]) ).
fof(f_294_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_294_2,plain,
! [U_924,U_923,U_922,U_921,U_920] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_921),U_922)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_923),U_924)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_921),U_923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_922),U_924))
| ~ class_Rings_Ocomm__semiring__1(U_920) ),
inference(variable_rename,[status(thm)],[f_294_1]) ).
fof(f_294_3,plain,
! [U_920,U_921,U_922,U_923,U_924] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_921),U_922)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_923),U_924)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_921),U_923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_922),U_924))
| ~ class_Rings_Ocomm__semiring__1(U_920) ),
inference(definitional_conversion,[status(esa)],[f_294_2]) ).
cnf(f_294_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_921),U_922)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_923),U_924)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_921),U_923)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_920),U_922),U_924))
| ~ class_Rings_Ocomm__semiring__1(U_920) ),
inference(clausify,[status(thm)],[f_294_3]) ).
fof(f_295_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_295_2,plain,
! [U_926,U_925] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_925),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_925,U_926)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_926))),
inference(variable_rename,[status(thm)],[f_295_1]) ).
fof(f_295_3,plain,
! [U_926,U_925] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_925),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_925,U_926)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_926))),
inference(definitional_conversion,[status(esa)],[f_295_2]) ).
cnf(f_295_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_925),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_925,U_926)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_926))),
inference(clausify,[status(thm)],[f_295_3]) ).
fof(f_296_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_296_2,plain,
! [U_929,U_928,U_927] :
( c_Groups_Oplus__class_Oplus(U_927,U_928,U_929) = c_Groups_Oplus__class_Oplus(U_927,U_929,U_928)
| ~ class_Rings_Ocomm__semiring__1(U_927) ),
inference(variable_rename,[status(thm)],[f_296_1]) ).
fof(f_296_3,plain,
! [U_928,U_927,U_929] :
( c_Groups_Oplus__class_Oplus(U_927,U_928,U_929) = c_Groups_Oplus__class_Oplus(U_927,U_929,U_928)
| ~ class_Rings_Ocomm__semiring__1(U_927) ),
inference(definitional_conversion,[status(esa)],[f_296_2]) ).
cnf(f_296_4,plain,
( c_Groups_Oplus__class_Oplus(U_927,U_928,U_929) = c_Groups_Oplus__class_Oplus(U_927,U_929,U_928)
| ~ class_Rings_Ocomm__semiring__1(U_927) ),
inference(clausify,[status(thm)],[f_296_3]) ).
fof(f_297_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_297_2,plain,
! [U_933,U_932,U_931,U_930] :
( c_Groups_Oplus__class_Oplus(U_930,U_931,c_Groups_Oplus__class_Oplus(U_930,U_932,U_933)) = c_Groups_Oplus__class_Oplus(U_930,U_932,c_Groups_Oplus__class_Oplus(U_930,U_931,U_933))
| ~ class_Rings_Ocomm__semiring__1(U_930) ),
inference(variable_rename,[status(thm)],[f_297_1]) ).
fof(f_297_3,plain,
! [U_930,U_931,U_932,U_933] :
( c_Groups_Oplus__class_Oplus(U_930,U_931,c_Groups_Oplus__class_Oplus(U_930,U_932,U_933)) = c_Groups_Oplus__class_Oplus(U_930,U_932,c_Groups_Oplus__class_Oplus(U_930,U_931,U_933))
| ~ class_Rings_Ocomm__semiring__1(U_930) ),
inference(definitional_conversion,[status(esa)],[f_297_2]) ).
cnf(f_297_4,plain,
( c_Groups_Oplus__class_Oplus(U_930,U_931,c_Groups_Oplus__class_Oplus(U_930,U_932,U_933)) = c_Groups_Oplus__class_Oplus(U_930,U_932,c_Groups_Oplus__class_Oplus(U_930,U_931,U_933))
| ~ class_Rings_Ocomm__semiring__1(U_930) ),
inference(clausify,[status(thm)],[f_297_3]) ).
fof(f_298_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_298_2,plain,
! [U_937,U_936,U_935,U_934] :
( c_Groups_Oplus__class_Oplus(U_934,U_935,c_Groups_Oplus__class_Oplus(U_934,U_936,U_937)) = c_Groups_Oplus__class_Oplus(U_934,c_Groups_Oplus__class_Oplus(U_934,U_935,U_936),U_937)
| ~ class_Rings_Ocomm__semiring__1(U_934) ),
inference(variable_rename,[status(thm)],[f_298_1]) ).
fof(f_298_3,plain,
! [U_935,U_934,U_936,U_937] :
( c_Groups_Oplus__class_Oplus(U_934,U_935,c_Groups_Oplus__class_Oplus(U_934,U_936,U_937)) = c_Groups_Oplus__class_Oplus(U_934,c_Groups_Oplus__class_Oplus(U_934,U_935,U_936),U_937)
| ~ class_Rings_Ocomm__semiring__1(U_934) ),
inference(definitional_conversion,[status(esa)],[f_298_2]) ).
cnf(f_298_4,plain,
( c_Groups_Oplus__class_Oplus(U_934,U_935,c_Groups_Oplus__class_Oplus(U_934,U_936,U_937)) = c_Groups_Oplus__class_Oplus(U_934,c_Groups_Oplus__class_Oplus(U_934,U_935,U_936),U_937)
| ~ class_Rings_Ocomm__semiring__1(U_934) ),
inference(clausify,[status(thm)],[f_298_3]) ).
fof(f_299_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_299_2,plain,
! [U_941,U_940,U_939,U_938] :
( c_Groups_Oplus__class_Oplus(U_938,c_Groups_Oplus__class_Oplus(U_938,U_939,U_940),U_941) = c_Groups_Oplus__class_Oplus(U_938,U_939,c_Groups_Oplus__class_Oplus(U_938,U_940,U_941))
| ~ class_Rings_Ocomm__semiring__1(U_938) ),
inference(variable_rename,[status(thm)],[f_299_1]) ).
fof(f_299_3,plain,
! [U_939,U_938,U_940,U_941] :
( c_Groups_Oplus__class_Oplus(U_938,c_Groups_Oplus__class_Oplus(U_938,U_939,U_940),U_941) = c_Groups_Oplus__class_Oplus(U_938,U_939,c_Groups_Oplus__class_Oplus(U_938,U_940,U_941))
| ~ class_Rings_Ocomm__semiring__1(U_938) ),
inference(definitional_conversion,[status(esa)],[f_299_2]) ).
cnf(f_299_4,plain,
( c_Groups_Oplus__class_Oplus(U_938,c_Groups_Oplus__class_Oplus(U_938,U_939,U_940),U_941) = c_Groups_Oplus__class_Oplus(U_938,U_939,c_Groups_Oplus__class_Oplus(U_938,U_940,U_941))
| ~ class_Rings_Ocomm__semiring__1(U_938) ),
inference(clausify,[status(thm)],[f_299_3]) ).
fof(f_300_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_300_2,plain,
! [U_945,U_944,U_943,U_942] :
( c_Groups_Oplus__class_Oplus(U_942,c_Groups_Oplus__class_Oplus(U_942,U_943,U_944),U_945) = c_Groups_Oplus__class_Oplus(U_942,c_Groups_Oplus__class_Oplus(U_942,U_943,U_945),U_944)
| ~ class_Rings_Ocomm__semiring__1(U_942) ),
inference(variable_rename,[status(thm)],[f_300_1]) ).
fof(f_300_3,plain,
! [U_943,U_942,U_944,U_945] :
( c_Groups_Oplus__class_Oplus(U_942,c_Groups_Oplus__class_Oplus(U_942,U_943,U_944),U_945) = c_Groups_Oplus__class_Oplus(U_942,c_Groups_Oplus__class_Oplus(U_942,U_943,U_945),U_944)
| ~ class_Rings_Ocomm__semiring__1(U_942) ),
inference(definitional_conversion,[status(esa)],[f_300_2]) ).
cnf(f_300_4,plain,
( c_Groups_Oplus__class_Oplus(U_942,c_Groups_Oplus__class_Oplus(U_942,U_943,U_944),U_945) = c_Groups_Oplus__class_Oplus(U_942,c_Groups_Oplus__class_Oplus(U_942,U_943,U_945),U_944)
| ~ class_Rings_Ocomm__semiring__1(U_942) ),
inference(clausify,[status(thm)],[f_300_3]) ).
fof(f_301_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_301_2,plain,
! [U_950,U_949,U_948,U_947,U_946] :
( c_Groups_Oplus__class_Oplus(U_946,c_Groups_Oplus__class_Oplus(U_946,U_947,U_948),c_Groups_Oplus__class_Oplus(U_946,U_949,U_950)) = c_Groups_Oplus__class_Oplus(U_946,c_Groups_Oplus__class_Oplus(U_946,U_947,U_949),c_Groups_Oplus__class_Oplus(U_946,U_948,U_950))
| ~ class_Rings_Ocomm__semiring__1(U_946) ),
inference(variable_rename,[status(thm)],[f_301_1]) ).
fof(f_301_3,plain,
! [U_947,U_946,U_948,U_949,U_950] :
( c_Groups_Oplus__class_Oplus(U_946,c_Groups_Oplus__class_Oplus(U_946,U_947,U_948),c_Groups_Oplus__class_Oplus(U_946,U_949,U_950)) = c_Groups_Oplus__class_Oplus(U_946,c_Groups_Oplus__class_Oplus(U_946,U_947,U_949),c_Groups_Oplus__class_Oplus(U_946,U_948,U_950))
| ~ class_Rings_Ocomm__semiring__1(U_946) ),
inference(definitional_conversion,[status(esa)],[f_301_2]) ).
cnf(f_301_4,plain,
( c_Groups_Oplus__class_Oplus(U_946,c_Groups_Oplus__class_Oplus(U_946,U_947,U_948),c_Groups_Oplus__class_Oplus(U_946,U_949,U_950)) = c_Groups_Oplus__class_Oplus(U_946,c_Groups_Oplus__class_Oplus(U_946,U_947,U_949),c_Groups_Oplus__class_Oplus(U_946,U_948,U_950))
| ~ class_Rings_Ocomm__semiring__1(U_946) ),
inference(clausify,[status(thm)],[f_301_3]) ).
fof(f_302_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_302_2,plain,
! [U_952,U_951] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_951),U_952),c_Groups_Ozero__class_Ozero(U_951)) = c_Groups_Ozero__class_Ozero(U_951)
| ~ class_Rings_Ocomm__semiring__1(U_951) ),
inference(variable_rename,[status(thm)],[f_302_1]) ).
fof(f_302_3,plain,
! [U_951,U_952] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_951),U_952),c_Groups_Ozero__class_Ozero(U_951)) = c_Groups_Ozero__class_Ozero(U_951)
| ~ class_Rings_Ocomm__semiring__1(U_951) ),
inference(definitional_conversion,[status(esa)],[f_302_2]) ).
cnf(f_302_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_951),U_952),c_Groups_Ozero__class_Ozero(U_951)) = c_Groups_Ozero__class_Ozero(U_951)
| ~ class_Rings_Ocomm__semiring__1(U_951) ),
inference(clausify,[status(thm)],[f_302_3]) ).
fof(f_303_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_303_2,plain,
! [U_954,U_953] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),c_Groups_Ozero__class_Ozero(U_953)),U_954) = c_Groups_Ozero__class_Ozero(U_953)
| ~ class_Rings_Ocomm__semiring__1(U_953) ),
inference(variable_rename,[status(thm)],[f_303_1]) ).
fof(f_303_3,plain,
! [U_953,U_954] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),c_Groups_Ozero__class_Ozero(U_953)),U_954) = c_Groups_Ozero__class_Ozero(U_953)
| ~ class_Rings_Ocomm__semiring__1(U_953) ),
inference(definitional_conversion,[status(esa)],[f_303_2]) ).
cnf(f_303_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),c_Groups_Ozero__class_Ozero(U_953)),U_954) = c_Groups_Ozero__class_Ozero(U_953)
| ~ class_Rings_Ocomm__semiring__1(U_953) ),
inference(clausify,[status(thm)],[f_303_3]) ).
fof(f_304_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_304_2,plain,
! [U_957,U_956,U_955] :
( ( ( U_956 = c_Groups_Oplus__class_Oplus(U_955,U_956,U_957)
| U_957 != c_Groups_Ozero__class_Ozero(U_955) )
& ( U_957 = c_Groups_Ozero__class_Ozero(U_955)
| U_956 != c_Groups_Oplus__class_Oplus(U_955,U_956,U_957) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_955) ),
inference(variable_rename,[status(thm)],[f_304_1]) ).
fof(f_304_3,plain,
( ! [U_955,U_956,U_957] :
( U_956 = c_Groups_Oplus__class_Oplus(U_955,U_956,U_957)
| U_957 != c_Groups_Ozero__class_Ozero(U_955)
| ~ sP93(U_955,U_956,U_957) )
& ! [U_955,U_956,U_957] :
( U_957 = c_Groups_Ozero__class_Ozero(U_955)
| U_956 != c_Groups_Oplus__class_Oplus(U_955,U_956,U_957)
| ~ sP93(U_955,U_956,U_957) )
& ! [U_955,U_956,U_957] :
( sP93(U_955,U_956,U_957)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_955) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP93])],[f_304_2]) ).
cnf(f_304_4,plain,
( sP93(U_955,U_956,U_957)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_955) ),
inference(clausify,[status(thm)],[f_304_3]) ).
cnf(f_304_5,plain,
( U_957 = c_Groups_Ozero__class_Ozero(U_955)
| U_956 != c_Groups_Oplus__class_Oplus(U_955,U_956,U_957)
| ~ sP93(U_955,U_956,U_957) ),
inference(clausify,[status(thm)],[f_304_3]) ).
cnf(f_304_6,plain,
( U_956 = c_Groups_Oplus__class_Oplus(U_955,U_956,U_957)
| U_957 != c_Groups_Ozero__class_Ozero(U_955)
| ~ sP93(U_955,U_956,U_957) ),
inference(clausify,[status(thm)],[f_304_3]) ).
fof(f_305_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_305_2,plain,
! [U_959,U_958] :
( c_Groups_Oplus__class_Oplus(U_958,U_959,c_Groups_Ozero__class_Ozero(U_958)) = U_959
| ~ class_Rings_Ocomm__semiring__1(U_958) ),
inference(variable_rename,[status(thm)],[f_305_1]) ).
fof(f_305_3,plain,
! [U_959,U_958] :
( c_Groups_Oplus__class_Oplus(U_958,U_959,c_Groups_Ozero__class_Ozero(U_958)) = U_959
| ~ class_Rings_Ocomm__semiring__1(U_958) ),
inference(definitional_conversion,[status(esa)],[f_305_2]) ).
cnf(f_305_4,plain,
( c_Groups_Oplus__class_Oplus(U_958,U_959,c_Groups_Ozero__class_Ozero(U_958)) = U_959
| ~ class_Rings_Ocomm__semiring__1(U_958) ),
inference(clausify,[status(thm)],[f_305_3]) ).
fof(f_306_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_306_2,plain,
! [U_961,U_960] :
( c_Groups_Oplus__class_Oplus(U_960,c_Groups_Ozero__class_Ozero(U_960),U_961) = U_961
| ~ class_Rings_Ocomm__semiring__1(U_960) ),
inference(variable_rename,[status(thm)],[f_306_1]) ).
fof(f_306_3,plain,
! [U_961,U_960] :
( c_Groups_Oplus__class_Oplus(U_960,c_Groups_Ozero__class_Ozero(U_960),U_961) = U_961
| ~ class_Rings_Ocomm__semiring__1(U_960) ),
inference(definitional_conversion,[status(esa)],[f_306_2]) ).
cnf(f_306_4,plain,
( c_Groups_Oplus__class_Oplus(U_960,c_Groups_Ozero__class_Ozero(U_960),U_961) = U_961
| ~ class_Rings_Ocomm__semiring__1(U_960) ),
inference(clausify,[status(thm)],[f_306_3]) ).
fof(f_307_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_307_2,plain,
! [U_965,U_964,U_963,U_962] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),c_Groups_Oplus__class_Oplus(U_962,U_964,U_965)) = c_Groups_Oplus__class_Oplus(U_962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),U_964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),U_965))
| ~ class_Rings_Ocomm__semiring__1(U_962) ),
inference(variable_rename,[status(thm)],[f_307_1]) ).
fof(f_307_3,plain,
! [U_962,U_963,U_964,U_965] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),c_Groups_Oplus__class_Oplus(U_962,U_964,U_965)) = c_Groups_Oplus__class_Oplus(U_962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),U_964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),U_965))
| ~ class_Rings_Ocomm__semiring__1(U_962) ),
inference(definitional_conversion,[status(esa)],[f_307_2]) ).
cnf(f_307_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),c_Groups_Oplus__class_Oplus(U_962,U_964,U_965)) = c_Groups_Oplus__class_Oplus(U_962,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),U_964),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_962),U_963),U_965))
| ~ class_Rings_Ocomm__semiring__1(U_962) ),
inference(clausify,[status(thm)],[f_307_3]) ).
fof(f_308_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( ( V_ca_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_ca_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_ca_2)) )
& ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_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_ca_2))
| V_ca_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_308_2,plain,
! [U_970,U_969,U_968,U_967,U_966] :
( ( ( ( U_969 != U_970
& U_967 != U_968 )
| c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_970)) = c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_969)) )
& ( c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_970)) != c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_969))
| U_969 = U_970
| U_967 = U_968 ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_966) ),
inference(variable_rename,[status(thm)],[f_308_1]) ).
fof(f_308_3,plain,
( ! [U_967,U_968,U_969,U_970] :
( U_969 != U_970
| ~ sP94(U_967,U_968,U_969,U_970) )
& ! [U_967,U_968,U_969,U_970] :
( U_967 != U_968
| ~ sP94(U_967,U_968,U_969,U_970) )
& ! [U_966,U_967,U_968,U_969,U_970] :
( sP94(U_967,U_968,U_969,U_970)
| c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_970)) = c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_969))
| ~ sP95(U_966,U_967,U_968,U_969,U_970) )
& ! [U_966,U_967,U_968,U_969,U_970] :
( c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_970)) != c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_969))
| U_969 = U_970
| U_967 = U_968
| ~ sP95(U_966,U_967,U_968,U_969,U_970) )
& ! [U_966,U_967,U_968,U_969,U_970] :
( sP95(U_966,U_967,U_968,U_969,U_970)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_966) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94,sP95])],[f_308_2]) ).
cnf(f_308_4,plain,
( sP95(U_966,U_967,U_968,U_969,U_970)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_966) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_5,plain,
( c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_970)) != c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_969))
| U_969 = U_970
| U_967 = U_968
| ~ sP95(U_966,U_967,U_968,U_969,U_970) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_6,plain,
( sP94(U_967,U_968,U_969,U_970)
| c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_969),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_970)) = c_Groups_Oplus__class_Oplus(U_966,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_967),U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_966),U_968),U_969))
| ~ sP95(U_966,U_967,U_968,U_969,U_970) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_7,plain,
( U_967 != U_968
| ~ sP94(U_967,U_968,U_969,U_970) ),
inference(clausify,[status(thm)],[f_308_3]) ).
cnf(f_308_8,plain,
( U_969 != U_970
| ~ sP94(U_967,U_968,U_969,U_970) ),
inference(clausify,[status(thm)],[f_308_3]) ).
fof(f_309_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_309_2,plain,
! [U_974,U_973,U_972,U_971] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_971),c_Groups_Oplus__class_Oplus(U_971,U_972,U_973)),U_974) = c_Groups_Oplus__class_Oplus(U_971,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_971),U_972),U_974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_971),U_973),U_974))
| ~ class_Rings_Ocomm__semiring__1(U_971) ),
inference(variable_rename,[status(thm)],[f_309_1]) ).
fof(f_309_3,plain,
! [U_974,U_973,U_972,U_971] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_971),c_Groups_Oplus__class_Oplus(U_971,U_972,U_973)),U_974) = c_Groups_Oplus__class_Oplus(U_971,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_971),U_972),U_974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_971),U_973),U_974))
| ~ class_Rings_Ocomm__semiring__1(U_971) ),
inference(definitional_conversion,[status(esa)],[f_309_2]) ).
cnf(f_309_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_971),c_Groups_Oplus__class_Oplus(U_971,U_972,U_973)),U_974) = c_Groups_Oplus__class_Oplus(U_971,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_971),U_972),U_974),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_971),U_973),U_974))
| ~ class_Rings_Ocomm__semiring__1(U_971) ),
inference(clausify,[status(thm)],[f_309_3]) ).
fof(f_310_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_310_2,plain,
! [U_978,U_977,U_976,U_975] :
( c_Groups_Oplus__class_Oplus(U_975,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_976),U_977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_978),U_977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),c_Groups_Oplus__class_Oplus(U_975,U_976,U_978)),U_977)
| ~ class_Rings_Ocomm__semiring__1(U_975) ),
inference(variable_rename,[status(thm)],[f_310_1]) ).
fof(f_310_3,plain,
! [U_975,U_976,U_977,U_978] :
( c_Groups_Oplus__class_Oplus(U_975,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_976),U_977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_978),U_977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),c_Groups_Oplus__class_Oplus(U_975,U_976,U_978)),U_977)
| ~ class_Rings_Ocomm__semiring__1(U_975) ),
inference(definitional_conversion,[status(esa)],[f_310_2]) ).
cnf(f_310_4,plain,
( c_Groups_Oplus__class_Oplus(U_975,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_976),U_977),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_978),U_977)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),c_Groups_Oplus__class_Oplus(U_975,U_976,U_978)),U_977)
| ~ class_Rings_Ocomm__semiring__1(U_975) ),
inference(clausify,[status(thm)],[f_310_3]) ).
fof(f_311_1,plain,
! [V_z_2,V_x_2,V_y_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_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) = c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2))
| ( V_y_2 != V_z_2
& V_w_2 != V_x_2 ) )
& ( V_y_2 = V_z_2
| V_w_2 = V_x_2
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_y_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_z_2)) != c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w_2),V_z_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_y_2)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) ),
inference(fof_nnf,[status(thm)],[fact_crossproduct__eq]) ).
fof(f_311_2,plain,
! [U_983,U_982,U_981,U_980,U_979] :
( ( ( c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_983)) = c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_981))
| ( U_981 != U_983
& U_980 != U_982 ) )
& ( U_981 = U_983
| U_980 = U_982
| c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_983)) != c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_981)) ) )
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_979) ),
inference(variable_rename,[status(thm)],[f_311_1]) ).
fof(f_311_3,plain,
( ! [U_980,U_981,U_982,U_983] :
( U_981 != U_983
| ~ sP96(U_980,U_981,U_982,U_983) )
& ! [U_980,U_981,U_982,U_983] :
( U_980 != U_982
| ~ sP96(U_980,U_981,U_982,U_983) )
& ! [U_979,U_980,U_981,U_982,U_983] :
( c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_983)) = c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_981))
| sP96(U_980,U_981,U_982,U_983)
| ~ sP97(U_979,U_980,U_981,U_982,U_983) )
& ! [U_979,U_980,U_981,U_982,U_983] :
( U_981 = U_983
| U_980 = U_982
| c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_983)) != c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_981))
| ~ sP97(U_979,U_980,U_981,U_982,U_983) )
& ! [U_979,U_980,U_981,U_982,U_983] :
( sP97(U_979,U_980,U_981,U_982,U_983)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_979) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96,sP97])],[f_311_2]) ).
cnf(f_311_4,plain,
( sP97(U_979,U_980,U_981,U_982,U_983)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_979) ),
inference(clausify,[status(thm)],[f_311_3]) ).
cnf(f_311_5,plain,
( U_981 = U_983
| U_980 = U_982
| c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_983)) != c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_981))
| ~ sP97(U_979,U_980,U_981,U_982,U_983) ),
inference(clausify,[status(thm)],[f_311_3]) ).
cnf(f_311_6,plain,
( c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_981),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_983)) = c_Groups_Oplus__class_Oplus(U_979,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_980),U_983),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_979),U_982),U_981))
| sP96(U_980,U_981,U_982,U_983)
| ~ sP97(U_979,U_980,U_981,U_982,U_983) ),
inference(clausify,[status(thm)],[f_311_3]) ).
cnf(f_311_7,plain,
( U_980 != U_982
| ~ sP96(U_980,U_981,U_982,U_983) ),
inference(clausify,[status(thm)],[f_311_3]) ).
cnf(f_311_8,plain,
( U_981 != U_983
| ~ sP96(U_980,U_981,U_982,U_983) ),
inference(clausify,[status(thm)],[f_311_3]) ).
fof(f_312_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_312_2,plain,
! [U_985,U_984] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_984),c_Groups_Oone__class_Oone(U_984)),U_985) = U_985
| ~ class_Rings_Ocomm__semiring__1(U_984) ),
inference(variable_rename,[status(thm)],[f_312_1]) ).
fof(f_312_3,plain,
! [U_985,U_984] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_984),c_Groups_Oone__class_Oone(U_984)),U_985) = U_985
| ~ class_Rings_Ocomm__semiring__1(U_984) ),
inference(definitional_conversion,[status(esa)],[f_312_2]) ).
cnf(f_312_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_984),c_Groups_Oone__class_Oone(U_984)),U_985) = U_985
| ~ class_Rings_Ocomm__semiring__1(U_984) ),
inference(clausify,[status(thm)],[f_312_3]) ).
fof(f_313_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_313_2,plain,
! [U_987,U_986] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_986),U_987),c_Groups_Oone__class_Oone(U_986)) = U_987
| ~ class_Rings_Ocomm__semiring__1(U_986) ),
inference(variable_rename,[status(thm)],[f_313_1]) ).
fof(f_313_3,plain,
! [U_986,U_987] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_986),U_987),c_Groups_Oone__class_Oone(U_986)) = U_987
| ~ class_Rings_Ocomm__semiring__1(U_986) ),
inference(definitional_conversion,[status(esa)],[f_313_2]) ).
cnf(f_313_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_986),U_987),c_Groups_Oone__class_Oone(U_986)) = U_987
| ~ class_Rings_Ocomm__semiring__1(U_986) ),
inference(clausify,[status(thm)],[f_313_3]) ).
fof(f_314_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_314_2,plain,
! [U_993,U_992,U_991,U_990,U_989,U_988] :
( c_Groups_Oplus__class_Oplus(U_988,U_990,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_988),U_989),U_992)) != c_Groups_Oplus__class_Oplus(U_988,U_991,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_988),U_989),U_993))
| U_992 = U_993
| U_990 != U_991
| U_989 = c_Groups_Ozero__class_Ozero(U_988)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_988) ),
inference(variable_rename,[status(thm)],[f_314_1]) ).
fof(f_314_3,plain,
! [U_989,U_988,U_990,U_991,U_992,U_993] :
( c_Groups_Oplus__class_Oplus(U_988,U_990,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_988),U_989),U_992)) != c_Groups_Oplus__class_Oplus(U_988,U_991,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_988),U_989),U_993))
| U_992 = U_993
| U_990 != U_991
| U_989 = c_Groups_Ozero__class_Ozero(U_988)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_988) ),
inference(definitional_conversion,[status(esa)],[f_314_2]) ).
cnf(f_314_4,plain,
( c_Groups_Oplus__class_Oplus(U_988,U_990,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_988),U_989),U_992)) != c_Groups_Oplus__class_Oplus(U_988,U_991,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_988),U_989),U_993))
| U_992 = U_993
| U_990 != U_991
| U_989 = c_Groups_Ozero__class_Ozero(U_988)
| ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_988) ),
inference(clausify,[status(thm)],[f_314_3]) ).
fof(f_315_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( ( V_y_2 = c_Groups_Ozero__class_Ozero(T_a)
& V_x_2 = c_Groups_Ozero__class_Ozero(T_a) )
| c_Groups_Oplus__class_Oplus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y_2),V_y_2)) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Olinordered__ring__strict(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sum__squares__eq__zero__iff]) ).
fof(f_315_2,plain,
! [U_996,U_995,U_994] :
( ( ( c_Groups_Oplus__class_Oplus(U_994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_995),U_995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_996),U_996)) = c_Groups_Ozero__class_Ozero(U_994)
| U_996 != c_Groups_Ozero__class_Ozero(U_994)
| U_995 != c_Groups_Ozero__class_Ozero(U_994) )
& ( ( U_996 = c_Groups_Ozero__class_Ozero(U_994)
& U_995 = c_Groups_Ozero__class_Ozero(U_994) )
| c_Groups_Oplus__class_Oplus(U_994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_995),U_995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_996),U_996)) != c_Groups_Ozero__class_Ozero(U_994) ) )
| ~ class_Rings_Olinordered__ring__strict(U_994) ),
inference(variable_rename,[status(thm)],[f_315_1]) ).
fof(f_315_3,plain,
( ! [U_994,U_995,U_996] :
( U_996 = c_Groups_Ozero__class_Ozero(U_994)
| ~ sP98(U_994,U_995,U_996) )
& ! [U_994,U_995,U_996] :
( U_995 = c_Groups_Ozero__class_Ozero(U_994)
| ~ sP98(U_994,U_995,U_996) )
& ! [U_994,U_995,U_996] :
( c_Groups_Oplus__class_Oplus(U_994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_995),U_995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_996),U_996)) = c_Groups_Ozero__class_Ozero(U_994)
| U_996 != c_Groups_Ozero__class_Ozero(U_994)
| U_995 != c_Groups_Ozero__class_Ozero(U_994)
| ~ sP99(U_994,U_995,U_996) )
& ! [U_994,U_995,U_996] :
( sP98(U_994,U_995,U_996)
| c_Groups_Oplus__class_Oplus(U_994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_995),U_995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_996),U_996)) != c_Groups_Ozero__class_Ozero(U_994)
| ~ sP99(U_994,U_995,U_996) )
& ! [U_994,U_995,U_996] :
( sP99(U_994,U_995,U_996)
| ~ class_Rings_Olinordered__ring__strict(U_994) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98,sP99])],[f_315_2]) ).
cnf(f_315_4,plain,
( sP99(U_994,U_995,U_996)
| ~ class_Rings_Olinordered__ring__strict(U_994) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_5,plain,
( sP98(U_994,U_995,U_996)
| c_Groups_Oplus__class_Oplus(U_994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_995),U_995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_996),U_996)) != c_Groups_Ozero__class_Ozero(U_994)
| ~ sP99(U_994,U_995,U_996) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_6,plain,
( c_Groups_Oplus__class_Oplus(U_994,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_995),U_995),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_994),U_996),U_996)) = c_Groups_Ozero__class_Ozero(U_994)
| U_996 != c_Groups_Ozero__class_Ozero(U_994)
| U_995 != c_Groups_Ozero__class_Ozero(U_994)
| ~ sP99(U_994,U_995,U_996) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_7,plain,
( U_995 = c_Groups_Ozero__class_Ozero(U_994)
| ~ sP98(U_994,U_995,U_996) ),
inference(clausify,[status(thm)],[f_315_3]) ).
cnf(f_315_8,plain,
( U_996 = c_Groups_Ozero__class_Ozero(U_994)
| ~ sP98(U_994,U_995,U_996) ),
inference(clausify,[status(thm)],[f_315_3]) ).
fof(f_316_1,plain,
! [V_q,V_p,V_a,T_a] :
( c_Polynomial_Opcompose(T_a,c_Polynomial_OpCons(T_a,V_a,V_p),V_q) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),V_q),c_Polynomial_Opcompose(T_a,V_p,V_q)))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pcompose__pCons]) ).
fof(f_316_2,plain,
! [U_1000,U_999,U_998,U_997] :
( c_Polynomial_Opcompose(U_997,c_Polynomial_OpCons(U_997,U_998,U_999),U_1000) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_997),c_Polynomial_OpCons(U_997,U_998,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_997))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_997)),U_1000),c_Polynomial_Opcompose(U_997,U_999,U_1000)))
| ~ class_Rings_Ocomm__semiring__0(U_997) ),
inference(variable_rename,[status(thm)],[f_316_1]) ).
fof(f_316_3,plain,
! [U_998,U_999,U_997,U_1000] :
( c_Polynomial_Opcompose(U_997,c_Polynomial_OpCons(U_997,U_998,U_999),U_1000) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_997),c_Polynomial_OpCons(U_997,U_998,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_997))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_997)),U_1000),c_Polynomial_Opcompose(U_997,U_999,U_1000)))
| ~ class_Rings_Ocomm__semiring__0(U_997) ),
inference(definitional_conversion,[status(esa)],[f_316_2]) ).
cnf(f_316_4,plain,
( c_Polynomial_Opcompose(U_997,c_Polynomial_OpCons(U_997,U_998,U_999),U_1000) = c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_997),c_Polynomial_OpCons(U_997,U_998,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_997))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_997)),U_1000),c_Polynomial_Opcompose(U_997,U_999,U_1000)))
| ~ class_Rings_Ocomm__semiring__0(U_997) ),
inference(clausify,[status(thm)],[f_316_3]) ).
fof(f_317_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_317_2,plain,
! [U_1002,U_1001] :
( ( ( c_Orderings_Oord__class_Oless(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1002),c_Groups_Ozero__class_Ozero(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,U_1002,c_Groups_Ozero__class_Ozero(U_1001)) )
& ( c_Orderings_Oord__class_Oless(U_1001,U_1002,c_Groups_Ozero__class_Ozero(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1002),c_Groups_Ozero__class_Ozero(U_1001)) ) )
| ~ class_Rings_Olinordered__idom(U_1001) ),
inference(variable_rename,[status(thm)],[f_317_1]) ).
fof(f_317_3,plain,
( ! [U_1002,U_1001] :
( c_Orderings_Oord__class_Oless(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1002),c_Groups_Ozero__class_Ozero(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,U_1002,c_Groups_Ozero__class_Ozero(U_1001))
| ~ sP100(U_1002,U_1001) )
& ! [U_1002,U_1001] :
( c_Orderings_Oord__class_Oless(U_1001,U_1002,c_Groups_Ozero__class_Ozero(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1002),c_Groups_Ozero__class_Ozero(U_1001))
| ~ sP100(U_1002,U_1001) )
& ! [U_1002,U_1001] :
( sP100(U_1002,U_1001)
| ~ class_Rings_Olinordered__idom(U_1001) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_317_2]) ).
cnf(f_317_4,plain,
( sP100(U_1002,U_1001)
| ~ class_Rings_Olinordered__idom(U_1001) ),
inference(clausify,[status(thm)],[f_317_3]) ).
cnf(f_317_5,plain,
( c_Orderings_Oord__class_Oless(U_1001,U_1002,c_Groups_Ozero__class_Ozero(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1002),c_Groups_Ozero__class_Ozero(U_1001))
| ~ sP100(U_1002,U_1001) ),
inference(clausify,[status(thm)],[f_317_3]) ).
cnf(f_317_6,plain,
( c_Orderings_Oord__class_Oless(U_1001,c_Groups_Oplus__class_Oplus(U_1001,U_1002,U_1002),c_Groups_Ozero__class_Ozero(U_1001))
| ~ c_Orderings_Oord__class_Oless(U_1001,U_1002,c_Groups_Ozero__class_Ozero(U_1001))
| ~ sP100(U_1002,U_1001) ),
inference(clausify,[status(thm)],[f_317_3]) ).
fof(f_318_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_318_2,plain,
! [U_1003] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1003,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_318_1]) ).
fof(f_318_3,plain,
! [U_1003] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1003,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_318_2]) ).
cnf(f_318_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1003,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_318_3]) ).
fof(f_319_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_319_2,plain,
! [U_1004] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1004),
inference(variable_rename,[status(thm)],[f_319_1]) ).
fof(f_319_3,plain,
! [U_1004] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1004),
inference(definitional_conversion,[status(esa)],[f_319_2]) ).
cnf(f_319_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1004),
inference(clausify,[status(thm)],[f_319_3]) ).
fof(f_320_1,plain,
! [V_p,V_c,T_a] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_c),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Osynthetic__div(T_a,V_p,V_c)),c_Polynomial_OpCons(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_c),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))) = V_p
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_synthetic__div__correct_H]) ).
fof(f_320_2,plain,
! [U_1007,U_1006,U_1005] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1005),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1005)),c_Polynomial_OpCons(U_1005,c_Groups_Ouminus__class_Ouminus(U_1005,U_1006),c_Polynomial_OpCons(U_1005,c_Groups_Oone__class_Oone(U_1005),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1005))))),c_Polynomial_Osynthetic__div(U_1005,U_1007,U_1006)),c_Polynomial_OpCons(U_1005,hAPP(c_Polynomial_Opoly(U_1005,U_1007),U_1006),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1005)))) = U_1007
| ~ class_Rings_Ocomm__ring__1(U_1005) ),
inference(variable_rename,[status(thm)],[f_320_1]) ).
fof(f_320_3,plain,
! [U_1006,U_1005,U_1007] :
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1005),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1005)),c_Polynomial_OpCons(U_1005,c_Groups_Ouminus__class_Ouminus(U_1005,U_1006),c_Polynomial_OpCons(U_1005,c_Groups_Oone__class_Oone(U_1005),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1005))))),c_Polynomial_Osynthetic__div(U_1005,U_1007,U_1006)),c_Polynomial_OpCons(U_1005,hAPP(c_Polynomial_Opoly(U_1005,U_1007),U_1006),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1005)))) = U_1007
| ~ class_Rings_Ocomm__ring__1(U_1005) ),
inference(definitional_conversion,[status(esa)],[f_320_2]) ).
cnf(f_320_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Polynomial_Opoly(U_1005),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Polynomial_Opoly(U_1005)),c_Polynomial_OpCons(U_1005,c_Groups_Ouminus__class_Ouminus(U_1005,U_1006),c_Polynomial_OpCons(U_1005,c_Groups_Oone__class_Oone(U_1005),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1005))))),c_Polynomial_Osynthetic__div(U_1005,U_1007,U_1006)),c_Polynomial_OpCons(U_1005,hAPP(c_Polynomial_Opoly(U_1005,U_1007),U_1006),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1005)))) = U_1007
| ~ class_Rings_Ocomm__ring__1(U_1005) ),
inference(clausify,[status(thm)],[f_320_3]) ).
fof(f_321_1,plain,
! [V_y,T_a] :
( ? [B_K] :
( ! [B_x] : 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),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Opos__bounded]) ).
fof(f_321_2,plain,
! [U_1011,U_1010] :
( ? [U_1009] :
( ! [U_1008] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1010,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1010),U_1008),U_1011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1010,U_1008)),U_1009))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1009) )
| ~ class_RealVector_Oreal__normed__algebra(U_1010) ),
inference(variable_rename,[status(thm)],[f_321_1]) ).
fof(f_321_3,plain,
! [U_1011,U_1010] :
( ( ! [U_1008] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1010,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1010),U_1008),U_1011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1010,U_1008)),sK7(U_1011,U_1010)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_1011,U_1010)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1010) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_1009,sK7(U_1011,U_1010))],[f_321_2]) ).
fof(f_321_4,plain,
( ! [U_1008,U_1010,U_1011] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1010,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1010),U_1008),U_1011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1010,U_1008)),sK7(U_1011,U_1010)))
| ~ sP101(U_1008,U_1010,U_1011) )
& ! [U_1008,U_1010,U_1011] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_1011,U_1010))
| ~ sP101(U_1008,U_1010,U_1011) )
& ! [U_1008,U_1010,U_1011] :
( sP101(U_1008,U_1010,U_1011)
| ~ class_RealVector_Oreal__normed__algebra(U_1010) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_321_3]) ).
cnf(f_321_5,plain,
( sP101(U_1008,U_1010,U_1011)
| ~ class_RealVector_Oreal__normed__algebra(U_1010) ),
inference(clausify,[status(thm)],[f_321_4]) ).
cnf(f_321_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK7(U_1011,U_1010))
| ~ sP101(U_1008,U_1010,U_1011) ),
inference(clausify,[status(thm)],[f_321_4]) ).
cnf(f_321_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1010,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1010),U_1008),U_1011)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1010,U_1008)),sK7(U_1011,U_1010)))
| ~ sP101(U_1008,U_1010,U_1011) ),
inference(clausify,[status(thm)],[f_321_4]) ).
fof(f_322_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_322_2,plain,
! [U_1012] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1012,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1012),U_1012)),
inference(variable_rename,[status(thm)],[f_322_1]) ).
fof(f_322_3,plain,
! [U_1012] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1012,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1012),U_1012)),
inference(definitional_conversion,[status(esa)],[f_322_2]) ).
cnf(f_322_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1012,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1012),U_1012)),
inference(clausify,[status(thm)],[f_322_3]) ).
fof(f_323_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_323_2,plain,
! [U_1014,U_1013] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1013,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1014,U_1013)),
inference(variable_rename,[status(thm)],[f_323_1]) ).
fof(f_323_3,plain,
! [U_1014,U_1013] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1013,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1014,U_1013)),
inference(definitional_conversion,[status(esa)],[f_323_2]) ).
cnf(f_323_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1013,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1014,U_1013)),
inference(clausify,[status(thm)],[f_323_3]) ).
fof(f_324_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_324_2,plain,
! [U_1016,U_1015] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1015,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1015,U_1016)),
inference(variable_rename,[status(thm)],[f_324_1]) ).
fof(f_324_3,plain,
! [U_1016,U_1015] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1015,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1015,U_1016)),
inference(definitional_conversion,[status(esa)],[f_324_2]) ).
cnf(f_324_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1015,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1015,U_1016)),
inference(clausify,[status(thm)],[f_324_3]) ).
fof(f_325_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_325_2,plain,
! [U_1017] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1017,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1017),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1017),U_1017))),
inference(variable_rename,[status(thm)],[f_325_1]) ).
fof(f_325_3,plain,
! [U_1017] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1017,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1017),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1017),U_1017))),
inference(definitional_conversion,[status(esa)],[f_325_2]) ).
cnf(f_325_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1017,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1017),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1017),U_1017))),
inference(clausify,[status(thm)],[f_325_3]) ).
fof(f_326_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_326_2,plain,
! [U_1021,U_1020] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1020,U_1021)
| ! [U_1019] : U_1021 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1020,U_1019) )
& ( ? [U_1018] : U_1021 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1020,U_1018)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1020,U_1021) ) ),
inference(variable_rename,[status(thm)],[f_326_1]) ).
fof(f_326_3,plain,
( ! [U_1025,U_1023] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1023,U_1025)
| ! [U_1019] : U_1025 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1023,U_1019) )
& ! [U_1024,U_1022] :
( ? [U_1018] : U_1024 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1022,U_1018)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1022,U_1024) ) ),
inference(miniscope,[status(thm)],[f_326_2]) ).
fof(f_326_4,plain,
( ! [U_1025,U_1023] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1023,U_1025)
| ! [U_1019] : U_1025 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1023,U_1019) )
& ! [U_1024,U_1022] :
( U_1024 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1022,sK8(U_1024,U_1022))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1022,U_1024) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_1018,sK8(U_1024,U_1022))],[f_326_3]) ).
fof(f_326_5,plain,
( ! [U_1023,U_1025,U_1019] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1023,U_1025)
| U_1025 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1023,U_1019) )
& ! [U_1022,U_1024] :
( U_1024 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1022,sK8(U_1024,U_1022))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1022,U_1024) ) ),
inference(definitional_conversion,[status(esa)],[f_326_4]) ).
cnf(f_326_6,plain,
( U_1024 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1022,sK8(U_1024,U_1022))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1022,U_1024) ),
inference(clausify,[status(thm)],[f_326_5]) ).
cnf(f_326_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1023,U_1025)
| U_1025 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1023,U_1019) ),
inference(clausify,[status(thm)],[f_326_5]) ).
fof(f_327_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ! [B_k] : V_n_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k) )
& ( ? [B_k] : V_n_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__iff__add]) ).
fof(f_327_2,plain,
! [U_1029,U_1028] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1028,U_1029)
| ! [U_1027] : U_1029 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1028,U_1027) )
& ( ? [U_1026] : U_1029 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1028,U_1026)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1028,U_1029) ) ),
inference(variable_rename,[status(thm)],[f_327_1]) ).
fof(f_327_3,plain,
( ! [U_1033,U_1031] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1031,U_1033)
| ! [U_1027] : U_1033 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1031,U_1027) )
& ! [U_1032,U_1030] :
( ? [U_1026] : U_1032 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1030,U_1026)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1030,U_1032) ) ),
inference(miniscope,[status(thm)],[f_327_2]) ).
fof(f_327_4,plain,
( ! [U_1033,U_1031] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1031,U_1033)
| ! [U_1027] : U_1033 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1031,U_1027) )
& ! [U_1032,U_1030] :
( U_1032 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1030,sK9(U_1032,U_1030))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1030,U_1032) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_1026,sK9(U_1032,U_1030))],[f_327_3]) ).
fof(f_327_5,plain,
( ! [U_1033,U_1027,U_1031] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1031,U_1033)
| U_1033 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1031,U_1027) )
& ! [U_1030,U_1032] :
( U_1032 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1030,sK9(U_1032,U_1030))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1030,U_1032) ) ),
inference(definitional_conversion,[status(esa)],[f_327_4]) ).
cnf(f_327_6,plain,
( U_1032 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1030,sK9(U_1032,U_1030))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1030,U_1032) ),
inference(clausify,[status(thm)],[f_327_5]) ).
cnf(f_327_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1031,U_1033)
| U_1033 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1031,U_1027) ),
inference(clausify,[status(thm)],[f_327_5]) ).
fof(f_328_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| V_ma_2 = V_n_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( ( V_ma_2 != V_n_2
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__le]) ).
fof(f_328_2,plain,
! [U_1035,U_1034] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1034,U_1035)
| U_1034 = U_1035
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1034,U_1035) )
& ( ( U_1034 != U_1035
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1034,U_1035) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1034,U_1035) ) ),
inference(variable_rename,[status(thm)],[f_328_1]) ).
fof(f_328_3,plain,
( ! [U_1039,U_1037] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1037,U_1039)
| U_1037 = U_1039
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1037,U_1039) )
& ! [U_1038,U_1036] :
( ( U_1036 != U_1038
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1036,U_1038) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1036,U_1038) ) ),
inference(miniscope,[status(thm)],[f_328_2]) ).
fof(f_328_4,plain,
( ! [U_1036,U_1038] :
( U_1036 != U_1038
| ~ sP102(U_1036,U_1038) )
& ! [U_1036,U_1038] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1036,U_1038)
| ~ sP102(U_1036,U_1038) )
& ! [U_1039,U_1037] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1037,U_1039)
| U_1037 = U_1039
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1037,U_1039) )
& ! [U_1036,U_1038] :
( sP102(U_1036,U_1038)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1036,U_1038) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_328_3]) ).
cnf(f_328_5,plain,
( sP102(U_1036,U_1038)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1036,U_1038) ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1037,U_1039)
| U_1037 = U_1039
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1037,U_1039) ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1036,U_1038)
| ~ sP102(U_1036,U_1038) ),
inference(clausify,[status(thm)],[f_328_4]) ).
cnf(f_328_8,plain,
( U_1036 != U_1038
| ~ sP102(U_1036,U_1038) ),
inference(clausify,[status(thm)],[f_328_4]) ).
fof(f_329_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ( V_ma_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) )
& ( V_ma_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_le__eq__less__or__eq]) ).
fof(f_329_2,plain,
! [U_1041,U_1040] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1040,U_1041)
| ( U_1040 != U_1041
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1040,U_1041) ) )
& ( U_1040 = U_1041
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1040,U_1041)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1040,U_1041) ) ),
inference(variable_rename,[status(thm)],[f_329_1]) ).
fof(f_329_3,plain,
( ! [U_1045,U_1043] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1043,U_1045)
| ( U_1043 != U_1045
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1043,U_1045) ) )
& ! [U_1044,U_1042] :
( U_1042 = U_1044
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1042,U_1044)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1042,U_1044) ) ),
inference(miniscope,[status(thm)],[f_329_2]) ).
fof(f_329_4,plain,
( ! [U_1043,U_1045] :
( U_1043 != U_1045
| ~ sP103(U_1043,U_1045) )
& ! [U_1043,U_1045] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1043,U_1045)
| ~ sP103(U_1043,U_1045) )
& ! [U_1043,U_1045] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1043,U_1045)
| sP103(U_1043,U_1045) )
& ! [U_1042,U_1044] :
( U_1042 = U_1044
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1042,U_1044)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1042,U_1044) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_329_3]) ).
cnf(f_329_5,plain,
( U_1042 = U_1044
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1042,U_1044)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1042,U_1044) ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1043,U_1045)
| sP103(U_1043,U_1045) ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1043,U_1045)
| ~ sP103(U_1043,U_1045) ),
inference(clausify,[status(thm)],[f_329_4]) ).
cnf(f_329_8,plain,
( U_1043 != U_1045
| ~ sP103(U_1043,U_1045) ),
inference(clausify,[status(thm)],[f_329_4]) ).
fof(f_330_1,plain,
! [V_n_2,V_ma_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_ma_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_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_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_ma_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_330_2,plain,
! [U_1048,U_1047,U_1046] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1046,U_1047),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1046,U_1048))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1047,U_1048) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1047,U_1048)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1046,U_1047),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1046,U_1048)) ) ),
inference(variable_rename,[status(thm)],[f_330_1]) ).
fof(f_330_3,plain,
( ! [U_1054,U_1052] :
( ! [U_1050] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1050,U_1052),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1050,U_1054))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1052,U_1054) )
& ! [U_1053,U_1051] :
( ! [U_1049] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1049,U_1051),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1049,U_1053))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1051,U_1053) ) ),
inference(miniscope,[status(thm)],[f_330_2]) ).
fof(f_330_4,plain,
( ! [U_1052,U_1050,U_1054] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1050,U_1052),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1050,U_1054))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1052,U_1054) )
& ! [U_1049,U_1051,U_1053] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1049,U_1051),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1049,U_1053))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1051,U_1053) ) ),
inference(definitional_conversion,[status(esa)],[f_330_3]) ).
cnf(f_330_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1049,U_1051),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1049,U_1053))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1051,U_1053) ),
inference(clausify,[status(thm)],[f_330_4]) ).
cnf(f_330_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1050,U_1052),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1050,U_1054))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1052,U_1054) ),
inference(clausify,[status(thm)],[f_330_4]) ).
fof(f_331_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_331_2,plain,
! [U_1056,U_1055] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1055,U_1056)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1055,U_1056) ),
inference(variable_rename,[status(thm)],[f_331_1]) ).
fof(f_331_3,plain,
! [U_1056,U_1055] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1055,U_1056)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1055,U_1056) ),
inference(definitional_conversion,[status(esa)],[f_331_2]) ).
cnf(f_331_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1055,U_1056)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1055,U_1056) ),
inference(clausify,[status(thm)],[f_331_3]) ).
fof(f_332_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_332_2,plain,
! [U_1059,U_1058,U_1057] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1057,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1058,U_1059))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1057,U_1058) ),
inference(variable_rename,[status(thm)],[f_332_1]) ).
fof(f_332_3,plain,
! [U_1058,U_1057,U_1059] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1057,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1058,U_1059))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1057,U_1058) ),
inference(definitional_conversion,[status(esa)],[f_332_2]) ).
cnf(f_332_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1057,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1058,U_1059))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1057,U_1058) ),
inference(clausify,[status(thm)],[f_332_3]) ).
fof(f_333_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_333_2,plain,
! [U_1062,U_1061,U_1060] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1060,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1062,U_1061))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1060,U_1061) ),
inference(variable_rename,[status(thm)],[f_333_1]) ).
fof(f_333_3,plain,
! [U_1061,U_1060,U_1062] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1060,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1062,U_1061))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1060,U_1061) ),
inference(definitional_conversion,[status(esa)],[f_333_2]) ).
cnf(f_333_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1060,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1062,U_1061))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1060,U_1061) ),
inference(clausify,[status(thm)],[f_333_3]) ).
fof(f_334_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_334_2,plain,
! [U_1065,U_1064,U_1063] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1063,U_1065),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1064,U_1065))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1063,U_1064) ),
inference(variable_rename,[status(thm)],[f_334_1]) ).
fof(f_334_3,plain,
! [U_1064,U_1063,U_1065] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1063,U_1065),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1064,U_1065))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1063,U_1064) ),
inference(definitional_conversion,[status(esa)],[f_334_2]) ).
cnf(f_334_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1063,U_1065),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1064,U_1065))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1063,U_1064) ),
inference(clausify,[status(thm)],[f_334_3]) ).
fof(f_335_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_335_2,plain,
! [U_1068,U_1067,U_1066] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1066),U_1068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1067),U_1068))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1066,U_1067) ),
inference(variable_rename,[status(thm)],[f_335_1]) ).
fof(f_335_3,plain,
! [U_1066,U_1067,U_1068] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1066),U_1068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1067),U_1068))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1066,U_1067) ),
inference(definitional_conversion,[status(esa)],[f_335_2]) ).
cnf(f_335_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1066),U_1068),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1067),U_1068))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1066,U_1067) ),
inference(clausify,[status(thm)],[f_335_3]) ).
fof(f_336_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_336_2,plain,
! [U_1071,U_1070,U_1069] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1070))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1069,U_1070) ),
inference(variable_rename,[status(thm)],[f_336_1]) ).
fof(f_336_3,plain,
! [U_1069,U_1070,U_1071] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1070))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1069,U_1070) ),
inference(definitional_conversion,[status(esa)],[f_336_2]) ).
cnf(f_336_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1069),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1071),U_1070))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1069,U_1070) ),
inference(clausify,[status(thm)],[f_336_3]) ).
fof(f_337_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_337_2,plain,
! [U_1073,U_1072] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1072,U_1073)
| U_1072 = U_1073
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1072,U_1073) ),
inference(variable_rename,[status(thm)],[f_337_1]) ).
fof(f_337_3,plain,
! [U_1072,U_1073] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1072,U_1073)
| U_1072 = U_1073
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1072,U_1073) ),
inference(definitional_conversion,[status(esa)],[f_337_2]) ).
cnf(f_337_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1072,U_1073)
| U_1072 = U_1073
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1072,U_1073) ),
inference(clausify,[status(thm)],[f_337_3]) ).
fof(f_338_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_338_2,plain,
! [U_1077,U_1076,U_1075,U_1074] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1074,U_1076),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1075,U_1077))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1076,U_1077)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1074,U_1075) ),
inference(variable_rename,[status(thm)],[f_338_1]) ).
fof(f_338_3,plain,
! [U_1076,U_1075,U_1074,U_1077] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1074,U_1076),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1075,U_1077))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1076,U_1077)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1074,U_1075) ),
inference(definitional_conversion,[status(esa)],[f_338_2]) ).
cnf(f_338_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1074,U_1076),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1075,U_1077))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1076,U_1077)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1074,U_1075) ),
inference(clausify,[status(thm)],[f_338_3]) ).
fof(f_339_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_339_2,plain,
! [U_1081,U_1080,U_1079,U_1078] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1078),U_1080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1079),U_1081))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1080,U_1081)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1078,U_1079) ),
inference(variable_rename,[status(thm)],[f_339_1]) ).
fof(f_339_3,plain,
! [U_1079,U_1078,U_1080,U_1081] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1078),U_1080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1079),U_1081))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1080,U_1081)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1078,U_1079) ),
inference(definitional_conversion,[status(esa)],[f_339_2]) ).
cnf(f_339_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1078),U_1080),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1079),U_1081))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1080,U_1081)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1078,U_1079) ),
inference(clausify,[status(thm)],[f_339_3]) ).
fof(f_340_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_340_2,plain,
! [U_1084,U_1083,U_1082] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1083,U_1084)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1082,U_1083),U_1084) ),
inference(variable_rename,[status(thm)],[f_340_1]) ).
fof(f_340_3,plain,
! [U_1084,U_1083] :
( ! [U_1082] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1082,U_1083),U_1084)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1083,U_1084) ),
inference(miniscope,[status(thm)],[f_340_2]) ).
fof(f_340_4,plain,
! [U_1084,U_1083,U_1082] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1082,U_1083),U_1084)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1083,U_1084) ),
inference(definitional_conversion,[status(esa)],[f_340_3]) ).
cnf(f_340_5,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1082,U_1083),U_1084)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1083,U_1084) ),
inference(clausify,[status(thm)],[f_340_4]) ).
fof(f_341_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_341_2,plain,
! [U_1087,U_1086,U_1085] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1085,U_1087)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1085,U_1086),U_1087) ),
inference(variable_rename,[status(thm)],[f_341_1]) ).
fof(f_341_3,plain,
! [U_1086,U_1085,U_1087] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1085,U_1087)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1085,U_1086),U_1087) ),
inference(definitional_conversion,[status(esa)],[f_341_2]) ).
cnf(f_341_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1085,U_1087)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1085,U_1086),U_1087) ),
inference(clausify,[status(thm)],[f_341_3]) ).
fof(f_342_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_342_2,plain,
! [U_1090,U_1089,U_1088] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1089,U_1090)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1088,U_1090) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1088,U_1089),U_1090) ),
inference(variable_rename,[status(thm)],[f_342_1]) ).
fof(f_342_3,plain,
( ! [U_1089,U_1088,U_1090] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1089,U_1090)
| ~ sP104(U_1089,U_1088,U_1090) )
& ! [U_1089,U_1088,U_1090] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1088,U_1090)
| ~ sP104(U_1089,U_1088,U_1090) )
& ! [U_1089,U_1088,U_1090] :
( sP104(U_1089,U_1088,U_1090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1088,U_1089),U_1090) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_342_2]) ).
cnf(f_342_4,plain,
( sP104(U_1089,U_1088,U_1090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1088,U_1089),U_1090) ),
inference(clausify,[status(thm)],[f_342_3]) ).
cnf(f_342_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1088,U_1090)
| ~ sP104(U_1089,U_1088,U_1090) ),
inference(clausify,[status(thm)],[f_342_3]) ).
cnf(f_342_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1089,U_1090)
| ~ sP104(U_1089,U_1088,U_1090) ),
inference(clausify,[status(thm)],[f_342_3]) ).
fof(f_343_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_343_2,plain,
! [U_1092,U_1091] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1091,U_1092)
| ( U_1091 != U_1092
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1091,U_1092) ) ),
inference(variable_rename,[status(thm)],[f_343_1]) ).
fof(f_343_3,plain,
( ! [U_1091,U_1092] :
( U_1091 != U_1092
| ~ sP105(U_1091,U_1092) )
& ! [U_1091,U_1092] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1091,U_1092)
| ~ sP105(U_1091,U_1092) )
& ! [U_1091,U_1092] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1091,U_1092)
| sP105(U_1091,U_1092) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_343_2]) ).
cnf(f_343_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1091,U_1092)
| sP105(U_1091,U_1092) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1091,U_1092)
| ~ sP105(U_1091,U_1092) ),
inference(clausify,[status(thm)],[f_343_3]) ).
cnf(f_343_6,plain,
( U_1091 != U_1092
| ~ sP105(U_1091,U_1092) ),
inference(clausify,[status(thm)],[f_343_3]) ).
fof(f_344_1,plain,
! [V_P_2,V_n_2,V_ma_2] :
( hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))
& V_ma_2 = V_n_2 )
| ( ~ hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_ma_2))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__cases]) ).
fof(f_344_2,plain,
! [U_1095,U_1094,U_1093] :
( hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
| ( ~ hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1094,U_1093) )
| ( ~ hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
& U_1093 = U_1094 )
| ( ~ hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1093,U_1094) ) ),
inference(variable_rename,[status(thm)],[f_344_1]) ).
fof(f_344_3,plain,
( ! [U_1094,U_1093,U_1095] :
( ~ hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
| ~ sP108(U_1094,U_1093,U_1095) )
& ! [U_1094,U_1093,U_1095] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1094,U_1093)
| ~ sP108(U_1094,U_1093,U_1095) )
& ! [U_1094,U_1093,U_1095] :
( ~ hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
| ~ sP107(U_1094,U_1093,U_1095) )
& ! [U_1094,U_1093,U_1095] :
( U_1093 = U_1094
| ~ sP107(U_1094,U_1093,U_1095) )
& ! [U_1094,U_1093,U_1095] :
( ~ hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
| ~ sP106(U_1094,U_1093,U_1095) )
& ! [U_1094,U_1093,U_1095] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1093,U_1094)
| ~ sP106(U_1094,U_1093,U_1095) )
& ! [U_1094,U_1093,U_1095] :
( hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
| sP108(U_1094,U_1093,U_1095)
| sP107(U_1094,U_1093,U_1095)
| sP106(U_1094,U_1093,U_1095) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106,sP107,sP108])],[f_344_2]) ).
cnf(f_344_4,plain,
( hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
| sP108(U_1094,U_1093,U_1095)
| sP107(U_1094,U_1093,U_1095)
| sP106(U_1094,U_1093,U_1095) ),
inference(clausify,[status(thm)],[f_344_3]) ).
cnf(f_344_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1093,U_1094)
| ~ sP106(U_1094,U_1093,U_1095) ),
inference(clausify,[status(thm)],[f_344_3]) ).
cnf(f_344_6,plain,
( ~ hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
| ~ sP106(U_1094,U_1093,U_1095) ),
inference(clausify,[status(thm)],[f_344_3]) ).
cnf(f_344_7,plain,
( U_1093 = U_1094
| ~ sP107(U_1094,U_1093,U_1095) ),
inference(clausify,[status(thm)],[f_344_3]) ).
cnf(f_344_8,plain,
( ~ hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
| ~ sP107(U_1094,U_1093,U_1095) ),
inference(clausify,[status(thm)],[f_344_3]) ).
cnf(f_344_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1094,U_1093)
| ~ sP108(U_1094,U_1093,U_1095) ),
inference(clausify,[status(thm)],[f_344_3]) ).
cnf(f_344_10,plain,
( ~ hBOOL(hAPP(hAPP(U_1095,U_1094),U_1093))
| ~ sP108(U_1094,U_1093,U_1095) ),
inference(clausify,[status(thm)],[f_344_3]) ).
fof(f_345_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_345_2,plain,
! [U_1098,U_1097,U_1096] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1096,U_1098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1096,U_1097),U_1098) ),
inference(variable_rename,[status(thm)],[f_345_1]) ).
fof(f_345_3,plain,
! [U_1097,U_1096,U_1098] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1096,U_1098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1096,U_1097),U_1098) ),
inference(definitional_conversion,[status(esa)],[f_345_2]) ).
cnf(f_345_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1096,U_1098)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1096,U_1097),U_1098) ),
inference(clausify,[status(thm)],[f_345_3]) ).
fof(f_346_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_346_2,plain,
! [U_1102,U_1101,U_1100,U_1099] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1101,U_1102)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1101,U_1100) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1099,U_1102)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1099,U_1100) ),
inference(variable_rename,[status(thm)],[f_346_1]) ).
fof(f_346_3,plain,
! [U_1100,U_1102,U_1099,U_1101] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1101,U_1102)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1101,U_1100) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1099,U_1102)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1099,U_1100) ),
inference(definitional_conversion,[status(esa)],[f_346_2]) ).
cnf(f_346_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1101,U_1102)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1101,U_1100) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1099,U_1102)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1099,U_1100) ),
inference(clausify,[status(thm)],[f_346_3]) ).
fof(f_347_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_347_2,plain,
! [U_1106,U_1105,U_1104,U_1103] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1103,U_1105),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1104,U_1106))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1105,U_1106)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1103,U_1104) ),
inference(variable_rename,[status(thm)],[f_347_1]) ).
fof(f_347_3,plain,
! [U_1104,U_1103,U_1105,U_1106] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1103,U_1105),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1104,U_1106))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1105,U_1106)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1103,U_1104) ),
inference(definitional_conversion,[status(esa)],[f_347_2]) ).
cnf(f_347_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1103,U_1105),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1104,U_1106))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1105,U_1106)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1103,U_1104) ),
inference(clausify,[status(thm)],[f_347_3]) ).
fof(f_348_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_348_2,plain,
! [U_1109,U_1108,U_1107] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1107,U_1109),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1108,U_1109))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1107,U_1108) ),
inference(variable_rename,[status(thm)],[f_348_1]) ).
fof(f_348_3,plain,
! [U_1107,U_1108,U_1109] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1107,U_1109),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1108,U_1109))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1107,U_1108) ),
inference(definitional_conversion,[status(esa)],[f_348_2]) ).
cnf(f_348_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1107,U_1109),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1108,U_1109))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1107,U_1108) ),
inference(clausify,[status(thm)],[f_348_3]) ).
fof(f_349_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_349_2,plain,
! [U_1112,U_1111,U_1110] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1110,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1112,U_1111))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1110,U_1111) ),
inference(variable_rename,[status(thm)],[f_349_1]) ).
fof(f_349_3,plain,
! [U_1111,U_1110,U_1112] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1110,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1112,U_1111))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1110,U_1111) ),
inference(definitional_conversion,[status(esa)],[f_349_2]) ).
cnf(f_349_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1110,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1112,U_1111))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1110,U_1111) ),
inference(clausify,[status(thm)],[f_349_3]) ).
fof(f_350_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_350_2,plain,
! [U_1115,U_1114,U_1113] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1113,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1114,U_1115))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1113,U_1114) ),
inference(variable_rename,[status(thm)],[f_350_1]) ).
fof(f_350_3,plain,
! [U_1114,U_1113,U_1115] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1113,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1114,U_1115))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1113,U_1114) ),
inference(definitional_conversion,[status(esa)],[f_350_2]) ).
cnf(f_350_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1113,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1114,U_1115))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1113,U_1114) ),
inference(clausify,[status(thm)],[f_350_3]) ).
fof(f_351_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_351_2,plain,
! [U_1117,U_1116] :
( U_1116 != U_1117
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1116,U_1117) ),
inference(variable_rename,[status(thm)],[f_351_1]) ).
fof(f_351_3,plain,
! [U_1117,U_1116] :
( U_1116 != U_1117
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1116,U_1117) ),
inference(definitional_conversion,[status(esa)],[f_351_2]) ).
cnf(f_351_4,plain,
( U_1116 != U_1117
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1116,U_1117) ),
inference(clausify,[status(thm)],[f_351_3]) ).
fof(f_352_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_352_2,plain,
! [U_1119,U_1118] :
( U_1119 != U_1118
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1118,U_1119) ),
inference(variable_rename,[status(thm)],[f_352_1]) ).
fof(f_352_3,plain,
! [U_1119,U_1118] :
( U_1119 != U_1118
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1118,U_1119) ),
inference(definitional_conversion,[status(esa)],[f_352_2]) ).
cnf(f_352_4,plain,
( U_1119 != U_1118
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1118,U_1119) ),
inference(clausify,[status(thm)],[f_352_3]) ).
fof(f_353_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_353_2,plain,
! [U_1120] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1120,U_1120),
inference(variable_rename,[status(thm)],[f_353_1]) ).
fof(f_353_3,plain,
! [U_1120] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1120,U_1120),
inference(definitional_conversion,[status(esa)],[f_353_2]) ).
cnf(f_353_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1120,U_1120),
inference(clausify,[status(thm)],[f_353_3]) ).
fof(f_354_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_354_2,plain,
! [U_1122,U_1121] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1122,U_1121)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1121,U_1122)
| U_1121 = U_1122 ),
inference(variable_rename,[status(thm)],[f_354_1]) ).
fof(f_354_3,plain,
! [U_1121,U_1122] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1122,U_1121)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1121,U_1122)
| U_1121 = U_1122 ),
inference(definitional_conversion,[status(esa)],[f_354_2]) ).
cnf(f_354_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1122,U_1121)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1121,U_1122)
| U_1121 = U_1122 ),
inference(clausify,[status(thm)],[f_354_3]) ).
fof(f_355_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_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_355_2,plain,
! [U_1125,U_1124,U_1123] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1123,U_1124),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1123,U_1125))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1124,U_1125) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1124,U_1125)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1123,U_1124),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1123,U_1125)) ) ),
inference(variable_rename,[status(thm)],[f_355_1]) ).
fof(f_355_3,plain,
( ! [U_1131,U_1129] :
( ! [U_1127] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1127,U_1129),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1127,U_1131))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1129,U_1131) )
& ! [U_1130,U_1128] :
( ! [U_1126] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1126,U_1128),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1126,U_1130))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1128,U_1130) ) ),
inference(miniscope,[status(thm)],[f_355_2]) ).
fof(f_355_4,plain,
( ! [U_1129,U_1127,U_1131] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1127,U_1129),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1127,U_1131))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1129,U_1131) )
& ! [U_1126,U_1128,U_1130] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1126,U_1128),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1126,U_1130))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1128,U_1130) ) ),
inference(definitional_conversion,[status(esa)],[f_355_3]) ).
cnf(f_355_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1126,U_1128),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1126,U_1130))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1128,U_1130) ),
inference(clausify,[status(thm)],[f_355_4]) ).
cnf(f_355_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1127,U_1129),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1127,U_1131))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1129,U_1131) ),
inference(clausify,[status(thm)],[f_355_4]) ).
fof(f_356_1,plain,
! [V_n_2,V_ma_2] :
( ( V_ma_2 != V_n_2
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| V_ma_2 = V_n_2 ) ),
inference(fof_nnf,[status(thm)],[fact_nat__neq__iff]) ).
fof(f_356_2,plain,
! [U_1133,U_1132] :
( ( U_1132 != U_1133
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1133,U_1132)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1132,U_1133) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1133,U_1132)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1132,U_1133)
| U_1132 = U_1133 ) ),
inference(variable_rename,[status(thm)],[f_356_1]) ).
fof(f_356_3,plain,
( ! [U_1137,U_1135] :
( U_1135 != U_1137
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1137,U_1135)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1135,U_1137) ) )
& ! [U_1136,U_1134] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1136,U_1134)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1134,U_1136)
| U_1134 = U_1136 ) ),
inference(miniscope,[status(thm)],[f_356_2]) ).
fof(f_356_4,plain,
( ! [U_1135,U_1137] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1137,U_1135)
| ~ sP109(U_1135,U_1137) )
& ! [U_1135,U_1137] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1135,U_1137)
| ~ sP109(U_1135,U_1137) )
& ! [U_1135,U_1137] :
( U_1135 != U_1137
| sP109(U_1135,U_1137) )
& ! [U_1136,U_1134] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1136,U_1134)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1134,U_1136)
| U_1134 = U_1136 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109])],[f_356_3]) ).
cnf(f_356_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1136,U_1134)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1134,U_1136)
| U_1134 = U_1136 ),
inference(clausify,[status(thm)],[f_356_4]) ).
cnf(f_356_6,plain,
( U_1135 != U_1137
| sP109(U_1135,U_1137) ),
inference(clausify,[status(thm)],[f_356_4]) ).
cnf(f_356_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1135,U_1137)
| ~ sP109(U_1135,U_1137) ),
inference(clausify,[status(thm)],[f_356_4]) ).
cnf(f_356_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1137,U_1135)
| ~ sP109(U_1135,U_1137) ),
inference(clausify,[status(thm)],[f_356_4]) ).
fof(f_357_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_357_2,plain,
! [U_1139,U_1138] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1138,U_1139),U_1139),
inference(variable_rename,[status(thm)],[f_357_1]) ).
fof(f_357_3,plain,
! [U_1138,U_1139] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1138,U_1139),U_1139),
inference(definitional_conversion,[status(esa)],[f_357_2]) ).
cnf(f_357_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1138,U_1139),U_1139),
inference(clausify,[status(thm)],[f_357_3]) ).
fof(f_358_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_358_2,plain,
! [U_1141,U_1140] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1140,U_1141),U_1140),
inference(variable_rename,[status(thm)],[f_358_1]) ).
fof(f_358_3,plain,
! [U_1140,U_1141] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1140,U_1141),U_1140),
inference(definitional_conversion,[status(esa)],[f_358_2]) ).
cnf(f_358_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1140,U_1141),U_1140),
inference(clausify,[status(thm)],[f_358_3]) ).
fof(f_359_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_359_2,plain,
! [U_1142] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1142,U_1142),
inference(variable_rename,[status(thm)],[f_359_1]) ).
fof(f_359_3,plain,
! [U_1142] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1142,U_1142),
inference(definitional_conversion,[status(esa)],[f_359_2]) ).
cnf(f_359_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1142,U_1142),
inference(clausify,[status(thm)],[f_359_3]) ).
fof(f_360_1,plain,
! [V_x,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p)),V_x) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x))
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__minus]) ).
fof(f_360_2,plain,
! [U_1145,U_1144,U_1143] :
( hAPP(c_Polynomial_Opoly(U_1143,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1143),U_1144)),U_1145) = c_Groups_Ouminus__class_Ouminus(U_1143,hAPP(c_Polynomial_Opoly(U_1143,U_1144),U_1145))
| ~ class_Rings_Ocomm__ring(U_1143) ),
inference(variable_rename,[status(thm)],[f_360_1]) ).
fof(f_360_3,plain,
! [U_1143,U_1144,U_1145] :
( hAPP(c_Polynomial_Opoly(U_1143,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1143),U_1144)),U_1145) = c_Groups_Ouminus__class_Ouminus(U_1143,hAPP(c_Polynomial_Opoly(U_1143,U_1144),U_1145))
| ~ class_Rings_Ocomm__ring(U_1143) ),
inference(definitional_conversion,[status(esa)],[f_360_2]) ).
cnf(f_360_4,plain,
( hAPP(c_Polynomial_Opoly(U_1143,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1143),U_1144)),U_1145) = c_Groups_Ouminus__class_Ouminus(U_1143,hAPP(c_Polynomial_Opoly(U_1143,U_1144),U_1145))
| ~ class_Rings_Ocomm__ring(U_1143) ),
inference(clausify,[status(thm)],[f_360_3]) ).
fof(f_361_1,plain,
! [V_p,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p)) = c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__pCons]) ).
fof(f_361_2,plain,
! [U_1148,U_1147,U_1146] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1146),c_Polynomial_OpCons(U_1146,U_1147,U_1148)) = c_Polynomial_OpCons(U_1146,c_Groups_Ouminus__class_Ouminus(U_1146,U_1147),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1146),U_1148))
| ~ class_Groups_Oab__group__add(U_1146) ),
inference(variable_rename,[status(thm)],[f_361_1]) ).
fof(f_361_3,plain,
! [U_1146,U_1147,U_1148] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1146),c_Polynomial_OpCons(U_1146,U_1147,U_1148)) = c_Polynomial_OpCons(U_1146,c_Groups_Ouminus__class_Ouminus(U_1146,U_1147),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1146),U_1148))
| ~ class_Groups_Oab__group__add(U_1146) ),
inference(definitional_conversion,[status(esa)],[f_361_2]) ).
cnf(f_361_4,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1146),c_Polynomial_OpCons(U_1146,U_1147,U_1148)) = c_Polynomial_OpCons(U_1146,c_Groups_Ouminus__class_Ouminus(U_1146,U_1147),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1146),U_1148))
| ~ class_Groups_Oab__group__add(U_1146) ),
inference(clausify,[status(thm)],[f_361_3]) ).
fof(f_362_1,plain,
! [V_p,V_a,T_b] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),c_Polynomial_OpCons(T_b,V_a,V_p)) = c_Polynomial_OpCons(T_b,c_Groups_Ouminus__class_Ouminus(T_b,V_a),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_b),V_p))
| ~ class_Groups_Oab__group__add(T_b) ),
inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I2_J]) ).
fof(f_362_2,plain,
! [U_1151,U_1150,U_1149] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1149),c_Polynomial_OpCons(U_1149,U_1150,U_1151)) = c_Polynomial_OpCons(U_1149,c_Groups_Ouminus__class_Ouminus(U_1149,U_1150),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1149),U_1151))
| ~ class_Groups_Oab__group__add(U_1149) ),
inference(variable_rename,[status(thm)],[f_362_1]) ).
fof(f_362_3,plain,
! [U_1149,U_1150,U_1151] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1149),c_Polynomial_OpCons(U_1149,U_1150,U_1151)) = c_Polynomial_OpCons(U_1149,c_Groups_Ouminus__class_Ouminus(U_1149,U_1150),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1149),U_1151))
| ~ class_Groups_Oab__group__add(U_1149) ),
inference(definitional_conversion,[status(esa)],[f_362_2]) ).
cnf(f_362_4,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1149),c_Polynomial_OpCons(U_1149,U_1150,U_1151)) = c_Polynomial_OpCons(U_1149,c_Groups_Ouminus__class_Ouminus(U_1149,U_1150),c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1149),U_1151))
| ~ class_Groups_Oab__group__add(U_1149) ),
inference(clausify,[status(thm)],[f_362_3]) ).
fof(f_363_1,plain,
! [V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = V_a
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__minus]) ).
fof(f_363_2,plain,
! [U_1153,U_1152] :
( c_Groups_Ouminus__class_Ouminus(U_1152,c_Groups_Ouminus__class_Ouminus(U_1152,U_1153)) = U_1153
| ~ class_Groups_Ogroup__add(U_1152) ),
inference(variable_rename,[status(thm)],[f_363_1]) ).
fof(f_363_3,plain,
! [U_1152,U_1153] :
( c_Groups_Ouminus__class_Ouminus(U_1152,c_Groups_Ouminus__class_Ouminus(U_1152,U_1153)) = U_1153
| ~ class_Groups_Ogroup__add(U_1152) ),
inference(definitional_conversion,[status(esa)],[f_363_2]) ).
cnf(f_363_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1152,c_Groups_Ouminus__class_Ouminus(U_1152,U_1153)) = U_1153
| ~ class_Groups_Ogroup__add(U_1152) ),
inference(clausify,[status(thm)],[f_363_3]) ).
fof(f_364_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_b_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) )
& ( V_b_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
| V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_equation__minus__iff]) ).
fof(f_364_2,plain,
! [U_1156,U_1155,U_1154] :
( ( ( U_1155 = c_Groups_Ouminus__class_Ouminus(U_1154,U_1156)
| U_1156 != c_Groups_Ouminus__class_Ouminus(U_1154,U_1155) )
& ( U_1156 = c_Groups_Ouminus__class_Ouminus(U_1154,U_1155)
| U_1155 != c_Groups_Ouminus__class_Ouminus(U_1154,U_1156) ) )
| ~ class_Groups_Ogroup__add(U_1154) ),
inference(variable_rename,[status(thm)],[f_364_1]) ).
fof(f_364_3,plain,
( ! [U_1154,U_1155,U_1156] :
( U_1155 = c_Groups_Ouminus__class_Ouminus(U_1154,U_1156)
| U_1156 != c_Groups_Ouminus__class_Ouminus(U_1154,U_1155)
| ~ sP110(U_1154,U_1155,U_1156) )
& ! [U_1154,U_1155,U_1156] :
( U_1156 = c_Groups_Ouminus__class_Ouminus(U_1154,U_1155)
| U_1155 != c_Groups_Ouminus__class_Ouminus(U_1154,U_1156)
| ~ sP110(U_1154,U_1155,U_1156) )
& ! [U_1154,U_1155,U_1156] :
( sP110(U_1154,U_1155,U_1156)
| ~ class_Groups_Ogroup__add(U_1154) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP110])],[f_364_2]) ).
cnf(f_364_4,plain,
( sP110(U_1154,U_1155,U_1156)
| ~ class_Groups_Ogroup__add(U_1154) ),
inference(clausify,[status(thm)],[f_364_3]) ).
cnf(f_364_5,plain,
( U_1156 = c_Groups_Ouminus__class_Ouminus(U_1154,U_1155)
| U_1155 != c_Groups_Ouminus__class_Ouminus(U_1154,U_1156)
| ~ sP110(U_1154,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_364_3]) ).
cnf(f_364_6,plain,
( U_1155 = c_Groups_Ouminus__class_Ouminus(U_1154,U_1156)
| U_1156 != c_Groups_Ouminus__class_Ouminus(U_1154,U_1155)
| ~ sP110(U_1154,U_1155,U_1156) ),
inference(clausify,[status(thm)],[f_364_3]) ).
fof(f_365_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_b_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) != V_a_2 )
& ( c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) = V_a_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != V_b_2 ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__equation__iff]) ).
fof(f_365_2,plain,
! [U_1159,U_1158,U_1157] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1157,U_1158) = U_1159
| c_Groups_Ouminus__class_Ouminus(U_1157,U_1159) != U_1158 )
& ( c_Groups_Ouminus__class_Ouminus(U_1157,U_1159) = U_1158
| c_Groups_Ouminus__class_Ouminus(U_1157,U_1158) != U_1159 ) )
| ~ class_Groups_Ogroup__add(U_1157) ),
inference(variable_rename,[status(thm)],[f_365_1]) ).
fof(f_365_3,plain,
( ! [U_1158,U_1159,U_1157] :
( c_Groups_Ouminus__class_Ouminus(U_1157,U_1158) = U_1159
| c_Groups_Ouminus__class_Ouminus(U_1157,U_1159) != U_1158
| ~ sP111(U_1158,U_1159,U_1157) )
& ! [U_1158,U_1159,U_1157] :
( c_Groups_Ouminus__class_Ouminus(U_1157,U_1159) = U_1158
| c_Groups_Ouminus__class_Ouminus(U_1157,U_1158) != U_1159
| ~ sP111(U_1158,U_1159,U_1157) )
& ! [U_1158,U_1159,U_1157] :
( sP111(U_1158,U_1159,U_1157)
| ~ class_Groups_Ogroup__add(U_1157) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP111])],[f_365_2]) ).
cnf(f_365_4,plain,
( sP111(U_1158,U_1159,U_1157)
| ~ class_Groups_Ogroup__add(U_1157) ),
inference(clausify,[status(thm)],[f_365_3]) ).
cnf(f_365_5,plain,
( c_Groups_Ouminus__class_Ouminus(U_1157,U_1159) = U_1158
| c_Groups_Ouminus__class_Ouminus(U_1157,U_1158) != U_1159
| ~ sP111(U_1158,U_1159,U_1157) ),
inference(clausify,[status(thm)],[f_365_3]) ).
cnf(f_365_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_1157,U_1158) = U_1159
| c_Groups_Ouminus__class_Ouminus(U_1157,U_1159) != U_1158
| ~ sP111(U_1158,U_1159,U_1157) ),
inference(clausify,[status(thm)],[f_365_3]) ).
fof(f_366_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_a_2 != V_b_2 )
& ( V_a_2 = V_b_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__iff__equal]) ).
fof(f_366_2,plain,
! [U_1162,U_1161,U_1160] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1160,U_1161) = c_Groups_Ouminus__class_Ouminus(U_1160,U_1162)
| U_1161 != U_1162 )
& ( U_1161 = U_1162
| c_Groups_Ouminus__class_Ouminus(U_1160,U_1161) != c_Groups_Ouminus__class_Ouminus(U_1160,U_1162) ) )
| ~ class_Groups_Ogroup__add(U_1160) ),
inference(variable_rename,[status(thm)],[f_366_1]) ).
fof(f_366_3,plain,
( ! [U_1162,U_1160,U_1161] :
( c_Groups_Ouminus__class_Ouminus(U_1160,U_1161) = c_Groups_Ouminus__class_Ouminus(U_1160,U_1162)
| U_1161 != U_1162
| ~ sP112(U_1162,U_1160,U_1161) )
& ! [U_1162,U_1160,U_1161] :
( U_1161 = U_1162
| c_Groups_Ouminus__class_Ouminus(U_1160,U_1161) != c_Groups_Ouminus__class_Ouminus(U_1160,U_1162)
| ~ sP112(U_1162,U_1160,U_1161) )
& ! [U_1162,U_1160,U_1161] :
( sP112(U_1162,U_1160,U_1161)
| ~ class_Groups_Ogroup__add(U_1160) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_366_2]) ).
cnf(f_366_4,plain,
( sP112(U_1162,U_1160,U_1161)
| ~ class_Groups_Ogroup__add(U_1160) ),
inference(clausify,[status(thm)],[f_366_3]) ).
cnf(f_366_5,plain,
( U_1161 = U_1162
| c_Groups_Ouminus__class_Ouminus(U_1160,U_1161) != c_Groups_Ouminus__class_Ouminus(U_1160,U_1162)
| ~ sP112(U_1162,U_1160,U_1161) ),
inference(clausify,[status(thm)],[f_366_3]) ).
cnf(f_366_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_1160,U_1161) = c_Groups_Ouminus__class_Ouminus(U_1160,U_1162)
| U_1161 != U_1162
| ~ sP112(U_1162,U_1160,U_1161) ),
inference(clausify,[status(thm)],[f_366_3]) ).
fof(f_367_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_367_2,plain,
! [U_1164,U_1163] :
( U_1163 = U_1164
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1164,U_1163)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1163,U_1164) ),
inference(variable_rename,[status(thm)],[f_367_1]) ).
fof(f_367_3,plain,
! [U_1164,U_1163] :
( U_1163 = U_1164
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1164,U_1163)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1163,U_1164) ),
inference(definitional_conversion,[status(esa)],[f_367_2]) ).
cnf(f_367_4,plain,
( U_1163 = U_1164
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1164,U_1163)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1163,U_1164) ),
inference(clausify,[status(thm)],[f_367_3]) ).
fof(f_368_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_368_2,plain,
! [U_1167,U_1166,U_1165] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1165,U_1167)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1166,U_1167)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1165,U_1166) ),
inference(variable_rename,[status(thm)],[f_368_1]) ).
fof(f_368_3,plain,
! [U_1165,U_1166,U_1167] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1165,U_1167)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1166,U_1167)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1165,U_1166) ),
inference(definitional_conversion,[status(esa)],[f_368_2]) ).
cnf(f_368_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1165,U_1167)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1166,U_1167)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1165,U_1166) ),
inference(clausify,[status(thm)],[f_368_3]) ).
fof(f_369_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_369_2,plain,
! [U_1169,U_1168] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1168,U_1169)
| U_1168 != U_1169 ),
inference(variable_rename,[status(thm)],[f_369_1]) ).
fof(f_369_3,plain,
! [U_1169,U_1168] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1168,U_1169)
| U_1168 != U_1169 ),
inference(definitional_conversion,[status(esa)],[f_369_2]) ).
cnf(f_369_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1168,U_1169)
| U_1168 != U_1169 ),
inference(clausify,[status(thm)],[f_369_3]) ).
fof(f_370_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_370_2,plain,
! [U_1171,U_1170] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1171,U_1170)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1170,U_1171) ),
inference(variable_rename,[status(thm)],[f_370_1]) ).
fof(f_370_3,plain,
! [U_1171,U_1170] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1171,U_1170)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1170,U_1171) ),
inference(definitional_conversion,[status(esa)],[f_370_2]) ).
cnf(f_370_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1171,U_1170)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1170,U_1171) ),
inference(clausify,[status(thm)],[f_370_3]) ).
fof(f_371_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_371_2,plain,
! [U_1172] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1172,U_1172),
inference(variable_rename,[status(thm)],[f_371_1]) ).
fof(f_371_3,plain,
! [U_1172] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1172,U_1172),
inference(definitional_conversion,[status(esa)],[f_371_2]) ).
cnf(f_371_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1172,U_1172),
inference(clausify,[status(thm)],[f_371_3]) ).
fof(f_372_1,plain,
! [T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__zero]) ).
fof(f_372_2,plain,
! [U_1173] :
( c_Groups_Ouminus__class_Ouminus(U_1173,c_Groups_Ozero__class_Ozero(U_1173)) = c_Groups_Ozero__class_Ozero(U_1173)
| ~ class_Groups_Ogroup__add(U_1173) ),
inference(variable_rename,[status(thm)],[f_372_1]) ).
fof(f_372_3,plain,
! [U_1173] :
( c_Groups_Ouminus__class_Ouminus(U_1173,c_Groups_Ozero__class_Ozero(U_1173)) = c_Groups_Ozero__class_Ozero(U_1173)
| ~ class_Groups_Ogroup__add(U_1173) ),
inference(definitional_conversion,[status(esa)],[f_372_2]) ).
cnf(f_372_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1173,c_Groups_Ozero__class_Ozero(U_1173)) = c_Groups_Ozero__class_Ozero(U_1173)
| ~ class_Groups_Ogroup__add(U_1173) ),
inference(clausify,[status(thm)],[f_372_3]) ).
fof(f_373_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ozero__class_Ozero(T_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
| c_Groups_Ozero__class_Ozero(T_a) != V_a_2 )
& ( c_Groups_Ozero__class_Ozero(T_a) = V_a_2
| c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__equal__iff__equal]) ).
fof(f_373_2,plain,
! [U_1175,U_1174] :
( ( ( c_Groups_Ozero__class_Ozero(U_1174) = c_Groups_Ouminus__class_Ouminus(U_1174,U_1175)
| c_Groups_Ozero__class_Ozero(U_1174) != U_1175 )
& ( c_Groups_Ozero__class_Ozero(U_1174) = U_1175
| c_Groups_Ozero__class_Ozero(U_1174) != c_Groups_Ouminus__class_Ouminus(U_1174,U_1175) ) )
| ~ class_Groups_Ogroup__add(U_1174) ),
inference(variable_rename,[status(thm)],[f_373_1]) ).
fof(f_373_3,plain,
( ! [U_1174,U_1175] :
( c_Groups_Ozero__class_Ozero(U_1174) = c_Groups_Ouminus__class_Ouminus(U_1174,U_1175)
| c_Groups_Ozero__class_Ozero(U_1174) != U_1175
| ~ sP113(U_1174,U_1175) )
& ! [U_1174,U_1175] :
( c_Groups_Ozero__class_Ozero(U_1174) = U_1175
| c_Groups_Ozero__class_Ozero(U_1174) != c_Groups_Ouminus__class_Ouminus(U_1174,U_1175)
| ~ sP113(U_1174,U_1175) )
& ! [U_1174,U_1175] :
( sP113(U_1174,U_1175)
| ~ class_Groups_Ogroup__add(U_1174) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113])],[f_373_2]) ).
cnf(f_373_4,plain,
( sP113(U_1174,U_1175)
| ~ class_Groups_Ogroup__add(U_1174) ),
inference(clausify,[status(thm)],[f_373_3]) ).
cnf(f_373_5,plain,
( c_Groups_Ozero__class_Ozero(U_1174) = U_1175
| c_Groups_Ozero__class_Ozero(U_1174) != c_Groups_Ouminus__class_Ouminus(U_1174,U_1175)
| ~ sP113(U_1174,U_1175) ),
inference(clausify,[status(thm)],[f_373_3]) ).
cnf(f_373_6,plain,
( c_Groups_Ozero__class_Ozero(U_1174) = c_Groups_Ouminus__class_Ouminus(U_1174,U_1175)
| c_Groups_Ozero__class_Ozero(U_1174) != U_1175
| ~ sP113(U_1174,U_1175) ),
inference(clausify,[status(thm)],[f_373_3]) ).
fof(f_374_1,plain,
! [V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_equal__neg__zero]) ).
fof(f_374_2,plain,
! [U_1177,U_1176] :
( ( ( U_1177 = c_Groups_Ouminus__class_Ouminus(U_1176,U_1177)
| U_1177 != c_Groups_Ozero__class_Ozero(U_1176) )
& ( U_1177 = c_Groups_Ozero__class_Ozero(U_1176)
| U_1177 != c_Groups_Ouminus__class_Ouminus(U_1176,U_1177) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1176) ),
inference(variable_rename,[status(thm)],[f_374_1]) ).
fof(f_374_3,plain,
( ! [U_1176,U_1177] :
( U_1177 = c_Groups_Ouminus__class_Ouminus(U_1176,U_1177)
| U_1177 != c_Groups_Ozero__class_Ozero(U_1176)
| ~ sP114(U_1176,U_1177) )
& ! [U_1176,U_1177] :
( U_1177 = c_Groups_Ozero__class_Ozero(U_1176)
| U_1177 != c_Groups_Ouminus__class_Ouminus(U_1176,U_1177)
| ~ sP114(U_1176,U_1177) )
& ! [U_1176,U_1177] :
( sP114(U_1176,U_1177)
| ~ class_Groups_Olinordered__ab__group__add(U_1176) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_374_2]) ).
cnf(f_374_4,plain,
( sP114(U_1176,U_1177)
| ~ class_Groups_Olinordered__ab__group__add(U_1176) ),
inference(clausify,[status(thm)],[f_374_3]) ).
cnf(f_374_5,plain,
( U_1177 = c_Groups_Ozero__class_Ozero(U_1176)
| U_1177 != c_Groups_Ouminus__class_Ouminus(U_1176,U_1177)
| ~ sP114(U_1176,U_1177) ),
inference(clausify,[status(thm)],[f_374_3]) ).
cnf(f_374_6,plain,
( U_1177 = c_Groups_Ouminus__class_Ouminus(U_1176,U_1177)
| U_1177 != c_Groups_Ozero__class_Ozero(U_1176)
| ~ sP114(U_1176,U_1177) ),
inference(clausify,[status(thm)],[f_374_3]) ).
fof(f_375_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__0__iff__equal]) ).
fof(f_375_2,plain,
! [U_1179,U_1178] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1178,U_1179) = c_Groups_Ozero__class_Ozero(U_1178)
| U_1179 != c_Groups_Ozero__class_Ozero(U_1178) )
& ( U_1179 = c_Groups_Ozero__class_Ozero(U_1178)
| c_Groups_Ouminus__class_Ouminus(U_1178,U_1179) != c_Groups_Ozero__class_Ozero(U_1178) ) )
| ~ class_Groups_Ogroup__add(U_1178) ),
inference(variable_rename,[status(thm)],[f_375_1]) ).
fof(f_375_3,plain,
( ! [U_1179,U_1178] :
( c_Groups_Ouminus__class_Ouminus(U_1178,U_1179) = c_Groups_Ozero__class_Ozero(U_1178)
| U_1179 != c_Groups_Ozero__class_Ozero(U_1178)
| ~ sP115(U_1179,U_1178) )
& ! [U_1179,U_1178] :
( U_1179 = c_Groups_Ozero__class_Ozero(U_1178)
| c_Groups_Ouminus__class_Ouminus(U_1178,U_1179) != c_Groups_Ozero__class_Ozero(U_1178)
| ~ sP115(U_1179,U_1178) )
& ! [U_1179,U_1178] :
( sP115(U_1179,U_1178)
| ~ class_Groups_Ogroup__add(U_1178) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_375_2]) ).
cnf(f_375_4,plain,
( sP115(U_1179,U_1178)
| ~ class_Groups_Ogroup__add(U_1178) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_5,plain,
( U_1179 = c_Groups_Ozero__class_Ozero(U_1178)
| c_Groups_Ouminus__class_Ouminus(U_1178,U_1179) != c_Groups_Ozero__class_Ozero(U_1178)
| ~ sP115(U_1179,U_1178) ),
inference(clausify,[status(thm)],[f_375_3]) ).
cnf(f_375_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_1178,U_1179) = c_Groups_Ozero__class_Ozero(U_1178)
| U_1179 != c_Groups_Ozero__class_Ozero(U_1178)
| ~ sP115(U_1179,U_1178) ),
inference(clausify,[status(thm)],[f_375_3]) ).
fof(f_376_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) = V_a_2
| V_a_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Ouminus__class_Ouminus(T_a,V_a_2) != V_a_2 ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__equal__zero]) ).
fof(f_376_2,plain,
! [U_1181,U_1180] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1180,U_1181) = U_1181
| U_1181 != c_Groups_Ozero__class_Ozero(U_1180) )
& ( U_1181 = c_Groups_Ozero__class_Ozero(U_1180)
| c_Groups_Ouminus__class_Ouminus(U_1180,U_1181) != U_1181 ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1180) ),
inference(variable_rename,[status(thm)],[f_376_1]) ).
fof(f_376_3,plain,
( ! [U_1181,U_1180] :
( c_Groups_Ouminus__class_Ouminus(U_1180,U_1181) = U_1181
| U_1181 != c_Groups_Ozero__class_Ozero(U_1180)
| ~ sP116(U_1181,U_1180) )
& ! [U_1181,U_1180] :
( U_1181 = c_Groups_Ozero__class_Ozero(U_1180)
| c_Groups_Ouminus__class_Ouminus(U_1180,U_1181) != U_1181
| ~ sP116(U_1181,U_1180) )
& ! [U_1181,U_1180] :
( sP116(U_1181,U_1180)
| ~ class_Groups_Olinordered__ab__group__add(U_1180) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_376_2]) ).
cnf(f_376_4,plain,
( sP116(U_1181,U_1180)
| ~ class_Groups_Olinordered__ab__group__add(U_1180) ),
inference(clausify,[status(thm)],[f_376_3]) ).
cnf(f_376_5,plain,
( U_1181 = c_Groups_Ozero__class_Ozero(U_1180)
| c_Groups_Ouminus__class_Ouminus(U_1180,U_1181) != U_1181
| ~ sP116(U_1181,U_1180) ),
inference(clausify,[status(thm)],[f_376_3]) ).
cnf(f_376_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_1180,U_1181) = U_1181
| U_1181 != c_Groups_Ozero__class_Ozero(U_1180)
| ~ sP116(U_1181,U_1180) ),
inference(clausify,[status(thm)],[f_376_3]) ).
fof(f_377_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__iff]) ).
fof(f_377_2,plain,
! [U_1184,U_1183,U_1182] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1182,U_1183,c_Groups_Ouminus__class_Ouminus(U_1182,U_1184))
| ~ c_Orderings_Oord__class_Oless__eq(U_1182,U_1184,c_Groups_Ouminus__class_Ouminus(U_1182,U_1183)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1182,U_1184,c_Groups_Ouminus__class_Ouminus(U_1182,U_1183))
| ~ c_Orderings_Oord__class_Oless__eq(U_1182,U_1183,c_Groups_Ouminus__class_Ouminus(U_1182,U_1184)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1182) ),
inference(variable_rename,[status(thm)],[f_377_1]) ).
fof(f_377_3,plain,
( ! [U_1183,U_1184,U_1182] :
( c_Orderings_Oord__class_Oless__eq(U_1182,U_1183,c_Groups_Ouminus__class_Ouminus(U_1182,U_1184))
| ~ c_Orderings_Oord__class_Oless__eq(U_1182,U_1184,c_Groups_Ouminus__class_Ouminus(U_1182,U_1183))
| ~ sP117(U_1183,U_1184,U_1182) )
& ! [U_1183,U_1184,U_1182] :
( c_Orderings_Oord__class_Oless__eq(U_1182,U_1184,c_Groups_Ouminus__class_Ouminus(U_1182,U_1183))
| ~ c_Orderings_Oord__class_Oless__eq(U_1182,U_1183,c_Groups_Ouminus__class_Ouminus(U_1182,U_1184))
| ~ sP117(U_1183,U_1184,U_1182) )
& ! [U_1183,U_1184,U_1182] :
( sP117(U_1183,U_1184,U_1182)
| ~ class_Groups_Oordered__ab__group__add(U_1182) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117])],[f_377_2]) ).
cnf(f_377_4,plain,
( sP117(U_1183,U_1184,U_1182)
| ~ class_Groups_Oordered__ab__group__add(U_1182) ),
inference(clausify,[status(thm)],[f_377_3]) ).
cnf(f_377_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1182,U_1184,c_Groups_Ouminus__class_Ouminus(U_1182,U_1183))
| ~ c_Orderings_Oord__class_Oless__eq(U_1182,U_1183,c_Groups_Ouminus__class_Ouminus(U_1182,U_1184))
| ~ sP117(U_1183,U_1184,U_1182) ),
inference(clausify,[status(thm)],[f_377_3]) ).
cnf(f_377_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1182,U_1183,c_Groups_Ouminus__class_Ouminus(U_1182,U_1184))
| ~ c_Orderings_Oord__class_Oless__eq(U_1182,U_1184,c_Groups_Ouminus__class_Ouminus(U_1182,U_1183))
| ~ sP117(U_1183,U_1184,U_1182) ),
inference(clausify,[status(thm)],[f_377_3]) ).
fof(f_378_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__iff]) ).
fof(f_378_2,plain,
! [U_1187,U_1186,U_1185] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1186),U_1187)
| ~ c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1187),U_1186) )
& ( c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1187),U_1186)
| ~ c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1186),U_1187) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1185) ),
inference(variable_rename,[status(thm)],[f_378_1]) ).
fof(f_378_3,plain,
( ! [U_1186,U_1185,U_1187] :
( c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1186),U_1187)
| ~ c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1187),U_1186)
| ~ sP118(U_1186,U_1185,U_1187) )
& ! [U_1186,U_1185,U_1187] :
( c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1187),U_1186)
| ~ c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1186),U_1187)
| ~ sP118(U_1186,U_1185,U_1187) )
& ! [U_1186,U_1185,U_1187] :
( sP118(U_1186,U_1185,U_1187)
| ~ class_Groups_Oordered__ab__group__add(U_1185) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP118])],[f_378_2]) ).
cnf(f_378_4,plain,
( sP118(U_1186,U_1185,U_1187)
| ~ class_Groups_Oordered__ab__group__add(U_1185) ),
inference(clausify,[status(thm)],[f_378_3]) ).
cnf(f_378_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1187),U_1186)
| ~ c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1186),U_1187)
| ~ sP118(U_1186,U_1185,U_1187) ),
inference(clausify,[status(thm)],[f_378_3]) ).
cnf(f_378_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1186),U_1187)
| ~ c_Orderings_Oord__class_Oless__eq(U_1185,c_Groups_Ouminus__class_Ouminus(U_1185,U_1187),U_1186)
| ~ sP118(U_1186,U_1185,U_1187) ),
inference(clausify,[status(thm)],[f_378_3]) ).
fof(f_379_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__iff__le]) ).
fof(f_379_2,plain,
! [U_1190,U_1189,U_1188] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1188,c_Groups_Ouminus__class_Ouminus(U_1188,U_1189),c_Groups_Ouminus__class_Ouminus(U_1188,U_1190))
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,U_1190,U_1189) )
& ( c_Orderings_Oord__class_Oless__eq(U_1188,U_1190,U_1189)
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,c_Groups_Ouminus__class_Ouminus(U_1188,U_1189),c_Groups_Ouminus__class_Ouminus(U_1188,U_1190)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1188) ),
inference(variable_rename,[status(thm)],[f_379_1]) ).
fof(f_379_3,plain,
( ! [U_1189,U_1190,U_1188] :
( c_Orderings_Oord__class_Oless__eq(U_1188,c_Groups_Ouminus__class_Ouminus(U_1188,U_1189),c_Groups_Ouminus__class_Ouminus(U_1188,U_1190))
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,U_1190,U_1189)
| ~ sP119(U_1189,U_1190,U_1188) )
& ! [U_1189,U_1190,U_1188] :
( c_Orderings_Oord__class_Oless__eq(U_1188,U_1190,U_1189)
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,c_Groups_Ouminus__class_Ouminus(U_1188,U_1189),c_Groups_Ouminus__class_Ouminus(U_1188,U_1190))
| ~ sP119(U_1189,U_1190,U_1188) )
& ! [U_1189,U_1190,U_1188] :
( sP119(U_1189,U_1190,U_1188)
| ~ class_Groups_Oordered__ab__group__add(U_1188) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP119])],[f_379_2]) ).
cnf(f_379_4,plain,
( sP119(U_1189,U_1190,U_1188)
| ~ class_Groups_Oordered__ab__group__add(U_1188) ),
inference(clausify,[status(thm)],[f_379_3]) ).
cnf(f_379_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1188,U_1190,U_1189)
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,c_Groups_Ouminus__class_Ouminus(U_1188,U_1189),c_Groups_Ouminus__class_Ouminus(U_1188,U_1190))
| ~ sP119(U_1189,U_1190,U_1188) ),
inference(clausify,[status(thm)],[f_379_3]) ).
cnf(f_379_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1188,c_Groups_Ouminus__class_Ouminus(U_1188,U_1189),c_Groups_Ouminus__class_Ouminus(U_1188,U_1190))
| ~ c_Orderings_Oord__class_Oless__eq(U_1188,U_1190,U_1189)
| ~ sP119(U_1189,U_1190,U_1188) ),
inference(clausify,[status(thm)],[f_379_3]) ).
fof(f_380_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__neg__le]) ).
fof(f_380_2,plain,
! [U_1193,U_1192,U_1191] :
( c_Orderings_Oord__class_Oless__eq(U_1191,c_Groups_Ouminus__class_Ouminus(U_1191,U_1193),c_Groups_Ouminus__class_Ouminus(U_1191,U_1192))
| ~ c_Orderings_Oord__class_Oless__eq(U_1191,U_1192,U_1193)
| ~ class_Groups_Oordered__ab__group__add(U_1191) ),
inference(variable_rename,[status(thm)],[f_380_1]) ).
fof(f_380_3,plain,
! [U_1192,U_1193,U_1191] :
( c_Orderings_Oord__class_Oless__eq(U_1191,c_Groups_Ouminus__class_Ouminus(U_1191,U_1193),c_Groups_Ouminus__class_Ouminus(U_1191,U_1192))
| ~ c_Orderings_Oord__class_Oless__eq(U_1191,U_1192,U_1193)
| ~ class_Groups_Oordered__ab__group__add(U_1191) ),
inference(definitional_conversion,[status(esa)],[f_380_2]) ).
cnf(f_380_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1191,c_Groups_Ouminus__class_Ouminus(U_1191,U_1193),c_Groups_Ouminus__class_Ouminus(U_1191,U_1192))
| ~ c_Orderings_Oord__class_Oless__eq(U_1191,U_1192,U_1193)
| ~ class_Groups_Oordered__ab__group__add(U_1191) ),
inference(clausify,[status(thm)],[f_380_3]) ).
fof(f_381_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_b_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__iff]) ).
fof(f_381_2,plain,
! [U_1196,U_1195,U_1194] :
( ( ( c_Orderings_Oord__class_Oless(U_1194,U_1195,c_Groups_Ouminus__class_Ouminus(U_1194,U_1196))
| ~ c_Orderings_Oord__class_Oless(U_1194,U_1196,c_Groups_Ouminus__class_Ouminus(U_1194,U_1195)) )
& ( c_Orderings_Oord__class_Oless(U_1194,U_1196,c_Groups_Ouminus__class_Ouminus(U_1194,U_1195))
| ~ c_Orderings_Oord__class_Oless(U_1194,U_1195,c_Groups_Ouminus__class_Ouminus(U_1194,U_1196)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1194) ),
inference(variable_rename,[status(thm)],[f_381_1]) ).
fof(f_381_3,plain,
( ! [U_1195,U_1196,U_1194] :
( c_Orderings_Oord__class_Oless(U_1194,U_1195,c_Groups_Ouminus__class_Ouminus(U_1194,U_1196))
| ~ c_Orderings_Oord__class_Oless(U_1194,U_1196,c_Groups_Ouminus__class_Ouminus(U_1194,U_1195))
| ~ sP120(U_1195,U_1196,U_1194) )
& ! [U_1195,U_1196,U_1194] :
( c_Orderings_Oord__class_Oless(U_1194,U_1196,c_Groups_Ouminus__class_Ouminus(U_1194,U_1195))
| ~ c_Orderings_Oord__class_Oless(U_1194,U_1195,c_Groups_Ouminus__class_Ouminus(U_1194,U_1196))
| ~ sP120(U_1195,U_1196,U_1194) )
& ! [U_1195,U_1196,U_1194] :
( sP120(U_1195,U_1196,U_1194)
| ~ class_Groups_Oordered__ab__group__add(U_1194) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP120])],[f_381_2]) ).
cnf(f_381_4,plain,
( sP120(U_1195,U_1196,U_1194)
| ~ class_Groups_Oordered__ab__group__add(U_1194) ),
inference(clausify,[status(thm)],[f_381_3]) ).
cnf(f_381_5,plain,
( c_Orderings_Oord__class_Oless(U_1194,U_1196,c_Groups_Ouminus__class_Ouminus(U_1194,U_1195))
| ~ c_Orderings_Oord__class_Oless(U_1194,U_1195,c_Groups_Ouminus__class_Ouminus(U_1194,U_1196))
| ~ sP120(U_1195,U_1196,U_1194) ),
inference(clausify,[status(thm)],[f_381_3]) ).
cnf(f_381_6,plain,
( c_Orderings_Oord__class_Oless(U_1194,U_1195,c_Groups_Ouminus__class_Ouminus(U_1194,U_1196))
| ~ c_Orderings_Oord__class_Oless(U_1194,U_1196,c_Groups_Ouminus__class_Ouminus(U_1194,U_1195))
| ~ sP120(U_1195,U_1196,U_1194) ),
inference(clausify,[status(thm)],[f_381_3]) ).
fof(f_382_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__less__iff]) ).
fof(f_382_2,plain,
! [U_1199,U_1198,U_1197] :
( ( ( c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1198),U_1199)
| ~ c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1199),U_1198) )
& ( c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1199),U_1198)
| ~ c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1198),U_1199) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1197) ),
inference(variable_rename,[status(thm)],[f_382_1]) ).
fof(f_382_3,plain,
( ! [U_1198,U_1199,U_1197] :
( c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1198),U_1199)
| ~ c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1199),U_1198)
| ~ sP121(U_1198,U_1199,U_1197) )
& ! [U_1198,U_1199,U_1197] :
( c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1199),U_1198)
| ~ c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1198),U_1199)
| ~ sP121(U_1198,U_1199,U_1197) )
& ! [U_1198,U_1199,U_1197] :
( sP121(U_1198,U_1199,U_1197)
| ~ class_Groups_Oordered__ab__group__add(U_1197) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121])],[f_382_2]) ).
cnf(f_382_4,plain,
( sP121(U_1198,U_1199,U_1197)
| ~ class_Groups_Oordered__ab__group__add(U_1197) ),
inference(clausify,[status(thm)],[f_382_3]) ).
cnf(f_382_5,plain,
( c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1199),U_1198)
| ~ c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1198),U_1199)
| ~ sP121(U_1198,U_1199,U_1197) ),
inference(clausify,[status(thm)],[f_382_3]) ).
cnf(f_382_6,plain,
( c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1198),U_1199)
| ~ c_Orderings_Oord__class_Oless(U_1197,c_Groups_Ouminus__class_Ouminus(U_1197,U_1199),U_1198)
| ~ sP121(U_1198,U_1199,U_1197) ),
inference(clausify,[status(thm)],[f_382_3]) ).
fof(f_383_1,plain,
! [V_a_2,V_b_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b_2),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__iff__less]) ).
fof(f_383_2,plain,
! [U_1202,U_1201,U_1200] :
( ( ( c_Orderings_Oord__class_Oless(U_1200,c_Groups_Ouminus__class_Ouminus(U_1200,U_1201),c_Groups_Ouminus__class_Ouminus(U_1200,U_1202))
| ~ c_Orderings_Oord__class_Oless(U_1200,U_1202,U_1201) )
& ( c_Orderings_Oord__class_Oless(U_1200,U_1202,U_1201)
| ~ c_Orderings_Oord__class_Oless(U_1200,c_Groups_Ouminus__class_Ouminus(U_1200,U_1201),c_Groups_Ouminus__class_Ouminus(U_1200,U_1202)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1200) ),
inference(variable_rename,[status(thm)],[f_383_1]) ).
fof(f_383_3,plain,
( ! [U_1202,U_1200,U_1201] :
( c_Orderings_Oord__class_Oless(U_1200,c_Groups_Ouminus__class_Ouminus(U_1200,U_1201),c_Groups_Ouminus__class_Ouminus(U_1200,U_1202))
| ~ c_Orderings_Oord__class_Oless(U_1200,U_1202,U_1201)
| ~ sP122(U_1202,U_1200,U_1201) )
& ! [U_1202,U_1200,U_1201] :
( c_Orderings_Oord__class_Oless(U_1200,U_1202,U_1201)
| ~ c_Orderings_Oord__class_Oless(U_1200,c_Groups_Ouminus__class_Ouminus(U_1200,U_1201),c_Groups_Ouminus__class_Ouminus(U_1200,U_1202))
| ~ sP122(U_1202,U_1200,U_1201) )
& ! [U_1202,U_1200,U_1201] :
( sP122(U_1202,U_1200,U_1201)
| ~ class_Groups_Oordered__ab__group__add(U_1200) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP122])],[f_383_2]) ).
cnf(f_383_4,plain,
( sP122(U_1202,U_1200,U_1201)
| ~ class_Groups_Oordered__ab__group__add(U_1200) ),
inference(clausify,[status(thm)],[f_383_3]) ).
cnf(f_383_5,plain,
( c_Orderings_Oord__class_Oless(U_1200,U_1202,U_1201)
| ~ c_Orderings_Oord__class_Oless(U_1200,c_Groups_Ouminus__class_Ouminus(U_1200,U_1201),c_Groups_Ouminus__class_Ouminus(U_1200,U_1202))
| ~ sP122(U_1202,U_1200,U_1201) ),
inference(clausify,[status(thm)],[f_383_3]) ).
cnf(f_383_6,plain,
( c_Orderings_Oord__class_Oless(U_1200,c_Groups_Ouminus__class_Ouminus(U_1200,U_1201),c_Groups_Ouminus__class_Ouminus(U_1200,U_1202))
| ~ c_Orderings_Oord__class_Oless(U_1200,U_1202,U_1201)
| ~ sP122(U_1202,U_1200,U_1201) ),
inference(clausify,[status(thm)],[f_383_3]) ).
fof(f_384_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ominus__right]) ).
fof(f_384_2,plain,
! [U_1205,U_1204,U_1203] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1203),U_1204),c_Groups_Ouminus__class_Ouminus(U_1203,U_1205)) = c_Groups_Ouminus__class_Ouminus(U_1203,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1203),U_1204),U_1205))
| ~ class_RealVector_Oreal__normed__algebra(U_1203) ),
inference(variable_rename,[status(thm)],[f_384_1]) ).
fof(f_384_3,plain,
! [U_1204,U_1203,U_1205] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1203),U_1204),c_Groups_Ouminus__class_Ouminus(U_1203,U_1205)) = c_Groups_Ouminus__class_Ouminus(U_1203,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1203),U_1204),U_1205))
| ~ class_RealVector_Oreal__normed__algebra(U_1203) ),
inference(definitional_conversion,[status(esa)],[f_384_2]) ).
cnf(f_384_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1203),U_1204),c_Groups_Ouminus__class_Ouminus(U_1203,U_1205)) = c_Groups_Ouminus__class_Ouminus(U_1203,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1203),U_1204),U_1205))
| ~ class_RealVector_Oreal__normed__algebra(U_1203) ),
inference(clausify,[status(thm)],[f_384_3]) ).
fof(f_385_1,plain,
! [V_x,V_xa,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_xa),V_x))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Ominus]) ).
fof(f_385_2,plain,
! [U_1208,U_1207,U_1206] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1206),U_1207),c_Groups_Ouminus__class_Ouminus(U_1206,U_1208)) = c_Groups_Ouminus__class_Ouminus(U_1206,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1206),U_1207),U_1208))
| ~ class_RealVector_Oreal__normed__algebra(U_1206) ),
inference(variable_rename,[status(thm)],[f_385_1]) ).
fof(f_385_3,plain,
! [U_1206,U_1207,U_1208] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1206),U_1207),c_Groups_Ouminus__class_Ouminus(U_1206,U_1208)) = c_Groups_Ouminus__class_Ouminus(U_1206,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1206),U_1207),U_1208))
| ~ class_RealVector_Oreal__normed__algebra(U_1206) ),
inference(definitional_conversion,[status(esa)],[f_385_2]) ).
cnf(f_385_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1206),U_1207),c_Groups_Ouminus__class_Ouminus(U_1206,U_1208)) = c_Groups_Ouminus__class_Ouminus(U_1206,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1206),U_1207),U_1208))
| ~ class_RealVector_Oreal__normed__algebra(U_1206) ),
inference(clausify,[status(thm)],[f_385_3]) ).
fof(f_386_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ominus__left]) ).
fof(f_386_2,plain,
! [U_1211,U_1210,U_1209] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1209),c_Groups_Ouminus__class_Ouminus(U_1209,U_1210)),U_1211) = c_Groups_Ouminus__class_Ouminus(U_1209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1209),U_1210),U_1211))
| ~ class_RealVector_Oreal__normed__algebra(U_1209) ),
inference(variable_rename,[status(thm)],[f_386_1]) ).
fof(f_386_3,plain,
! [U_1209,U_1210,U_1211] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1209),c_Groups_Ouminus__class_Ouminus(U_1209,U_1210)),U_1211) = c_Groups_Ouminus__class_Ouminus(U_1209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1209),U_1210),U_1211))
| ~ class_RealVector_Oreal__normed__algebra(U_1209) ),
inference(definitional_conversion,[status(esa)],[f_386_2]) ).
cnf(f_386_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1209),c_Groups_Ouminus__class_Ouminus(U_1209,U_1210)),U_1211) = c_Groups_Ouminus__class_Ouminus(U_1209,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1209),U_1210),U_1211))
| ~ class_RealVector_Oreal__normed__algebra(U_1209) ),
inference(clausify,[status(thm)],[f_386_3]) ).
fof(f_387_1,plain,
! [V_y,V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_x)),V_y) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y))
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Ominus]) ).
fof(f_387_2,plain,
! [U_1214,U_1213,U_1212] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1212),c_Groups_Ouminus__class_Ouminus(U_1212,U_1213)),U_1214) = c_Groups_Ouminus__class_Ouminus(U_1212,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1212),U_1213),U_1214))
| ~ class_RealVector_Oreal__normed__algebra(U_1212) ),
inference(variable_rename,[status(thm)],[f_387_1]) ).
fof(f_387_3,plain,
! [U_1212,U_1213,U_1214] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1212),c_Groups_Ouminus__class_Ouminus(U_1212,U_1213)),U_1214) = c_Groups_Ouminus__class_Ouminus(U_1212,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1212),U_1213),U_1214))
| ~ class_RealVector_Oreal__normed__algebra(U_1212) ),
inference(definitional_conversion,[status(esa)],[f_387_2]) ).
cnf(f_387_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1212),c_Groups_Ouminus__class_Ouminus(U_1212,U_1213)),U_1214) = c_Groups_Ouminus__class_Ouminus(U_1212,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1212),U_1213),U_1214))
| ~ class_RealVector_Oreal__normed__algebra(U_1212) ),
inference(clausify,[status(thm)],[f_387_3]) ).
fof(f_388_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2)
| ( V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
& V_a_2 != V_b_2 ) )
& ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| V_a_2 = V_b_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_a_2) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_b_2) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__iff]) ).
fof(f_388_2,plain,
! [U_1217,U_1216,U_1215] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1216),U_1216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1217),U_1217)
| ( U_1216 != c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
& U_1216 != U_1217 ) )
& ( U_1216 = c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| U_1216 = U_1217
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1216),U_1216) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1217),U_1217) ) )
| ~ class_Rings_Oidom(U_1215) ),
inference(variable_rename,[status(thm)],[f_388_1]) ).
fof(f_388_3,plain,
( ! [U_1215,U_1216,U_1217] :
( U_1216 != c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| ~ sP123(U_1215,U_1216,U_1217) )
& ! [U_1215,U_1216,U_1217] :
( U_1216 != U_1217
| ~ sP123(U_1215,U_1216,U_1217) )
& ! [U_1215,U_1216,U_1217] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1216),U_1216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1217),U_1217)
| sP123(U_1215,U_1216,U_1217)
| ~ sP124(U_1215,U_1216,U_1217) )
& ! [U_1215,U_1216,U_1217] :
( U_1216 = c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| U_1216 = U_1217
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1216),U_1216) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1217),U_1217)
| ~ sP124(U_1215,U_1216,U_1217) )
& ! [U_1215,U_1216,U_1217] :
( sP124(U_1215,U_1216,U_1217)
| ~ class_Rings_Oidom(U_1215) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP123,sP124])],[f_388_2]) ).
cnf(f_388_4,plain,
( sP124(U_1215,U_1216,U_1217)
| ~ class_Rings_Oidom(U_1215) ),
inference(clausify,[status(thm)],[f_388_3]) ).
cnf(f_388_5,plain,
( U_1216 = c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| U_1216 = U_1217
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1216),U_1216) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1217),U_1217)
| ~ sP124(U_1215,U_1216,U_1217) ),
inference(clausify,[status(thm)],[f_388_3]) ).
cnf(f_388_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1216),U_1216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1215),U_1217),U_1217)
| sP123(U_1215,U_1216,U_1217)
| ~ sP124(U_1215,U_1216,U_1217) ),
inference(clausify,[status(thm)],[f_388_3]) ).
cnf(f_388_7,plain,
( U_1216 != U_1217
| ~ sP123(U_1215,U_1216,U_1217) ),
inference(clausify,[status(thm)],[f_388_3]) ).
cnf(f_388_8,plain,
( U_1216 != c_Groups_Ouminus__class_Ouminus(U_1215,U_1217)
| ~ sP123(U_1215,U_1216,U_1217) ),
inference(clausify,[status(thm)],[f_388_3]) ).
fof(f_389_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__minus]) ).
fof(f_389_2,plain,
! [U_1220,U_1219,U_1218] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1218),c_Groups_Ouminus__class_Ouminus(U_1218,U_1219)),c_Groups_Ouminus__class_Ouminus(U_1218,U_1220)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1218),U_1219),U_1220)
| ~ class_Rings_Oring(U_1218) ),
inference(variable_rename,[status(thm)],[f_389_1]) ).
fof(f_389_3,plain,
! [U_1218,U_1219,U_1220] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1218),c_Groups_Ouminus__class_Ouminus(U_1218,U_1219)),c_Groups_Ouminus__class_Ouminus(U_1218,U_1220)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1218),U_1219),U_1220)
| ~ class_Rings_Oring(U_1218) ),
inference(definitional_conversion,[status(esa)],[f_389_2]) ).
cnf(f_389_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1218),c_Groups_Ouminus__class_Ouminus(U_1218,U_1219)),c_Groups_Ouminus__class_Ouminus(U_1218,U_1220)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1218),U_1219),U_1220)
| ~ class_Rings_Oring(U_1218) ),
inference(clausify,[status(thm)],[f_389_3]) ).
fof(f_390_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__commute]) ).
fof(f_390_2,plain,
! [U_1223,U_1222,U_1221] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1221),c_Groups_Ouminus__class_Ouminus(U_1221,U_1222)),U_1223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1221),U_1222),c_Groups_Ouminus__class_Ouminus(U_1221,U_1223))
| ~ class_Rings_Oring(U_1221) ),
inference(variable_rename,[status(thm)],[f_390_1]) ).
fof(f_390_3,plain,
! [U_1223,U_1221,U_1222] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1221),c_Groups_Ouminus__class_Ouminus(U_1221,U_1222)),U_1223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1221),U_1222),c_Groups_Ouminus__class_Ouminus(U_1221,U_1223))
| ~ class_Rings_Oring(U_1221) ),
inference(definitional_conversion,[status(esa)],[f_390_2]) ).
cnf(f_390_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1221),c_Groups_Ouminus__class_Ouminus(U_1221,U_1222)),U_1223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1221),U_1222),c_Groups_Ouminus__class_Ouminus(U_1221,U_1223))
| ~ class_Rings_Oring(U_1221) ),
inference(clausify,[status(thm)],[f_390_3]) ).
fof(f_391_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(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_Ouminus__class_Ouminus(T_a,V_a)),V_b)
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__left]) ).
fof(f_391_2,plain,
! [U_1226,U_1225,U_1224] :
( c_Groups_Ouminus__class_Ouminus(U_1224,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1224),U_1225),U_1226)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1224),c_Groups_Ouminus__class_Ouminus(U_1224,U_1225)),U_1226)
| ~ class_Rings_Oring(U_1224) ),
inference(variable_rename,[status(thm)],[f_391_1]) ).
fof(f_391_3,plain,
! [U_1224,U_1225,U_1226] :
( c_Groups_Ouminus__class_Ouminus(U_1224,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1224),U_1225),U_1226)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1224),c_Groups_Ouminus__class_Ouminus(U_1224,U_1225)),U_1226)
| ~ class_Rings_Oring(U_1224) ),
inference(definitional_conversion,[status(esa)],[f_391_2]) ).
cnf(f_391_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1224,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1224),U_1225),U_1226)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1224),c_Groups_Ouminus__class_Ouminus(U_1224,U_1225)),U_1226)
| ~ class_Rings_Oring(U_1224) ),
inference(clausify,[status(thm)],[f_391_3]) ).
fof(f_392_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(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),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Rings_Oring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__mult__right]) ).
fof(f_392_2,plain,
! [U_1229,U_1228,U_1227] :
( c_Groups_Ouminus__class_Ouminus(U_1227,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1227),U_1228),U_1229)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1227),U_1228),c_Groups_Ouminus__class_Ouminus(U_1227,U_1229))
| ~ class_Rings_Oring(U_1227) ),
inference(variable_rename,[status(thm)],[f_392_1]) ).
fof(f_392_3,plain,
! [U_1227,U_1228,U_1229] :
( c_Groups_Ouminus__class_Ouminus(U_1227,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1227),U_1228),U_1229)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1227),U_1228),c_Groups_Ouminus__class_Ouminus(U_1227,U_1229))
| ~ class_Rings_Oring(U_1227) ),
inference(definitional_conversion,[status(esa)],[f_392_2]) ).
cnf(f_392_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1227,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1227),U_1228),U_1229)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1227),U_1228),c_Groups_Ouminus__class_Ouminus(U_1227,U_1229))
| ~ class_Rings_Oring(U_1227) ),
inference(clausify,[status(thm)],[f_392_3]) ).
fof(f_393_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = V_b
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add__cancel]) ).
fof(f_393_2,plain,
! [U_1232,U_1231,U_1230] :
( c_Groups_Oplus__class_Oplus(U_1230,c_Groups_Ouminus__class_Ouminus(U_1230,U_1231),c_Groups_Oplus__class_Oplus(U_1230,U_1231,U_1232)) = U_1232
| ~ class_Groups_Ogroup__add(U_1230) ),
inference(variable_rename,[status(thm)],[f_393_1]) ).
fof(f_393_3,plain,
! [U_1231,U_1230,U_1232] :
( c_Groups_Oplus__class_Oplus(U_1230,c_Groups_Ouminus__class_Ouminus(U_1230,U_1231),c_Groups_Oplus__class_Oplus(U_1230,U_1231,U_1232)) = U_1232
| ~ class_Groups_Ogroup__add(U_1230) ),
inference(definitional_conversion,[status(esa)],[f_393_2]) ).
cnf(f_393_4,plain,
( c_Groups_Oplus__class_Oplus(U_1230,c_Groups_Ouminus__class_Ouminus(U_1230,U_1231),c_Groups_Oplus__class_Oplus(U_1230,U_1231,U_1232)) = U_1232
| ~ class_Groups_Ogroup__add(U_1230) ),
inference(clausify,[status(thm)],[f_393_3]) ).
fof(f_394_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)) = V_b
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__minus__cancel]) ).
fof(f_394_2,plain,
! [U_1235,U_1234,U_1233] :
( c_Groups_Oplus__class_Oplus(U_1233,U_1234,c_Groups_Oplus__class_Oplus(U_1233,c_Groups_Ouminus__class_Ouminus(U_1233,U_1234),U_1235)) = U_1235
| ~ class_Groups_Ogroup__add(U_1233) ),
inference(variable_rename,[status(thm)],[f_394_1]) ).
fof(f_394_3,plain,
! [U_1233,U_1234,U_1235] :
( c_Groups_Oplus__class_Oplus(U_1233,U_1234,c_Groups_Oplus__class_Oplus(U_1233,c_Groups_Ouminus__class_Ouminus(U_1233,U_1234),U_1235)) = U_1235
| ~ class_Groups_Ogroup__add(U_1233) ),
inference(definitional_conversion,[status(esa)],[f_394_2]) ).
cnf(f_394_4,plain,
( c_Groups_Oplus__class_Oplus(U_1233,U_1234,c_Groups_Oplus__class_Oplus(U_1233,c_Groups_Ouminus__class_Ouminus(U_1233,U_1234),U_1235)) = U_1235
| ~ class_Groups_Ogroup__add(U_1233) ),
inference(clausify,[status(thm)],[f_394_3]) ).
fof(f_395_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b),c_Groups_Ouminus__class_Ouminus(T_a,V_a))
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add]) ).
fof(f_395_2,plain,
! [U_1238,U_1237,U_1236] :
( c_Groups_Ouminus__class_Ouminus(U_1236,c_Groups_Oplus__class_Oplus(U_1236,U_1237,U_1238)) = c_Groups_Oplus__class_Oplus(U_1236,c_Groups_Ouminus__class_Ouminus(U_1236,U_1238),c_Groups_Ouminus__class_Ouminus(U_1236,U_1237))
| ~ class_Groups_Ogroup__add(U_1236) ),
inference(variable_rename,[status(thm)],[f_395_1]) ).
fof(f_395_3,plain,
! [U_1236,U_1237,U_1238] :
( c_Groups_Ouminus__class_Ouminus(U_1236,c_Groups_Oplus__class_Oplus(U_1236,U_1237,U_1238)) = c_Groups_Oplus__class_Oplus(U_1236,c_Groups_Ouminus__class_Ouminus(U_1236,U_1238),c_Groups_Ouminus__class_Ouminus(U_1236,U_1237))
| ~ class_Groups_Ogroup__add(U_1236) ),
inference(definitional_conversion,[status(esa)],[f_395_2]) ).
cnf(f_395_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1236,c_Groups_Oplus__class_Oplus(U_1236,U_1237,U_1238)) = c_Groups_Oplus__class_Oplus(U_1236,c_Groups_Ouminus__class_Ouminus(U_1236,U_1238),c_Groups_Ouminus__class_Ouminus(U_1236,U_1237))
| ~ class_Groups_Ogroup__add(U_1236) ),
inference(clausify,[status(thm)],[f_395_3]) ).
fof(f_396_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__add__distrib]) ).
fof(f_396_2,plain,
! [U_1241,U_1240,U_1239] :
( c_Groups_Ouminus__class_Ouminus(U_1239,c_Groups_Oplus__class_Oplus(U_1239,U_1240,U_1241)) = c_Groups_Oplus__class_Oplus(U_1239,c_Groups_Ouminus__class_Ouminus(U_1239,U_1240),c_Groups_Ouminus__class_Ouminus(U_1239,U_1241))
| ~ class_Groups_Oab__group__add(U_1239) ),
inference(variable_rename,[status(thm)],[f_396_1]) ).
fof(f_396_3,plain,
! [U_1239,U_1240,U_1241] :
( c_Groups_Ouminus__class_Ouminus(U_1239,c_Groups_Oplus__class_Oplus(U_1239,U_1240,U_1241)) = c_Groups_Oplus__class_Oplus(U_1239,c_Groups_Ouminus__class_Ouminus(U_1239,U_1240),c_Groups_Ouminus__class_Ouminus(U_1239,U_1241))
| ~ class_Groups_Oab__group__add(U_1239) ),
inference(definitional_conversion,[status(esa)],[f_396_2]) ).
cnf(f_396_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1239,c_Groups_Oplus__class_Oplus(U_1239,U_1240,U_1241)) = c_Groups_Oplus__class_Oplus(U_1239,c_Groups_Ouminus__class_Ouminus(U_1239,U_1240),c_Groups_Ouminus__class_Ouminus(U_1239,U_1241))
| ~ class_Groups_Oab__group__add(U_1239) ),
inference(clausify,[status(thm)],[f_396_3]) ).
fof(f_397_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Oabs__class_Oabs(T_a,V_a)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__minus__cancel]) ).
fof(f_397_2,plain,
! [U_1243,U_1242] :
( c_Groups_Oabs__class_Oabs(U_1242,c_Groups_Ouminus__class_Ouminus(U_1242,U_1243)) = c_Groups_Oabs__class_Oabs(U_1242,U_1243)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1242) ),
inference(variable_rename,[status(thm)],[f_397_1]) ).
fof(f_397_3,plain,
! [U_1242,U_1243] :
( c_Groups_Oabs__class_Oabs(U_1242,c_Groups_Ouminus__class_Ouminus(U_1242,U_1243)) = c_Groups_Oabs__class_Oabs(U_1242,U_1243)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1242) ),
inference(definitional_conversion,[status(esa)],[f_397_2]) ).
cnf(f_397_4,plain,
( c_Groups_Oabs__class_Oabs(U_1242,c_Groups_Ouminus__class_Ouminus(U_1242,U_1243)) = c_Groups_Oabs__class_Oabs(U_1242,U_1243)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1242) ),
inference(clausify,[status(thm)],[f_397_3]) ).
fof(f_398_1,plain,
! [V_x,T_a] :
( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_RealVector_Onorm__class_Onorm(T_a,V_x)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__minus__cancel]) ).
fof(f_398_2,plain,
! [U_1245,U_1244] :
( c_RealVector_Onorm__class_Onorm(U_1244,c_Groups_Ouminus__class_Ouminus(U_1244,U_1245)) = c_RealVector_Onorm__class_Onorm(U_1244,U_1245)
| ~ class_RealVector_Oreal__normed__vector(U_1244) ),
inference(variable_rename,[status(thm)],[f_398_1]) ).
fof(f_398_3,plain,
! [U_1244,U_1245] :
( c_RealVector_Onorm__class_Onorm(U_1244,c_Groups_Ouminus__class_Ouminus(U_1244,U_1245)) = c_RealVector_Onorm__class_Onorm(U_1244,U_1245)
| ~ class_RealVector_Oreal__normed__vector(U_1244) ),
inference(definitional_conversion,[status(esa)],[f_398_2]) ).
cnf(f_398_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1244,c_Groups_Ouminus__class_Ouminus(U_1244,U_1245)) = c_RealVector_Onorm__class_Onorm(U_1244,U_1245)
| ~ class_RealVector_Oreal__normed__vector(U_1244) ),
inference(clausify,[status(thm)],[f_398_3]) ).
fof(f_399_1,plain,
! [T_a] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__poly__code_I1_J]) ).
fof(f_399_2,plain,
! [U_1246] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1246),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1246))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1246))
| ~ class_Groups_Oab__group__add(U_1246) ),
inference(variable_rename,[status(thm)],[f_399_1]) ).
fof(f_399_3,plain,
! [U_1246] :
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1246),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1246))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1246))
| ~ class_Groups_Oab__group__add(U_1246) ),
inference(definitional_conversion,[status(esa)],[f_399_2]) ).
cnf(f_399_4,plain,
( c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1246),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1246))) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1246))
| ~ class_Groups_Oab__group__add(U_1246) ),
inference(clausify,[status(thm)],[f_399_3]) ).
fof(f_400_1,plain,
! [V_x,T_a] :
( ( ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = V_x
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) )
& ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_x)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),V_x,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__poly__def]) ).
fof(f_400_2,plain,
! [U_1248,U_1247] :
( ( ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1247),U_1248) = U_1248
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1247),U_1248,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1247))) )
& ( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1247),U_1248) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1247),U_1248)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1247),U_1248,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1247))) ) )
| ~ class_Rings_Olinordered__idom(U_1247) ),
inference(variable_rename,[status(thm)],[f_400_1]) ).
fof(f_400_3,plain,
( ! [U_1247,U_1248] :
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1247),U_1248) = U_1248
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1247),U_1248,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1247)))
| ~ sP125(U_1247,U_1248) )
& ! [U_1247,U_1248] :
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1247),U_1248) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1247),U_1248)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1247),U_1248,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1247)))
| ~ sP125(U_1247,U_1248) )
& ! [U_1247,U_1248] :
( sP125(U_1247,U_1248)
| ~ class_Rings_Olinordered__idom(U_1247) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_400_2]) ).
cnf(f_400_4,plain,
( sP125(U_1247,U_1248)
| ~ class_Rings_Olinordered__idom(U_1247) ),
inference(clausify,[status(thm)],[f_400_3]) ).
cnf(f_400_5,plain,
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1247),U_1248) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1247),U_1248)
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1247),U_1248,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1247)))
| ~ sP125(U_1247,U_1248) ),
inference(clausify,[status(thm)],[f_400_3]) ).
cnf(f_400_6,plain,
( c_Groups_Oabs__class_Oabs(tc_Polynomial_Opoly(U_1247),U_1248) = U_1248
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1247),U_1248,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1247)))
| ~ sP125(U_1247,U_1248) ),
inference(clausify,[status(thm)],[f_400_3]) ).
fof(f_401_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__le__iff__le]) ).
fof(f_401_2,plain,
! [U_1250,U_1249] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),c_Groups_Ouminus__class_Ouminus(U_1249,U_1250))
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,c_Groups_Ozero__class_Ozero(U_1249)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,c_Groups_Ozero__class_Ozero(U_1249))
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),c_Groups_Ouminus__class_Ouminus(U_1249,U_1250)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1249) ),
inference(variable_rename,[status(thm)],[f_401_1]) ).
fof(f_401_3,plain,
( ! [U_1250,U_1249] :
( c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),c_Groups_Ouminus__class_Ouminus(U_1249,U_1250))
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,c_Groups_Ozero__class_Ozero(U_1249))
| ~ sP126(U_1250,U_1249) )
& ! [U_1250,U_1249] :
( c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,c_Groups_Ozero__class_Ozero(U_1249))
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),c_Groups_Ouminus__class_Ouminus(U_1249,U_1250))
| ~ sP126(U_1250,U_1249) )
& ! [U_1250,U_1249] :
( sP126(U_1250,U_1249)
| ~ class_Groups_Oordered__ab__group__add(U_1249) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_401_2]) ).
cnf(f_401_4,plain,
( sP126(U_1250,U_1249)
| ~ class_Groups_Oordered__ab__group__add(U_1249) ),
inference(clausify,[status(thm)],[f_401_3]) ).
cnf(f_401_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,c_Groups_Ozero__class_Ozero(U_1249))
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),c_Groups_Ouminus__class_Ouminus(U_1249,U_1250))
| ~ sP126(U_1250,U_1249) ),
inference(clausify,[status(thm)],[f_401_3]) ).
cnf(f_401_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1249,c_Groups_Ozero__class_Ozero(U_1249),c_Groups_Ouminus__class_Ouminus(U_1249,U_1250))
| ~ c_Orderings_Oord__class_Oless__eq(U_1249,U_1250,c_Groups_Ozero__class_Ozero(U_1249))
| ~ sP126(U_1250,U_1249) ),
inference(clausify,[status(thm)],[f_401_3]) ).
fof(f_402_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__minus__self__iff]) ).
fof(f_402_2,plain,
! [U_1252,U_1251] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ouminus__class_Ouminus(U_1251,U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ozero__class_Ozero(U_1251)) )
& ( c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ozero__class_Ozero(U_1251))
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ouminus__class_Ouminus(U_1251,U_1252)) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1251) ),
inference(variable_rename,[status(thm)],[f_402_1]) ).
fof(f_402_3,plain,
( ! [U_1252,U_1251] :
( c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ouminus__class_Ouminus(U_1251,U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ozero__class_Ozero(U_1251))
| ~ sP127(U_1252,U_1251) )
& ! [U_1252,U_1251] :
( c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ozero__class_Ozero(U_1251))
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ouminus__class_Ouminus(U_1251,U_1252))
| ~ sP127(U_1252,U_1251) )
& ! [U_1252,U_1251] :
( sP127(U_1252,U_1251)
| ~ class_Groups_Olinordered__ab__group__add(U_1251) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_402_2]) ).
cnf(f_402_4,plain,
( sP127(U_1252,U_1251)
| ~ class_Groups_Olinordered__ab__group__add(U_1251) ),
inference(clausify,[status(thm)],[f_402_3]) ).
cnf(f_402_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ozero__class_Ozero(U_1251))
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ouminus__class_Ouminus(U_1251,U_1252))
| ~ sP127(U_1252,U_1251) ),
inference(clausify,[status(thm)],[f_402_3]) ).
cnf(f_402_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ouminus__class_Ouminus(U_1251,U_1252))
| ~ c_Orderings_Oord__class_Oless__eq(U_1251,U_1252,c_Groups_Ozero__class_Ozero(U_1251))
| ~ sP127(U_1252,U_1251) ),
inference(clausify,[status(thm)],[f_402_3]) ).
fof(f_403_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__le__0__iff__le]) ).
fof(f_403_2,plain,
! [U_1254,U_1253] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ouminus__class_Ouminus(U_1253,U_1254),c_Groups_Ozero__class_Ozero(U_1253))
| ~ c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ozero__class_Ozero(U_1253),U_1254) )
& ( c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ozero__class_Ozero(U_1253),U_1254)
| ~ c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ouminus__class_Ouminus(U_1253,U_1254),c_Groups_Ozero__class_Ozero(U_1253)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1253) ),
inference(variable_rename,[status(thm)],[f_403_1]) ).
fof(f_403_3,plain,
( ! [U_1254,U_1253] :
( c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ouminus__class_Ouminus(U_1253,U_1254),c_Groups_Ozero__class_Ozero(U_1253))
| ~ c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ozero__class_Ozero(U_1253),U_1254)
| ~ sP128(U_1254,U_1253) )
& ! [U_1254,U_1253] :
( c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ozero__class_Ozero(U_1253),U_1254)
| ~ c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ouminus__class_Ouminus(U_1253,U_1254),c_Groups_Ozero__class_Ozero(U_1253))
| ~ sP128(U_1254,U_1253) )
& ! [U_1254,U_1253] :
( sP128(U_1254,U_1253)
| ~ class_Groups_Oordered__ab__group__add(U_1253) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_403_2]) ).
cnf(f_403_4,plain,
( sP128(U_1254,U_1253)
| ~ class_Groups_Oordered__ab__group__add(U_1253) ),
inference(clausify,[status(thm)],[f_403_3]) ).
cnf(f_403_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ozero__class_Ozero(U_1253),U_1254)
| ~ c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ouminus__class_Ouminus(U_1253,U_1254),c_Groups_Ozero__class_Ozero(U_1253))
| ~ sP128(U_1254,U_1253) ),
inference(clausify,[status(thm)],[f_403_3]) ).
cnf(f_403_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ouminus__class_Ouminus(U_1253,U_1254),c_Groups_Ozero__class_Ozero(U_1253))
| ~ c_Orderings_Oord__class_Oless__eq(U_1253,c_Groups_Ozero__class_Ozero(U_1253),U_1254)
| ~ sP128(U_1254,U_1253) ),
inference(clausify,[status(thm)],[f_403_3]) ).
fof(f_404_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__le__self__iff]) ).
fof(f_404_2,plain,
! [U_1256,U_1255] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ouminus__class_Ouminus(U_1255,U_1256),U_1256)
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ozero__class_Ozero(U_1255),U_1256) )
& ( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ozero__class_Ozero(U_1255),U_1256)
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ouminus__class_Ouminus(U_1255,U_1256),U_1256) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1255) ),
inference(variable_rename,[status(thm)],[f_404_1]) ).
fof(f_404_3,plain,
( ! [U_1256,U_1255] :
( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ouminus__class_Ouminus(U_1255,U_1256),U_1256)
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ozero__class_Ozero(U_1255),U_1256)
| ~ sP129(U_1256,U_1255) )
& ! [U_1256,U_1255] :
( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ozero__class_Ozero(U_1255),U_1256)
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ouminus__class_Ouminus(U_1255,U_1256),U_1256)
| ~ sP129(U_1256,U_1255) )
& ! [U_1256,U_1255] :
( sP129(U_1256,U_1255)
| ~ class_Groups_Olinordered__ab__group__add(U_1255) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_404_2]) ).
cnf(f_404_4,plain,
( sP129(U_1256,U_1255)
| ~ class_Groups_Olinordered__ab__group__add(U_1255) ),
inference(clausify,[status(thm)],[f_404_3]) ).
cnf(f_404_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ozero__class_Ozero(U_1255),U_1256)
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ouminus__class_Ouminus(U_1255,U_1256),U_1256)
| ~ sP129(U_1256,U_1255) ),
inference(clausify,[status(thm)],[f_404_3]) ).
cnf(f_404_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ouminus__class_Ouminus(U_1255,U_1256),U_1256)
| ~ c_Orderings_Oord__class_Oless__eq(U_1255,c_Groups_Ozero__class_Ozero(U_1255),U_1256)
| ~ sP129(U_1256,U_1255) ),
inference(clausify,[status(thm)],[f_404_3]) ).
fof(f_405_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__0__less__iff__less]) ).
fof(f_405_2,plain,
! [U_1258,U_1257] :
( ( ( c_Orderings_Oord__class_Oless(U_1257,c_Groups_Ozero__class_Ozero(U_1257),c_Groups_Ouminus__class_Ouminus(U_1257,U_1258))
| ~ c_Orderings_Oord__class_Oless(U_1257,U_1258,c_Groups_Ozero__class_Ozero(U_1257)) )
& ( c_Orderings_Oord__class_Oless(U_1257,U_1258,c_Groups_Ozero__class_Ozero(U_1257))
| ~ c_Orderings_Oord__class_Oless(U_1257,c_Groups_Ozero__class_Ozero(U_1257),c_Groups_Ouminus__class_Ouminus(U_1257,U_1258)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1257) ),
inference(variable_rename,[status(thm)],[f_405_1]) ).
fof(f_405_3,plain,
( ! [U_1258,U_1257] :
( c_Orderings_Oord__class_Oless(U_1257,c_Groups_Ozero__class_Ozero(U_1257),c_Groups_Ouminus__class_Ouminus(U_1257,U_1258))
| ~ c_Orderings_Oord__class_Oless(U_1257,U_1258,c_Groups_Ozero__class_Ozero(U_1257))
| ~ sP130(U_1258,U_1257) )
& ! [U_1258,U_1257] :
( c_Orderings_Oord__class_Oless(U_1257,U_1258,c_Groups_Ozero__class_Ozero(U_1257))
| ~ c_Orderings_Oord__class_Oless(U_1257,c_Groups_Ozero__class_Ozero(U_1257),c_Groups_Ouminus__class_Ouminus(U_1257,U_1258))
| ~ sP130(U_1258,U_1257) )
& ! [U_1258,U_1257] :
( sP130(U_1258,U_1257)
| ~ class_Groups_Oordered__ab__group__add(U_1257) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_405_2]) ).
cnf(f_405_4,plain,
( sP130(U_1258,U_1257)
| ~ class_Groups_Oordered__ab__group__add(U_1257) ),
inference(clausify,[status(thm)],[f_405_3]) ).
cnf(f_405_5,plain,
( c_Orderings_Oord__class_Oless(U_1257,U_1258,c_Groups_Ozero__class_Ozero(U_1257))
| ~ c_Orderings_Oord__class_Oless(U_1257,c_Groups_Ozero__class_Ozero(U_1257),c_Groups_Ouminus__class_Ouminus(U_1257,U_1258))
| ~ sP130(U_1258,U_1257) ),
inference(clausify,[status(thm)],[f_405_3]) ).
cnf(f_405_6,plain,
( c_Orderings_Oord__class_Oless(U_1257,c_Groups_Ozero__class_Ozero(U_1257),c_Groups_Ouminus__class_Ouminus(U_1257,U_1258))
| ~ c_Orderings_Oord__class_Oless(U_1257,U_1258,c_Groups_Ozero__class_Ozero(U_1257))
| ~ sP130(U_1258,U_1257) ),
inference(clausify,[status(thm)],[f_405_3]) ).
fof(f_406_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__minus__self__iff]) ).
fof(f_406_2,plain,
! [U_1260,U_1259] :
( ( ( c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ouminus__class_Ouminus(U_1259,U_1260))
| ~ c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ozero__class_Ozero(U_1259)) )
& ( c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ozero__class_Ozero(U_1259))
| ~ c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ouminus__class_Ouminus(U_1259,U_1260)) ) )
| ~ class_Rings_Olinordered__idom(U_1259) ),
inference(variable_rename,[status(thm)],[f_406_1]) ).
fof(f_406_3,plain,
( ! [U_1260,U_1259] :
( c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ouminus__class_Ouminus(U_1259,U_1260))
| ~ c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ozero__class_Ozero(U_1259))
| ~ sP131(U_1260,U_1259) )
& ! [U_1260,U_1259] :
( c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ozero__class_Ozero(U_1259))
| ~ c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ouminus__class_Ouminus(U_1259,U_1260))
| ~ sP131(U_1260,U_1259) )
& ! [U_1260,U_1259] :
( sP131(U_1260,U_1259)
| ~ class_Rings_Olinordered__idom(U_1259) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131])],[f_406_2]) ).
cnf(f_406_4,plain,
( sP131(U_1260,U_1259)
| ~ class_Rings_Olinordered__idom(U_1259) ),
inference(clausify,[status(thm)],[f_406_3]) ).
cnf(f_406_5,plain,
( c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ozero__class_Ozero(U_1259))
| ~ c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ouminus__class_Ouminus(U_1259,U_1260))
| ~ sP131(U_1260,U_1259) ),
inference(clausify,[status(thm)],[f_406_3]) ).
cnf(f_406_6,plain,
( c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ouminus__class_Ouminus(U_1259,U_1260))
| ~ c_Orderings_Oord__class_Oless(U_1259,U_1260,c_Groups_Ozero__class_Ozero(U_1259))
| ~ sP131(U_1260,U_1259) ),
inference(clausify,[status(thm)],[f_406_3]) ).
fof(f_407_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__0__iff__less]) ).
fof(f_407_2,plain,
! [U_1262,U_1261] :
( ( ( c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ouminus__class_Ouminus(U_1261,U_1262),c_Groups_Ozero__class_Ozero(U_1261))
| ~ c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ozero__class_Ozero(U_1261),U_1262) )
& ( c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ozero__class_Ozero(U_1261),U_1262)
| ~ c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ouminus__class_Ouminus(U_1261,U_1262),c_Groups_Ozero__class_Ozero(U_1261)) ) )
| ~ class_Groups_Oordered__ab__group__add(U_1261) ),
inference(variable_rename,[status(thm)],[f_407_1]) ).
fof(f_407_3,plain,
( ! [U_1262,U_1261] :
( c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ouminus__class_Ouminus(U_1261,U_1262),c_Groups_Ozero__class_Ozero(U_1261))
| ~ c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ozero__class_Ozero(U_1261),U_1262)
| ~ sP132(U_1262,U_1261) )
& ! [U_1262,U_1261] :
( c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ozero__class_Ozero(U_1261),U_1262)
| ~ c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ouminus__class_Ouminus(U_1261,U_1262),c_Groups_Ozero__class_Ozero(U_1261))
| ~ sP132(U_1262,U_1261) )
& ! [U_1262,U_1261] :
( sP132(U_1262,U_1261)
| ~ class_Groups_Oordered__ab__group__add(U_1261) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132])],[f_407_2]) ).
cnf(f_407_4,plain,
( sP132(U_1262,U_1261)
| ~ class_Groups_Oordered__ab__group__add(U_1261) ),
inference(clausify,[status(thm)],[f_407_3]) ).
cnf(f_407_5,plain,
( c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ozero__class_Ozero(U_1261),U_1262)
| ~ c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ouminus__class_Ouminus(U_1261,U_1262),c_Groups_Ozero__class_Ozero(U_1261))
| ~ sP132(U_1262,U_1261) ),
inference(clausify,[status(thm)],[f_407_3]) ).
cnf(f_407_6,plain,
( c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ouminus__class_Ouminus(U_1261,U_1262),c_Groups_Ozero__class_Ozero(U_1261))
| ~ c_Orderings_Oord__class_Oless(U_1261,c_Groups_Ozero__class_Ozero(U_1261),U_1262)
| ~ sP132(U_1262,U_1261) ),
inference(clausify,[status(thm)],[f_407_3]) ).
fof(f_408_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_a_2) ) )
| ~ class_Groups_Olinordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_neg__less__nonneg]) ).
fof(f_408_2,plain,
! [U_1264,U_1263] :
( ( ( c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ouminus__class_Ouminus(U_1263,U_1264),U_1264)
| ~ c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ozero__class_Ozero(U_1263),U_1264) )
& ( c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ozero__class_Ozero(U_1263),U_1264)
| ~ c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ouminus__class_Ouminus(U_1263,U_1264),U_1264) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1263) ),
inference(variable_rename,[status(thm)],[f_408_1]) ).
fof(f_408_3,plain,
( ! [U_1264,U_1263] :
( c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ouminus__class_Ouminus(U_1263,U_1264),U_1264)
| ~ c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ozero__class_Ozero(U_1263),U_1264)
| ~ sP133(U_1264,U_1263) )
& ! [U_1264,U_1263] :
( c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ozero__class_Ozero(U_1263),U_1264)
| ~ c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ouminus__class_Ouminus(U_1263,U_1264),U_1264)
| ~ sP133(U_1264,U_1263) )
& ! [U_1264,U_1263] :
( sP133(U_1264,U_1263)
| ~ class_Groups_Olinordered__ab__group__add(U_1263) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133])],[f_408_2]) ).
cnf(f_408_4,plain,
( sP133(U_1264,U_1263)
| ~ class_Groups_Olinordered__ab__group__add(U_1263) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_5,plain,
( c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ozero__class_Ozero(U_1263),U_1264)
| ~ c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ouminus__class_Ouminus(U_1263,U_1264),U_1264)
| ~ sP133(U_1264,U_1263) ),
inference(clausify,[status(thm)],[f_408_3]) ).
cnf(f_408_6,plain,
( c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ouminus__class_Ouminus(U_1263,U_1264),U_1264)
| ~ c_Orderings_Oord__class_Oless(U_1263,c_Groups_Ozero__class_Ozero(U_1263),U_1264)
| ~ sP133(U_1264,U_1263) ),
inference(clausify,[status(thm)],[f_408_3]) ).
fof(f_409_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_right__minus]) ).
fof(f_409_2,plain,
! [U_1266,U_1265] :
( c_Groups_Oplus__class_Oplus(U_1265,U_1266,c_Groups_Ouminus__class_Ouminus(U_1265,U_1266)) = c_Groups_Ozero__class_Ozero(U_1265)
| ~ class_Groups_Ogroup__add(U_1265) ),
inference(variable_rename,[status(thm)],[f_409_1]) ).
fof(f_409_3,plain,
! [U_1266,U_1265] :
( c_Groups_Oplus__class_Oplus(U_1265,U_1266,c_Groups_Ouminus__class_Ouminus(U_1265,U_1266)) = c_Groups_Ozero__class_Ozero(U_1265)
| ~ class_Groups_Ogroup__add(U_1265) ),
inference(definitional_conversion,[status(esa)],[f_409_2]) ).
cnf(f_409_4,plain,
( c_Groups_Oplus__class_Oplus(U_1265,U_1266,c_Groups_Ouminus__class_Ouminus(U_1265,U_1266)) = c_Groups_Ozero__class_Ozero(U_1265)
| ~ class_Groups_Ogroup__add(U_1265) ),
inference(clausify,[status(thm)],[f_409_3]) ).
fof(f_410_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_b_2)
| c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) != c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_b_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_a_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_b_2) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_eq__neg__iff__add__eq__0]) ).
fof(f_410_2,plain,
! [U_1269,U_1268,U_1267] :
( ( ( U_1268 = c_Groups_Ouminus__class_Ouminus(U_1267,U_1269)
| c_Groups_Oplus__class_Oplus(U_1267,U_1268,U_1269) != c_Groups_Ozero__class_Ozero(U_1267) )
& ( c_Groups_Oplus__class_Oplus(U_1267,U_1268,U_1269) = c_Groups_Ozero__class_Ozero(U_1267)
| U_1268 != c_Groups_Ouminus__class_Ouminus(U_1267,U_1269) ) )
| ~ class_Groups_Ogroup__add(U_1267) ),
inference(variable_rename,[status(thm)],[f_410_1]) ).
fof(f_410_3,plain,
( ! [U_1267,U_1268,U_1269] :
( U_1268 = c_Groups_Ouminus__class_Ouminus(U_1267,U_1269)
| c_Groups_Oplus__class_Oplus(U_1267,U_1268,U_1269) != c_Groups_Ozero__class_Ozero(U_1267)
| ~ sP134(U_1267,U_1268,U_1269) )
& ! [U_1267,U_1268,U_1269] :
( c_Groups_Oplus__class_Oplus(U_1267,U_1268,U_1269) = c_Groups_Ozero__class_Ozero(U_1267)
| U_1268 != c_Groups_Ouminus__class_Ouminus(U_1267,U_1269)
| ~ sP134(U_1267,U_1268,U_1269) )
& ! [U_1267,U_1268,U_1269] :
( sP134(U_1267,U_1268,U_1269)
| ~ class_Groups_Ogroup__add(U_1267) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134])],[f_410_2]) ).
cnf(f_410_4,plain,
( sP134(U_1267,U_1268,U_1269)
| ~ class_Groups_Ogroup__add(U_1267) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_5,plain,
( c_Groups_Oplus__class_Oplus(U_1267,U_1268,U_1269) = c_Groups_Ozero__class_Ozero(U_1267)
| U_1268 != c_Groups_Ouminus__class_Ouminus(U_1267,U_1269)
| ~ sP134(U_1267,U_1268,U_1269) ),
inference(clausify,[status(thm)],[f_410_3]) ).
cnf(f_410_6,plain,
( U_1268 = c_Groups_Ouminus__class_Ouminus(U_1267,U_1269)
| c_Groups_Oplus__class_Oplus(U_1267,U_1268,U_1269) != c_Groups_Ozero__class_Ozero(U_1267)
| ~ sP134(U_1267,U_1268,U_1269) ),
inference(clausify,[status(thm)],[f_410_3]) ).
fof(f_411_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_left__minus]) ).
fof(f_411_2,plain,
! [U_1271,U_1270] :
( c_Groups_Oplus__class_Oplus(U_1270,c_Groups_Ouminus__class_Ouminus(U_1270,U_1271),U_1271) = c_Groups_Ozero__class_Ozero(U_1270)
| ~ class_Groups_Ogroup__add(U_1270) ),
inference(variable_rename,[status(thm)],[f_411_1]) ).
fof(f_411_3,plain,
! [U_1271,U_1270] :
( c_Groups_Oplus__class_Oplus(U_1270,c_Groups_Ouminus__class_Ouminus(U_1270,U_1271),U_1271) = c_Groups_Ozero__class_Ozero(U_1270)
| ~ class_Groups_Ogroup__add(U_1270) ),
inference(definitional_conversion,[status(esa)],[f_411_2]) ).
cnf(f_411_4,plain,
( c_Groups_Oplus__class_Oplus(U_1270,c_Groups_Ouminus__class_Ouminus(U_1270,U_1271),U_1271) = c_Groups_Ozero__class_Ozero(U_1270)
| ~ class_Groups_Ogroup__add(U_1270) ),
inference(clausify,[status(thm)],[f_411_3]) ).
fof(f_412_1,plain,
! [V_a,T_a] :
( c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__left__minus]) ).
fof(f_412_2,plain,
! [U_1273,U_1272] :
( c_Groups_Oplus__class_Oplus(U_1272,c_Groups_Ouminus__class_Ouminus(U_1272,U_1273),U_1273) = c_Groups_Ozero__class_Ozero(U_1272)
| ~ class_Groups_Oab__group__add(U_1272) ),
inference(variable_rename,[status(thm)],[f_412_1]) ).
fof(f_412_3,plain,
! [U_1273,U_1272] :
( c_Groups_Oplus__class_Oplus(U_1272,c_Groups_Ouminus__class_Ouminus(U_1272,U_1273),U_1273) = c_Groups_Ozero__class_Ozero(U_1272)
| ~ class_Groups_Oab__group__add(U_1272) ),
inference(definitional_conversion,[status(esa)],[f_412_2]) ).
cnf(f_412_4,plain,
( c_Groups_Oplus__class_Oplus(U_1272,c_Groups_Ouminus__class_Ouminus(U_1272,U_1273),U_1273) = c_Groups_Ozero__class_Ozero(U_1272)
| ~ class_Groups_Oab__group__add(U_1272) ),
inference(clausify,[status(thm)],[f_412_3]) ).
fof(f_413_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,V_a) = V_b
| c_Groups_Oplus__class_Oplus(T_a,V_a,V_b) != c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__unique]) ).
fof(f_413_2,plain,
! [U_1276,U_1275,U_1274] :
( c_Groups_Ouminus__class_Ouminus(U_1274,U_1275) = U_1276
| c_Groups_Oplus__class_Oplus(U_1274,U_1275,U_1276) != c_Groups_Ozero__class_Ozero(U_1274)
| ~ class_Groups_Ogroup__add(U_1274) ),
inference(variable_rename,[status(thm)],[f_413_1]) ).
fof(f_413_3,plain,
! [U_1274,U_1275,U_1276] :
( c_Groups_Ouminus__class_Ouminus(U_1274,U_1275) = U_1276
| c_Groups_Oplus__class_Oplus(U_1274,U_1275,U_1276) != c_Groups_Ozero__class_Ozero(U_1274)
| ~ class_Groups_Ogroup__add(U_1274) ),
inference(definitional_conversion,[status(esa)],[f_413_2]) ).
cnf(f_413_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1274,U_1275) = U_1276
| c_Groups_Oplus__class_Oplus(U_1274,U_1275,U_1276) != c_Groups_Ozero__class_Ozero(U_1274)
| ~ class_Groups_Ogroup__add(U_1274) ),
inference(clausify,[status(thm)],[f_413_3]) ).
fof(f_414_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_y_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) )
& ( V_y_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_x_2)
| c_Groups_Oplus__class_Oplus(T_a,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_add__eq__0__iff]) ).
fof(f_414_2,plain,
! [U_1279,U_1278,U_1277] :
( ( ( c_Groups_Oplus__class_Oplus(U_1277,U_1278,U_1279) = c_Groups_Ozero__class_Ozero(U_1277)
| U_1279 != c_Groups_Ouminus__class_Ouminus(U_1277,U_1278) )
& ( U_1279 = c_Groups_Ouminus__class_Ouminus(U_1277,U_1278)
| c_Groups_Oplus__class_Oplus(U_1277,U_1278,U_1279) != c_Groups_Ozero__class_Ozero(U_1277) ) )
| ~ class_Groups_Ogroup__add(U_1277) ),
inference(variable_rename,[status(thm)],[f_414_1]) ).
fof(f_414_3,plain,
( ! [U_1278,U_1277,U_1279] :
( c_Groups_Oplus__class_Oplus(U_1277,U_1278,U_1279) = c_Groups_Ozero__class_Ozero(U_1277)
| U_1279 != c_Groups_Ouminus__class_Ouminus(U_1277,U_1278)
| ~ sP135(U_1278,U_1277,U_1279) )
& ! [U_1278,U_1277,U_1279] :
( U_1279 = c_Groups_Ouminus__class_Ouminus(U_1277,U_1278)
| c_Groups_Oplus__class_Oplus(U_1277,U_1278,U_1279) != c_Groups_Ozero__class_Ozero(U_1277)
| ~ sP135(U_1278,U_1277,U_1279) )
& ! [U_1278,U_1277,U_1279] :
( sP135(U_1278,U_1277,U_1279)
| ~ class_Groups_Ogroup__add(U_1277) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135])],[f_414_2]) ).
cnf(f_414_4,plain,
( sP135(U_1278,U_1277,U_1279)
| ~ class_Groups_Ogroup__add(U_1277) ),
inference(clausify,[status(thm)],[f_414_3]) ).
cnf(f_414_5,plain,
( U_1279 = c_Groups_Ouminus__class_Ouminus(U_1277,U_1278)
| c_Groups_Oplus__class_Oplus(U_1277,U_1278,U_1279) != c_Groups_Ozero__class_Ozero(U_1277)
| ~ sP135(U_1278,U_1277,U_1279) ),
inference(clausify,[status(thm)],[f_414_3]) ).
cnf(f_414_6,plain,
( c_Groups_Oplus__class_Oplus(U_1277,U_1278,U_1279) = c_Groups_Ozero__class_Ozero(U_1277)
| U_1279 != c_Groups_Ouminus__class_Ouminus(U_1277,U_1278)
| ~ sP135(U_1278,U_1277,U_1279) ),
inference(clausify,[status(thm)],[f_414_3]) ).
fof(f_415_1,plain,
! [V_x_2,T_a] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a)
| ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
& V_x_2 != c_Groups_Oone__class_Oone(T_a) ) )
& ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| V_x_2 = c_Groups_Oone__class_Oone(T_a)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(T_a) ),
inference(fof_nnf,[status(thm)],[fact_square__eq__1__iff]) ).
fof(f_415_2,plain,
! [U_1281,U_1280] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1280),U_1281),U_1281) = c_Groups_Oone__class_Oone(U_1280)
| ( U_1281 != c_Groups_Ouminus__class_Ouminus(U_1280,c_Groups_Oone__class_Oone(U_1280))
& U_1281 != c_Groups_Oone__class_Oone(U_1280) ) )
& ( U_1281 = c_Groups_Ouminus__class_Ouminus(U_1280,c_Groups_Oone__class_Oone(U_1280))
| U_1281 = c_Groups_Oone__class_Oone(U_1280)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1280),U_1281),U_1281) != c_Groups_Oone__class_Oone(U_1280) ) )
| ~ class_Rings_Oring__1__no__zero__divisors(U_1280) ),
inference(variable_rename,[status(thm)],[f_415_1]) ).
fof(f_415_3,plain,
( ! [U_1281,U_1280] :
( U_1281 != c_Groups_Ouminus__class_Ouminus(U_1280,c_Groups_Oone__class_Oone(U_1280))
| ~ sP136(U_1281,U_1280) )
& ! [U_1281,U_1280] :
( U_1281 != c_Groups_Oone__class_Oone(U_1280)
| ~ sP136(U_1281,U_1280) )
& ! [U_1281,U_1280] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1280),U_1281),U_1281) = c_Groups_Oone__class_Oone(U_1280)
| sP136(U_1281,U_1280)
| ~ sP137(U_1281,U_1280) )
& ! [U_1281,U_1280] :
( U_1281 = c_Groups_Ouminus__class_Ouminus(U_1280,c_Groups_Oone__class_Oone(U_1280))
| U_1281 = c_Groups_Oone__class_Oone(U_1280)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1280),U_1281),U_1281) != c_Groups_Oone__class_Oone(U_1280)
| ~ sP137(U_1281,U_1280) )
& ! [U_1281,U_1280] :
( sP137(U_1281,U_1280)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1280) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136,sP137])],[f_415_2]) ).
cnf(f_415_4,plain,
( sP137(U_1281,U_1280)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1280) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_5,plain,
( U_1281 = c_Groups_Ouminus__class_Ouminus(U_1280,c_Groups_Oone__class_Oone(U_1280))
| U_1281 = c_Groups_Oone__class_Oone(U_1280)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1280),U_1281),U_1281) != c_Groups_Oone__class_Oone(U_1280)
| ~ sP137(U_1281,U_1280) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1280),U_1281),U_1281) = c_Groups_Oone__class_Oone(U_1280)
| sP136(U_1281,U_1280)
| ~ sP137(U_1281,U_1280) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_7,plain,
( U_1281 != c_Groups_Oone__class_Oone(U_1280)
| ~ sP136(U_1281,U_1280) ),
inference(clausify,[status(thm)],[f_415_3]) ).
cnf(f_415_8,plain,
( U_1281 != c_Groups_Ouminus__class_Ouminus(U_1280,c_Groups_Oone__class_Oone(U_1280))
| ~ sP136(U_1281,U_1280) ),
inference(clausify,[status(thm)],[f_415_3]) ).
fof(f_416_1,plain,
! [V_x,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,V_x) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_x)
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J]) ).
fof(f_416_2,plain,
! [U_1283,U_1282] :
( c_Groups_Ouminus__class_Ouminus(U_1282,U_1283) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1282),c_Groups_Ouminus__class_Ouminus(U_1282,c_Groups_Oone__class_Oone(U_1282))),U_1283)
| ~ class_Rings_Ocomm__ring__1(U_1282) ),
inference(variable_rename,[status(thm)],[f_416_1]) ).
fof(f_416_3,plain,
! [U_1282,U_1283] :
( c_Groups_Ouminus__class_Ouminus(U_1282,U_1283) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1282),c_Groups_Ouminus__class_Ouminus(U_1282,c_Groups_Oone__class_Oone(U_1282))),U_1283)
| ~ class_Rings_Ocomm__ring__1(U_1282) ),
inference(definitional_conversion,[status(esa)],[f_416_2]) ).
cnf(f_416_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1282,U_1283) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1282),c_Groups_Ouminus__class_Ouminus(U_1282,c_Groups_Oone__class_Oone(U_1282))),U_1283)
| ~ class_Rings_Ocomm__ring__1(U_1282) ),
inference(clausify,[status(thm)],[f_416_3]) ).
fof(f_417_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Groups_Oabs__class_Oabs(T_a,V_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__ge__minus__self]) ).
fof(f_417_2,plain,
! [U_1285,U_1284] :
( c_Orderings_Oord__class_Oless__eq(U_1284,c_Groups_Ouminus__class_Ouminus(U_1284,U_1285),c_Groups_Oabs__class_Oabs(U_1284,U_1285))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1284) ),
inference(variable_rename,[status(thm)],[f_417_1]) ).
fof(f_417_3,plain,
! [U_1285,U_1284] :
( c_Orderings_Oord__class_Oless__eq(U_1284,c_Groups_Ouminus__class_Ouminus(U_1284,U_1285),c_Groups_Oabs__class_Oabs(U_1284,U_1285))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1284) ),
inference(definitional_conversion,[status(esa)],[f_417_2]) ).
cnf(f_417_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1284,c_Groups_Ouminus__class_Ouminus(U_1284,U_1285),c_Groups_Oabs__class_Oabs(U_1284,U_1285))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1284) ),
inference(clausify,[status(thm)],[f_417_3]) ).
fof(f_418_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless__eq(T_a,V_a_2,V_b_2) )
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__iff]) ).
fof(f_418_2,plain,
! [U_1288,U_1287,U_1286] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Oabs__class_Oabs(U_1286,U_1287),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Ouminus__class_Ouminus(U_1286,U_1287),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(U_1286,U_1287,U_1288) )
& ( ( c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Ouminus__class_Ouminus(U_1286,U_1287),U_1288)
& c_Orderings_Oord__class_Oless__eq(U_1286,U_1287,U_1288) )
| ~ c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Oabs__class_Oabs(U_1286,U_1287),U_1288) ) )
| ~ class_Groups_Oordered__ab__group__add__abs(U_1286) ),
inference(variable_rename,[status(thm)],[f_418_1]) ).
fof(f_418_3,plain,
( ! [U_1288,U_1287,U_1286] :
( c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Ouminus__class_Ouminus(U_1286,U_1287),U_1288)
| ~ sP138(U_1288,U_1287,U_1286) )
& ! [U_1288,U_1287,U_1286] :
( c_Orderings_Oord__class_Oless__eq(U_1286,U_1287,U_1288)
| ~ sP138(U_1288,U_1287,U_1286) )
& ! [U_1288,U_1287,U_1286] :
( c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Oabs__class_Oabs(U_1286,U_1287),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Ouminus__class_Ouminus(U_1286,U_1287),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(U_1286,U_1287,U_1288)
| ~ sP139(U_1288,U_1287,U_1286) )
& ! [U_1288,U_1287,U_1286] :
( sP138(U_1288,U_1287,U_1286)
| ~ c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Oabs__class_Oabs(U_1286,U_1287),U_1288)
| ~ sP139(U_1288,U_1287,U_1286) )
& ! [U_1288,U_1287,U_1286] :
( sP139(U_1288,U_1287,U_1286)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1286) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138,sP139])],[f_418_2]) ).
cnf(f_418_4,plain,
( sP139(U_1288,U_1287,U_1286)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1286) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_5,plain,
( sP138(U_1288,U_1287,U_1286)
| ~ c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Oabs__class_Oabs(U_1286,U_1287),U_1288)
| ~ sP139(U_1288,U_1287,U_1286) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Oabs__class_Oabs(U_1286,U_1287),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Ouminus__class_Ouminus(U_1286,U_1287),U_1288)
| ~ c_Orderings_Oord__class_Oless__eq(U_1286,U_1287,U_1288)
| ~ sP139(U_1288,U_1287,U_1286) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_1286,U_1287,U_1288)
| ~ sP138(U_1288,U_1287,U_1286) ),
inference(clausify,[status(thm)],[f_418_3]) ).
cnf(f_418_8,plain,
( c_Orderings_Oord__class_Oless__eq(U_1286,c_Groups_Ouminus__class_Ouminus(U_1286,U_1287),U_1288)
| ~ sP138(U_1288,U_1287,U_1286) ),
inference(clausify,[status(thm)],[f_418_3]) ).
fof(f_419_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,V_b)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__leI]) ).
fof(f_419_2,plain,
! [U_1291,U_1290,U_1289] :
( c_Orderings_Oord__class_Oless__eq(U_1289,c_Groups_Oabs__class_Oabs(U_1289,U_1290),U_1291)
| ~ c_Orderings_Oord__class_Oless__eq(U_1289,c_Groups_Ouminus__class_Ouminus(U_1289,U_1290),U_1291)
| ~ c_Orderings_Oord__class_Oless__eq(U_1289,U_1290,U_1291)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1289) ),
inference(variable_rename,[status(thm)],[f_419_1]) ).
fof(f_419_3,plain,
! [U_1289,U_1290,U_1291] :
( c_Orderings_Oord__class_Oless__eq(U_1289,c_Groups_Oabs__class_Oabs(U_1289,U_1290),U_1291)
| ~ c_Orderings_Oord__class_Oless__eq(U_1289,c_Groups_Ouminus__class_Ouminus(U_1289,U_1290),U_1291)
| ~ c_Orderings_Oord__class_Oless__eq(U_1289,U_1290,U_1291)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1289) ),
inference(definitional_conversion,[status(esa)],[f_419_2]) ).
cnf(f_419_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1289,c_Groups_Oabs__class_Oabs(U_1289,U_1290),U_1291)
| ~ c_Orderings_Oord__class_Oless__eq(U_1289,c_Groups_Ouminus__class_Ouminus(U_1289,U_1290),U_1291)
| ~ c_Orderings_Oord__class_Oless__eq(U_1289,U_1290,U_1291)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1289) ),
inference(clausify,[status(thm)],[f_419_3]) ).
fof(f_420_1,plain,
! [V_b,V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a),V_b)
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__D2]) ).
fof(f_420_2,plain,
! [U_1294,U_1293,U_1292] :
( c_Orderings_Oord__class_Oless__eq(U_1292,c_Groups_Ouminus__class_Ouminus(U_1292,U_1293),U_1294)
| ~ c_Orderings_Oord__class_Oless__eq(U_1292,c_Groups_Oabs__class_Oabs(U_1292,U_1293),U_1294)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1292) ),
inference(variable_rename,[status(thm)],[f_420_1]) ).
fof(f_420_3,plain,
! [U_1292,U_1294,U_1293] :
( c_Orderings_Oord__class_Oless__eq(U_1292,c_Groups_Ouminus__class_Ouminus(U_1292,U_1293),U_1294)
| ~ c_Orderings_Oord__class_Oless__eq(U_1292,c_Groups_Oabs__class_Oabs(U_1292,U_1293),U_1294)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1292) ),
inference(definitional_conversion,[status(esa)],[f_420_2]) ).
cnf(f_420_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1292,c_Groups_Ouminus__class_Ouminus(U_1292,U_1293),U_1294)
| ~ c_Orderings_Oord__class_Oless__eq(U_1292,c_Groups_Oabs__class_Oabs(U_1292,U_1293),U_1294)
| ~ class_Groups_Oordered__ab__group__add__abs(U_1292) ),
inference(clausify,[status(thm)],[f_420_3]) ).
fof(f_421_1,plain,
! [V_b_2,V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
& ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a_2),V_b_2)
& c_Orderings_Oord__class_Oless(T_a,V_a_2,V_b_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a_2),V_b_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__less__iff]) ).
fof(f_421_2,plain,
! [U_1297,U_1296,U_1295] :
( ( ( c_Orderings_Oord__class_Oless(U_1295,c_Groups_Oabs__class_Oabs(U_1295,U_1296),U_1297)
| ~ c_Orderings_Oord__class_Oless(U_1295,c_Groups_Ouminus__class_Ouminus(U_1295,U_1296),U_1297)
| ~ c_Orderings_Oord__class_Oless(U_1295,U_1296,U_1297) )
& ( ( c_Orderings_Oord__class_Oless(U_1295,c_Groups_Ouminus__class_Ouminus(U_1295,U_1296),U_1297)
& c_Orderings_Oord__class_Oless(U_1295,U_1296,U_1297) )
| ~ c_Orderings_Oord__class_Oless(U_1295,c_Groups_Oabs__class_Oabs(U_1295,U_1296),U_1297) ) )
| ~ class_Rings_Olinordered__idom(U_1295) ),
inference(variable_rename,[status(thm)],[f_421_1]) ).
fof(f_421_3,plain,
( ! [U_1297,U_1296,U_1295] :
( c_Orderings_Oord__class_Oless(U_1295,c_Groups_Ouminus__class_Ouminus(U_1295,U_1296),U_1297)
| ~ sP140(U_1297,U_1296,U_1295) )
& ! [U_1297,U_1296,U_1295] :
( c_Orderings_Oord__class_Oless(U_1295,U_1296,U_1297)
| ~ sP140(U_1297,U_1296,U_1295) )
& ! [U_1297,U_1296,U_1295] :
( c_Orderings_Oord__class_Oless(U_1295,c_Groups_Oabs__class_Oabs(U_1295,U_1296),U_1297)
| ~ c_Orderings_Oord__class_Oless(U_1295,c_Groups_Ouminus__class_Ouminus(U_1295,U_1296),U_1297)
| ~ c_Orderings_Oord__class_Oless(U_1295,U_1296,U_1297)
| ~ sP141(U_1297,U_1296,U_1295) )
& ! [U_1297,U_1296,U_1295] :
( sP140(U_1297,U_1296,U_1295)
| ~ c_Orderings_Oord__class_Oless(U_1295,c_Groups_Oabs__class_Oabs(U_1295,U_1296),U_1297)
| ~ sP141(U_1297,U_1296,U_1295) )
& ! [U_1297,U_1296,U_1295] :
( sP141(U_1297,U_1296,U_1295)
| ~ class_Rings_Olinordered__idom(U_1295) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140,sP141])],[f_421_2]) ).
cnf(f_421_4,plain,
( sP141(U_1297,U_1296,U_1295)
| ~ class_Rings_Olinordered__idom(U_1295) ),
inference(clausify,[status(thm)],[f_421_3]) ).
cnf(f_421_5,plain,
( sP140(U_1297,U_1296,U_1295)
| ~ c_Orderings_Oord__class_Oless(U_1295,c_Groups_Oabs__class_Oabs(U_1295,U_1296),U_1297)
| ~ sP141(U_1297,U_1296,U_1295) ),
inference(clausify,[status(thm)],[f_421_3]) ).
cnf(f_421_6,plain,
( c_Orderings_Oord__class_Oless(U_1295,c_Groups_Oabs__class_Oabs(U_1295,U_1296),U_1297)
| ~ c_Orderings_Oord__class_Oless(U_1295,c_Groups_Ouminus__class_Ouminus(U_1295,U_1296),U_1297)
| ~ c_Orderings_Oord__class_Oless(U_1295,U_1296,U_1297)
| ~ sP141(U_1297,U_1296,U_1295) ),
inference(clausify,[status(thm)],[f_421_3]) ).
cnf(f_421_7,plain,
( c_Orderings_Oord__class_Oless(U_1295,U_1296,U_1297)
| ~ sP140(U_1297,U_1296,U_1295) ),
inference(clausify,[status(thm)],[f_421_3]) ).
cnf(f_421_8,plain,
( c_Orderings_Oord__class_Oless(U_1295,c_Groups_Ouminus__class_Ouminus(U_1295,U_1296),U_1297)
| ~ sP140(U_1297,U_1296,U_1295) ),
inference(clausify,[status(thm)],[f_421_3]) ).
fof(f_422_1,plain,
! [V_x,V_u] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_u),V_u)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_x),V_x)),
inference(fof_nnf,[status(thm)],[fact_real__minus__mult__self__le]) ).
fof(f_422_2,plain,
! [U_1299,U_1298] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1298),U_1298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1299),U_1299)),
inference(variable_rename,[status(thm)],[f_422_1]) ).
fof(f_422_3,plain,
! [U_1298,U_1299] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1298),U_1298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1299),U_1299)),
inference(definitional_conversion,[status(esa)],[f_422_2]) ).
cnf(f_422_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1298),U_1298)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_1299),U_1299)),
inference(clausify,[status(thm)],[f_422_3]) ).
fof(f_423_1,plain,
! [V_a_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x_2 != V_a_2 )
& ( V_x_2 = V_a_2
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a_2)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__minus__iff]) ).
fof(f_423_2,plain,
! [U_1301,U_1300] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1300,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1301)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1300 != U_1301 )
& ( U_1300 = U_1301
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1300,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1301)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_423_1]) ).
fof(f_423_3,plain,
( ! [U_1305,U_1303] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1303,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1305)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1303 != U_1305 )
& ! [U_1304,U_1302] :
( U_1302 = U_1304
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1302,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1304)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_423_2]) ).
fof(f_423_4,plain,
( ! [U_1303,U_1305] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1303,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1305)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1303 != U_1305 )
& ! [U_1302,U_1304] :
( U_1302 = U_1304
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1302,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1304)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa)],[f_423_3]) ).
cnf(f_423_5,plain,
( U_1302 = U_1304
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1302,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1304)) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_423_4]) ).
cnf(f_423_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1303,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1305)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1303 != U_1305 ),
inference(clausify,[status(thm)],[f_423_4]) ).
fof(f_424_1,plain,
! [V_y_2,V_x_2] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_y_2 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2) )
& ( V_y_2 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__eq__0__iff]) ).
fof(f_424_2,plain,
! [U_1307,U_1306] :
( ( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1306,U_1307) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1307 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1306) )
& ( U_1307 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1306)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1306,U_1307) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_424_1]) ).
fof(f_424_3,plain,
( ! [U_1311,U_1309] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1309,U_1311) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1311 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1309) )
& ! [U_1310,U_1308] :
( U_1310 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1308)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1308,U_1310) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_424_2]) ).
fof(f_424_4,plain,
( ! [U_1311,U_1309] :
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1309,U_1311) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1311 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1309) )
& ! [U_1308,U_1310] :
( U_1310 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1308)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1308,U_1310) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa)],[f_424_3]) ).
cnf(f_424_5,plain,
( U_1310 = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1308)
| c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1308,U_1310) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_424_4]) ).
cnf(f_424_6,plain,
( c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1309,U_1311) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1311 != c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1309) ),
inference(clausify,[status(thm)],[f_424_4]) ).
fof(f_425_1,plain,
! [V_ra_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_ra_2)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_ra_2),V_x_2) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_x_2),V_ra_2) ) ),
inference(fof_nnf,[status(thm)],[fact_abs__le__interval__iff]) ).
fof(f_425_2,plain,
! [U_1313,U_1312] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1312),U_1313)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1312,U_1313)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1313),U_1312) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1312,U_1313)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1313),U_1312) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1312),U_1313) ) ),
inference(variable_rename,[status(thm)],[f_425_1]) ).
fof(f_425_3,plain,
( ! [U_1317,U_1315] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1315),U_1317)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1315,U_1317)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1317),U_1315) )
& ! [U_1316,U_1314] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1314,U_1316)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1316),U_1314) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1314),U_1316) ) ),
inference(miniscope,[status(thm)],[f_425_2]) ).
fof(f_425_4,plain,
( ! [U_1314,U_1316] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1314,U_1316)
| ~ sP142(U_1314,U_1316) )
& ! [U_1314,U_1316] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1316),U_1314)
| ~ sP142(U_1314,U_1316) )
& ! [U_1315,U_1317] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1315),U_1317)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1315,U_1317)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1317),U_1315) )
& ! [U_1314,U_1316] :
( sP142(U_1314,U_1316)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1314),U_1316) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142])],[f_425_3]) ).
cnf(f_425_5,plain,
( sP142(U_1314,U_1316)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1314),U_1316) ),
inference(clausify,[status(thm)],[f_425_4]) ).
cnf(f_425_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1315),U_1317)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1315,U_1317)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1317),U_1315) ),
inference(clausify,[status(thm)],[f_425_4]) ).
cnf(f_425_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1316),U_1314)
| ~ sP142(U_1314,U_1316) ),
inference(clausify,[status(thm)],[f_425_4]) ).
cnf(f_425_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1314,U_1316)
| ~ sP142(U_1314,U_1316) ),
inference(clausify,[status(thm)],[f_425_4]) ).
fof(f_426_1,plain,
! [V_y,V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x))),
inference(fof_nnf,[status(thm)],[fact_abs__minus__add__cancel]) ).
fof(f_426_2,plain,
! [U_1319,U_1318] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1318,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1319))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1319,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1318))),
inference(variable_rename,[status(thm)],[f_426_1]) ).
fof(f_426_3,plain,
! [U_1319,U_1318] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1318,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1319))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1319,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1318))),
inference(definitional_conversion,[status(esa)],[f_426_2]) ).
cnf(f_426_4,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1318,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1319))) = c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1319,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1318))),
inference(clausify,[status(thm)],[f_426_3]) ).
fof(f_427_1,plain,
! [V_p,T_a] :
( c_Polynomial_Opos__poly(T_a,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_p))
| c_Polynomial_Opos__poly(T_a,V_p)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pos__poly__total]) ).
fof(f_427_2,plain,
! [U_1321,U_1320] :
( c_Polynomial_Opos__poly(U_1320,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1320),U_1321))
| c_Polynomial_Opos__poly(U_1320,U_1321)
| U_1321 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1320))
| ~ class_Rings_Olinordered__idom(U_1320) ),
inference(variable_rename,[status(thm)],[f_427_1]) ).
fof(f_427_3,plain,
! [U_1320,U_1321] :
( c_Polynomial_Opos__poly(U_1320,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1320),U_1321))
| c_Polynomial_Opos__poly(U_1320,U_1321)
| U_1321 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1320))
| ~ class_Rings_Olinordered__idom(U_1320) ),
inference(definitional_conversion,[status(esa)],[f_427_2]) ).
cnf(f_427_4,plain,
( c_Polynomial_Opos__poly(U_1320,c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1320),U_1321))
| c_Polynomial_Opos__poly(U_1320,U_1321)
| U_1321 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1320))
| ~ class_Rings_Olinordered__idom(U_1320) ),
inference(clausify,[status(thm)],[f_427_3]) ).
fof(f_428_1,plain,
! [V_q,T_a] :
( c_Polynomial_Opcompose(T_a,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_pcompose__0]) ).
fof(f_428_2,plain,
! [U_1323,U_1322] :
( c_Polynomial_Opcompose(U_1322,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1322)),U_1323) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1322))
| ~ class_Rings_Ocomm__semiring__0(U_1322) ),
inference(variable_rename,[status(thm)],[f_428_1]) ).
fof(f_428_3,plain,
! [U_1323,U_1322] :
( c_Polynomial_Opcompose(U_1322,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1322)),U_1323) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1322))
| ~ class_Rings_Ocomm__semiring__0(U_1322) ),
inference(definitional_conversion,[status(esa)],[f_428_2]) ).
cnf(f_428_4,plain,
( c_Polynomial_Opcompose(U_1322,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1322)),U_1323) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1322))
| ~ class_Rings_Ocomm__semiring__0(U_1322) ),
inference(clausify,[status(thm)],[f_428_3]) ).
fof(f_429_1,plain,
! [V_a,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oabs__class_Oabs(T_a,V_a)),c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__minus__le__zero]) ).
fof(f_429_2,plain,
! [U_1325,U_1324] :
( c_Orderings_Oord__class_Oless__eq(U_1324,c_Groups_Ouminus__class_Ouminus(U_1324,c_Groups_Oabs__class_Oabs(U_1324,U_1325)),c_Groups_Ozero__class_Ozero(U_1324))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1324) ),
inference(variable_rename,[status(thm)],[f_429_1]) ).
fof(f_429_3,plain,
! [U_1324,U_1325] :
( c_Orderings_Oord__class_Oless__eq(U_1324,c_Groups_Ouminus__class_Ouminus(U_1324,c_Groups_Oabs__class_Oabs(U_1324,U_1325)),c_Groups_Ozero__class_Ozero(U_1324))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1324) ),
inference(definitional_conversion,[status(esa)],[f_429_2]) ).
cnf(f_429_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1324,c_Groups_Ouminus__class_Ouminus(U_1324,c_Groups_Oabs__class_Oabs(U_1324,U_1325)),c_Groups_Ozero__class_Ozero(U_1324))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1324) ),
inference(clausify,[status(thm)],[f_429_3]) ).
fof(f_430_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__nonpos]) ).
fof(f_430_2,plain,
! [U_1327,U_1326] :
( c_Groups_Oabs__class_Oabs(U_1326,U_1327) = c_Groups_Ouminus__class_Ouminus(U_1326,U_1327)
| ~ c_Orderings_Oord__class_Oless__eq(U_1326,U_1327,c_Groups_Ozero__class_Ozero(U_1326))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1326) ),
inference(variable_rename,[status(thm)],[f_430_1]) ).
fof(f_430_3,plain,
! [U_1326,U_1327] :
( c_Groups_Oabs__class_Oabs(U_1326,U_1327) = c_Groups_Ouminus__class_Ouminus(U_1326,U_1327)
| ~ c_Orderings_Oord__class_Oless__eq(U_1326,U_1327,c_Groups_Ozero__class_Ozero(U_1326))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1326) ),
inference(definitional_conversion,[status(esa)],[f_430_2]) ).
cnf(f_430_4,plain,
( c_Groups_Oabs__class_Oabs(U_1326,U_1327) = c_Groups_Ouminus__class_Ouminus(U_1326,U_1327)
| ~ c_Orderings_Oord__class_Oless__eq(U_1326,U_1327,c_Groups_Ozero__class_Ozero(U_1326))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1326) ),
inference(clausify,[status(thm)],[f_430_3]) ).
fof(f_431_1,plain,
! [V_a,T_a] :
( ( ( c_Groups_Oabs__class_Oabs(T_a,V_a) = V_a
| c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Groups_Oabs__if(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__if]) ).
fof(f_431_2,plain,
! [U_1329,U_1328] :
( ( ( c_Groups_Oabs__class_Oabs(U_1328,U_1329) = U_1329
| c_Orderings_Oord__class_Oless(U_1328,U_1329,c_Groups_Ozero__class_Ozero(U_1328)) )
& ( c_Groups_Oabs__class_Oabs(U_1328,U_1329) = c_Groups_Ouminus__class_Ouminus(U_1328,U_1329)
| ~ c_Orderings_Oord__class_Oless(U_1328,U_1329,c_Groups_Ozero__class_Ozero(U_1328)) ) )
| ~ class_Groups_Oabs__if(U_1328) ),
inference(variable_rename,[status(thm)],[f_431_1]) ).
fof(f_431_3,plain,
( ! [U_1329,U_1328] :
( c_Groups_Oabs__class_Oabs(U_1328,U_1329) = U_1329
| c_Orderings_Oord__class_Oless(U_1328,U_1329,c_Groups_Ozero__class_Ozero(U_1328))
| ~ sP143(U_1329,U_1328) )
& ! [U_1329,U_1328] :
( c_Groups_Oabs__class_Oabs(U_1328,U_1329) = c_Groups_Ouminus__class_Ouminus(U_1328,U_1329)
| ~ c_Orderings_Oord__class_Oless(U_1328,U_1329,c_Groups_Ozero__class_Ozero(U_1328))
| ~ sP143(U_1329,U_1328) )
& ! [U_1329,U_1328] :
( sP143(U_1329,U_1328)
| ~ class_Groups_Oabs__if(U_1328) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143])],[f_431_2]) ).
cnf(f_431_4,plain,
( sP143(U_1329,U_1328)
| ~ class_Groups_Oabs__if(U_1328) ),
inference(clausify,[status(thm)],[f_431_3]) ).
cnf(f_431_5,plain,
( c_Groups_Oabs__class_Oabs(U_1328,U_1329) = c_Groups_Ouminus__class_Ouminus(U_1328,U_1329)
| ~ c_Orderings_Oord__class_Oless(U_1328,U_1329,c_Groups_Ozero__class_Ozero(U_1328))
| ~ sP143(U_1329,U_1328) ),
inference(clausify,[status(thm)],[f_431_3]) ).
cnf(f_431_6,plain,
( c_Groups_Oabs__class_Oabs(U_1328,U_1329) = U_1329
| c_Orderings_Oord__class_Oless(U_1328,U_1329,c_Groups_Ozero__class_Ozero(U_1328))
| ~ sP143(U_1329,U_1328) ),
inference(clausify,[status(thm)],[f_431_3]) ).
fof(f_432_1,plain,
! [V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ c_Orderings_Oord__class_Oless(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Groups_Oordered__ab__group__add__abs(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__of__neg]) ).
fof(f_432_2,plain,
! [U_1331,U_1330] :
( c_Groups_Oabs__class_Oabs(U_1330,U_1331) = c_Groups_Ouminus__class_Ouminus(U_1330,U_1331)
| ~ c_Orderings_Oord__class_Oless(U_1330,U_1331,c_Groups_Ozero__class_Ozero(U_1330))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1330) ),
inference(variable_rename,[status(thm)],[f_432_1]) ).
fof(f_432_3,plain,
! [U_1331,U_1330] :
( c_Groups_Oabs__class_Oabs(U_1330,U_1331) = c_Groups_Ouminus__class_Ouminus(U_1330,U_1331)
| ~ c_Orderings_Oord__class_Oless(U_1330,U_1331,c_Groups_Ozero__class_Ozero(U_1330))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1330) ),
inference(definitional_conversion,[status(esa)],[f_432_2]) ).
cnf(f_432_4,plain,
( c_Groups_Oabs__class_Oabs(U_1330,U_1331) = c_Groups_Ouminus__class_Ouminus(U_1330,U_1331)
| ~ c_Orderings_Oord__class_Oless(U_1330,U_1331,c_Groups_Ozero__class_Ozero(U_1330))
| ~ class_Groups_Oordered__ab__group__add__abs(U_1330) ),
inference(clausify,[status(thm)],[f_432_3]) ).
fof(f_433_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Polynomial_Opcompose(T_a,V_p,V_q)),V_x) = hAPP(c_Polynomial_Opoly(T_a,V_p),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__semiring__0(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__pcompose]) ).
fof(f_433_2,plain,
! [U_1335,U_1334,U_1333,U_1332] :
( hAPP(c_Polynomial_Opoly(U_1332,c_Polynomial_Opcompose(U_1332,U_1333,U_1334)),U_1335) = hAPP(c_Polynomial_Opoly(U_1332,U_1333),hAPP(c_Polynomial_Opoly(U_1332,U_1334),U_1335))
| ~ class_Rings_Ocomm__semiring__0(U_1332) ),
inference(variable_rename,[status(thm)],[f_433_1]) ).
fof(f_433_3,plain,
! [U_1332,U_1333,U_1334,U_1335] :
( hAPP(c_Polynomial_Opoly(U_1332,c_Polynomial_Opcompose(U_1332,U_1333,U_1334)),U_1335) = hAPP(c_Polynomial_Opoly(U_1332,U_1333),hAPP(c_Polynomial_Opoly(U_1332,U_1334),U_1335))
| ~ class_Rings_Ocomm__semiring__0(U_1332) ),
inference(definitional_conversion,[status(esa)],[f_433_2]) ).
cnf(f_433_4,plain,
( hAPP(c_Polynomial_Opoly(U_1332,c_Polynomial_Opcompose(U_1332,U_1333,U_1334)),U_1335) = hAPP(c_Polynomial_Opoly(U_1332,U_1333),hAPP(c_Polynomial_Opoly(U_1332,U_1334),U_1335))
| ~ class_Rings_Ocomm__semiring__0(U_1332) ),
inference(clausify,[status(thm)],[f_433_3]) ).
fof(f_434_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__le__add__iff]) ).
fof(f_434_2,plain,
! [U_1337,U_1336] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1336,U_1337))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1336),U_1337) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1336),U_1337)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1336,U_1337)) ) ),
inference(variable_rename,[status(thm)],[f_434_1]) ).
fof(f_434_3,plain,
( ! [U_1341,U_1339] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1339,U_1341))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1339),U_1341) )
& ! [U_1340,U_1338] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1338),U_1340)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1338,U_1340)) ) ),
inference(miniscope,[status(thm)],[f_434_2]) ).
fof(f_434_4,plain,
( ! [U_1339,U_1341] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1339,U_1341))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1339),U_1341) )
& ! [U_1338,U_1340] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1338),U_1340)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1338,U_1340)) ) ),
inference(definitional_conversion,[status(esa)],[f_434_3]) ).
cnf(f_434_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1338),U_1340)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1338,U_1340)) ),
inference(clausify,[status(thm)],[f_434_4]) ).
cnf(f_434_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1339,U_1341))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1339),U_1341) ),
inference(clausify,[status(thm)],[f_434_4]) ).
fof(f_435_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__le__0__iff]) ).
fof(f_435_2,plain,
! [U_1343,U_1342] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1342,U_1343),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1343,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1342)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1343,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1342))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1342,U_1343),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_435_1]) ).
fof(f_435_3,plain,
( ! [U_1347,U_1345] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1345,U_1347),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1347,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1345)) )
& ! [U_1346,U_1344] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1346,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1344))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1344,U_1346),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_435_2]) ).
fof(f_435_4,plain,
( ! [U_1347,U_1345] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1345,U_1347),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1347,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1345)) )
& ! [U_1344,U_1346] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1346,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1344))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1344,U_1346),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_435_3]) ).
cnf(f_435_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1346,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1344))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1344,U_1346),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_435_4]) ).
cnf(f_435_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1345,U_1347),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1347,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1345)) ),
inference(clausify,[status(thm)],[f_435_4]) ).
fof(f_436_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2),V_y_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__0__less__add__iff]) ).
fof(f_436_2,plain,
! [U_1349,U_1348] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1348,U_1349))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1348),U_1349) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1348),U_1349)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1348,U_1349)) ) ),
inference(variable_rename,[status(thm)],[f_436_1]) ).
fof(f_436_3,plain,
( ! [U_1353,U_1351] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1351,U_1353))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1351),U_1353) )
& ! [U_1352,U_1350] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1350),U_1352)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1350,U_1352)) ) ),
inference(miniscope,[status(thm)],[f_436_2]) ).
fof(f_436_4,plain,
( ! [U_1353,U_1351] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1351,U_1353))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1351),U_1353) )
& ! [U_1352,U_1350] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1350),U_1352)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1350,U_1352)) ) ),
inference(definitional_conversion,[status(esa)],[f_436_3]) ).
cnf(f_436_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1350),U_1352)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1350,U_1352)) ),
inference(clausify,[status(thm)],[f_436_4]) ).
cnf(f_436_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1351,U_1353))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1351),U_1353) ),
inference(clausify,[status(thm)],[f_436_4]) ).
fof(f_437_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_y_2,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_x_2))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__add__less__0__iff]) ).
fof(f_437_2,plain,
! [U_1355,U_1354] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1354,U_1355),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1355,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1354)) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1355,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1354))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1354,U_1355),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_437_1]) ).
fof(f_437_3,plain,
( ! [U_1359,U_1357] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1357,U_1359),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1359,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1357)) )
& ! [U_1358,U_1356] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1358,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1356))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1356,U_1358),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_437_2]) ).
fof(f_437_4,plain,
( ! [U_1357,U_1359] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1357,U_1359),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1359,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1357)) )
& ! [U_1358,U_1356] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1358,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1356))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1356,U_1358),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_437_3]) ).
cnf(f_437_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1358,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1356))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1356,U_1358),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_437_4]) ).
cnf(f_437_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1357,U_1359),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1359,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1357)) ),
inference(clausify,[status(thm)],[f_437_4]) ).
fof(f_438_1,plain,
! [V_a] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = V_a
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_a)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_a,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_abs__real__def]) ).
fof(f_438_2,plain,
! [U_1360] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1360) = U_1360
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1360,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1360) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1360)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1360,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_438_1]) ).
fof(f_438_3,plain,
( ! [U_1362] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1362) = U_1362
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1362,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1361] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1361) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1361)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1361,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_438_2]) ).
fof(f_438_4,plain,
( ! [U_1362] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1362) = U_1362
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1362,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1361] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1361) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1361)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1361,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_438_3]) ).
cnf(f_438_5,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1361) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1361)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1361,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_438_4]) ).
cnf(f_438_6,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1362) = U_1362
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1362,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_438_4]) ).
fof(f_439_1,plain,
! [V_r] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = V_r
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,V_r) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_r)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__abs__def]) ).
fof(f_439_2,plain,
! [U_1363] :
( ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1363) = U_1363
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1363,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1363) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1363)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1363,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_439_1]) ).
fof(f_439_3,plain,
( ! [U_1365] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1365) = U_1365
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1365,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1364] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1364) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1364)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1364,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_439_2]) ).
fof(f_439_4,plain,
( ! [U_1365] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1365) = U_1365
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1365,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_1364] :
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1364) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1364)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1364,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_439_3]) ).
cnf(f_439_5,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1364) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1364)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1364,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_439_4]) ).
cnf(f_439_6,plain,
( c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,U_1365) = U_1365
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_1365,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_439_4]) ).
fof(f_440_1,plain,
! [V_m,V_l,V_y,V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,V_y),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_l))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_y,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_m))))),
inference(fof_nnf,[status(thm)],[fact_abs__sum__triangle__ineq]) ).
fof(f_440_2,plain,
! [U_1369,U_1368,U_1367,U_1366] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1366,U_1367),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1368),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1369)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1366,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1368))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1367,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1369))))),
inference(variable_rename,[status(thm)],[f_440_1]) ).
fof(f_440_3,plain,
! [U_1366,U_1367,U_1368,U_1369] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1366,U_1367),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1368),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1369)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1366,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1368))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1367,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1369))))),
inference(definitional_conversion,[status(esa)],[f_440_2]) ).
cnf(f_440_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1366,U_1367),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1368),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1369)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1366,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1368))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1367,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_1369))))),
inference(clausify,[status(thm)],[f_440_3]) ).
fof(f_441_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_441_2,plain,
! [U_1370] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1370,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_441_1]) ).
fof(f_441_3,plain,
! [U_1370] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1370,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_441_2]) ).
cnf(f_441_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1370,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_441_3]) ).
fof(f_442_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_442_2,plain,
! [U_1371] :
( ( U_1371 != 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_1371) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1371)
| U_1371 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_442_1]) ).
fof(f_442_3,plain,
( ! [U_1373] :
( U_1373 != 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_1373) )
& ! [U_1372] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1372)
| U_1372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_442_2]) ).
fof(f_442_4,plain,
( ! [U_1373] :
( U_1373 != 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_1373) )
& ! [U_1372] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1372)
| U_1372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_442_3]) ).
cnf(f_442_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1372)
| U_1372 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_442_4]) ).
cnf(f_442_6,plain,
( U_1373 != 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_1373) ),
inference(clausify,[status(thm)],[f_442_4]) ).
fof(f_443_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_443_2,plain,
! [U_1374] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1374),
inference(variable_rename,[status(thm)],[f_443_1]) ).
fof(f_443_3,plain,
! [U_1374] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1374),
inference(definitional_conversion,[status(esa)],[f_443_2]) ).
cnf(f_443_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1374),
inference(clausify,[status(thm)],[f_443_3]) ).
fof(f_444_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_444_2,plain,
! [U_1375] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1375,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_444_1]) ).
fof(f_444_3,plain,
! [U_1375] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1375,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_444_2]) ).
cnf(f_444_4,plain,
~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1375,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_444_3]) ).
fof(f_445_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_445_2,plain,
! [U_1376] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1376,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1376 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_1376 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1376,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_445_1]) ).
fof(f_445_3,plain,
( ! [U_1378] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1378,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1378 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1377] :
( U_1377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1377,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_445_2]) ).
fof(f_445_4,plain,
( ! [U_1378] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1378,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1378 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1377] :
( U_1377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1377,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa)],[f_445_3]) ).
cnf(f_445_5,plain,
( U_1377 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1377,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_445_4]) ).
cnf(f_445_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1378,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_1378 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_445_4]) ).
fof(f_446_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_446_2,plain,
! [U_1380,U_1379] :
( U_1380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1379,U_1380) ),
inference(variable_rename,[status(thm)],[f_446_1]) ).
fof(f_446_3,plain,
! [U_1380] :
( ! [U_1379] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1379,U_1380)
| U_1380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_446_2]) ).
fof(f_446_4,plain,
! [U_1380,U_1379] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1379,U_1380)
| U_1380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_446_3]) ).
cnf(f_446_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1379,U_1380)
| U_1380 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_446_4]) ).
fof(f_447_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_447_2,plain,
! [U_1381] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1381)
| U_1381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_447_1]) ).
fof(f_447_3,plain,
! [U_1381] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1381)
| U_1381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_447_2]) ).
cnf(f_447_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1381)
| U_1381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_447_3]) ).
fof(f_448_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_448_2,plain,
! [U_1382] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1382) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_448_1]) ).
fof(f_448_3,plain,
! [U_1382] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1382) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_448_2]) ).
cnf(f_448_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1382) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_448_3]) ).
fof(f_449_1,plain,
! [V_n_2,V_ma_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_ma_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_ma_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_ma_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_ma_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__0__less__mult__iff]) ).
fof(f_449_2,plain,
! [U_1384,U_1383] :
( ( 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_1383),U_1384))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1384)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1383) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1384)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1383) )
| ~ 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_1383),U_1384)) ) ),
inference(variable_rename,[status(thm)],[f_449_1]) ).
fof(f_449_3,plain,
( ! [U_1388,U_1386] :
( 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_1386),U_1388))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1388)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1386) )
& ! [U_1387,U_1385] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1387)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1385) )
| ~ 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_1385),U_1387)) ) ),
inference(miniscope,[status(thm)],[f_449_2]) ).
fof(f_449_4,plain,
( ! [U_1385,U_1387] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1387)
| ~ sP144(U_1385,U_1387) )
& ! [U_1385,U_1387] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1385)
| ~ sP144(U_1385,U_1387) )
& ! [U_1388,U_1386] :
( 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_1386),U_1388))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1388)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1386) )
& ! [U_1385,U_1387] :
( sP144(U_1385,U_1387)
| ~ 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_1385),U_1387)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP144])],[f_449_3]) ).
cnf(f_449_5,plain,
( sP144(U_1385,U_1387)
| ~ 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_1385),U_1387)) ),
inference(clausify,[status(thm)],[f_449_4]) ).
cnf(f_449_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_1386),U_1388))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1388)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1386) ),
inference(clausify,[status(thm)],[f_449_4]) ).
cnf(f_449_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1385)
| ~ sP144(U_1385,U_1387) ),
inference(clausify,[status(thm)],[f_449_4]) ).
cnf(f_449_8,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1387)
| ~ sP144(U_1385,U_1387) ),
inference(clausify,[status(thm)],[f_449_4]) ).
fof(f_450_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_450_2,plain,
! [U_1389] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1389),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_450_1]) ).
fof(f_450_3,plain,
! [U_1389] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1389),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_450_2]) ).
cnf(f_450_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1389),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_450_3]) ).
fof(f_451_1,plain,
! [V_n_2,V_ma_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__is__0]) ).
fof(f_451_2,plain,
! [U_1391,U_1390] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1390),U_1391) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_1391 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1390 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1391 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1390 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1390),U_1391) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_451_1]) ).
fof(f_451_3,plain,
( ! [U_1395,U_1393] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1393),U_1395) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ( U_1395 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1393 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1394,U_1392] :
( U_1394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1392 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1392),U_1394) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_451_2]) ).
fof(f_451_4,plain,
( ! [U_1395,U_1393] :
( U_1395 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP145(U_1395,U_1393) )
& ! [U_1395,U_1393] :
( U_1393 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP145(U_1395,U_1393) )
& ! [U_1395,U_1393] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1393),U_1395) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP145(U_1395,U_1393) )
& ! [U_1394,U_1392] :
( U_1394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1392 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1392),U_1394) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145])],[f_451_3]) ).
cnf(f_451_5,plain,
( U_1394 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1392 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1392),U_1394) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_451_4]) ).
cnf(f_451_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1393),U_1395) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| sP145(U_1395,U_1393) ),
inference(clausify,[status(thm)],[f_451_4]) ).
cnf(f_451_7,plain,
( U_1393 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP145(U_1395,U_1393) ),
inference(clausify,[status(thm)],[f_451_4]) ).
cnf(f_451_8,plain,
( U_1395 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP145(U_1395,U_1393) ),
inference(clausify,[status(thm)],[f_451_4]) ).
fof(f_452_1,plain,
! [V_n_2,V_ma_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_ma_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_ma_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_ma_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_ma_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_452_2,plain,
! [U_1398,U_1397,U_1396] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1396),U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1396),U_1398))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1397,U_1398)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1396) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1397,U_1398)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1396) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1396),U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1396),U_1398)) ) ),
inference(variable_rename,[status(thm)],[f_452_1]) ).
fof(f_452_3,plain,
( ! [U_1404,U_1402,U_1400] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1400),U_1402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1400),U_1404))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1402,U_1404)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1400) )
& ! [U_1403,U_1401,U_1399] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1401,U_1403)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1399) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1399),U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1399),U_1403)) ) ),
inference(miniscope,[status(thm)],[f_452_2]) ).
fof(f_452_4,plain,
( ! [U_1401,U_1399,U_1403] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1401,U_1403)
| ~ sP146(U_1401,U_1399,U_1403) )
& ! [U_1401,U_1399,U_1403] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1399)
| ~ sP146(U_1401,U_1399,U_1403) )
& ! [U_1404,U_1400,U_1402] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1400),U_1402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1400),U_1404))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1402,U_1404)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1400) )
& ! [U_1401,U_1399,U_1403] :
( sP146(U_1401,U_1399,U_1403)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1399),U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1399),U_1403)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146])],[f_452_3]) ).
cnf(f_452_5,plain,
( sP146(U_1401,U_1399,U_1403)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1399),U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1399),U_1403)) ),
inference(clausify,[status(thm)],[f_452_4]) ).
cnf(f_452_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1400),U_1402),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1400),U_1404))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1402,U_1404)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1400) ),
inference(clausify,[status(thm)],[f_452_4]) ).
cnf(f_452_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1399)
| ~ sP146(U_1401,U_1399,U_1403) ),
inference(clausify,[status(thm)],[f_452_4]) ).
cnf(f_452_8,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1401,U_1403)
| ~ sP146(U_1401,U_1399,U_1403) ),
inference(clausify,[status(thm)],[f_452_4]) ).
fof(f_453_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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_ma_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_ma_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_ma_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_453_2,plain,
! [U_1407,U_1406,U_1405] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1405),U_1406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1407),U_1406))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1405,U_1407)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1406) )
& ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1405,U_1407)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1406) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1405),U_1406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1407),U_1406)) ) ),
inference(variable_rename,[status(thm)],[f_453_1]) ).
fof(f_453_3,plain,
( ! [U_1413,U_1411,U_1409] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1409),U_1411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1413),U_1411))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1409,U_1413)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1411) )
& ! [U_1412,U_1410,U_1408] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1408,U_1412)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1410) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1408),U_1410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1412),U_1410)) ) ),
inference(miniscope,[status(thm)],[f_453_2]) ).
fof(f_453_4,plain,
( ! [U_1408,U_1410,U_1412] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1408,U_1412)
| ~ sP147(U_1408,U_1410,U_1412) )
& ! [U_1408,U_1410,U_1412] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1410)
| ~ sP147(U_1408,U_1410,U_1412) )
& ! [U_1409,U_1411,U_1413] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1409),U_1411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1413),U_1411))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1409,U_1413)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1411) )
& ! [U_1408,U_1410,U_1412] :
( sP147(U_1408,U_1410,U_1412)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1408),U_1410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1412),U_1410)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147])],[f_453_3]) ).
cnf(f_453_5,plain,
( sP147(U_1408,U_1410,U_1412)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1408),U_1410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1412),U_1410)) ),
inference(clausify,[status(thm)],[f_453_4]) ).
cnf(f_453_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1409),U_1411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1413),U_1411))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1409,U_1413)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1411) ),
inference(clausify,[status(thm)],[f_453_4]) ).
cnf(f_453_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1410)
| ~ sP147(U_1408,U_1410,U_1412) ),
inference(clausify,[status(thm)],[f_453_4]) ).
cnf(f_453_8,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1408,U_1412)
| ~ sP147(U_1408,U_1410,U_1412) ),
inference(clausify,[status(thm)],[f_453_4]) ).
fof(f_454_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_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__eq(tc_Nat_Onat,V_ma_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__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_mult__le__cancel1]) ).
fof(f_454_2,plain,
! [U_1416,U_1415,U_1414] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1414),U_1415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1414),U_1416))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1415,U_1416)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1414) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1415,U_1416)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1414)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1414),U_1415),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1414),U_1416)) ) ),
inference(variable_rename,[status(thm)],[f_454_1]) ).
fof(f_454_3,plain,
( ! [U_1422,U_1420,U_1418] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1418),U_1420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1418),U_1422))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1420,U_1422)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1418) ) )
& ! [U_1421,U_1419,U_1417] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1419,U_1421)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1417)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1417),U_1419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1417),U_1421)) ) ),
inference(miniscope,[status(thm)],[f_454_2]) ).
fof(f_454_4,plain,
( ! [U_1418,U_1420,U_1422] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1420,U_1422)
| ~ sP148(U_1418,U_1420,U_1422) )
& ! [U_1418,U_1420,U_1422] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1418)
| ~ sP148(U_1418,U_1420,U_1422) )
& ! [U_1418,U_1420,U_1422] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1418),U_1420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1418),U_1422))
| sP148(U_1418,U_1420,U_1422) )
& ! [U_1417,U_1419,U_1421] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1419,U_1421)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1417)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1417),U_1419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1417),U_1421)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148])],[f_454_3]) ).
cnf(f_454_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1419,U_1421)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1417)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1417),U_1419),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1417),U_1421)) ),
inference(clausify,[status(thm)],[f_454_4]) ).
cnf(f_454_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1418),U_1420),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1418),U_1422))
| sP148(U_1418,U_1420,U_1422) ),
inference(clausify,[status(thm)],[f_454_4]) ).
cnf(f_454_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1418)
| ~ sP148(U_1418,U_1420,U_1422) ),
inference(clausify,[status(thm)],[f_454_4]) ).
cnf(f_454_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1420,U_1422)
| ~ sP148(U_1418,U_1420,U_1422) ),
inference(clausify,[status(thm)],[f_454_4]) ).
fof(f_455_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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__eq(tc_Nat_Onat,V_ma_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__eq(tc_Nat_Onat,V_ma_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__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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__le__cancel2]) ).
fof(f_455_2,plain,
! [U_1425,U_1424,U_1423] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1423),U_1424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1425),U_1424))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1423,U_1425)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1424) ) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1423,U_1425)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1424)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1423),U_1424),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1425),U_1424)) ) ),
inference(variable_rename,[status(thm)],[f_455_1]) ).
fof(f_455_3,plain,
( ! [U_1431,U_1429,U_1427] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1427),U_1429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1431),U_1429))
| ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1427,U_1431)
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1429) ) )
& ! [U_1430,U_1428,U_1426] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1426,U_1430)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1428)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1426),U_1428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1430),U_1428)) ) ),
inference(miniscope,[status(thm)],[f_455_2]) ).
fof(f_455_4,plain,
( ! [U_1429,U_1431,U_1427] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1427,U_1431)
| ~ sP149(U_1429,U_1431,U_1427) )
& ! [U_1429,U_1431,U_1427] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1429)
| ~ sP149(U_1429,U_1431,U_1427) )
& ! [U_1429,U_1431,U_1427] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1427),U_1429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1431),U_1429))
| sP149(U_1429,U_1431,U_1427) )
& ! [U_1428,U_1430,U_1426] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1426,U_1430)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1428)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1426),U_1428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1430),U_1428)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP149])],[f_455_3]) ).
cnf(f_455_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1426,U_1430)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1428)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1426),U_1428),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1430),U_1428)) ),
inference(clausify,[status(thm)],[f_455_4]) ).
cnf(f_455_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1427),U_1429),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1431),U_1429))
| sP149(U_1429,U_1431,U_1427) ),
inference(clausify,[status(thm)],[f_455_4]) ).
cnf(f_455_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1429)
| ~ sP149(U_1429,U_1431,U_1427) ),
inference(clausify,[status(thm)],[f_455_4]) ).
cnf(f_455_8,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1427,U_1431)
| ~ sP149(U_1429,U_1431,U_1427) ),
inference(clausify,[status(thm)],[f_455_4]) ).
fof(f_456_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_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_ma_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_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_456_2,plain,
! [U_1434,U_1433,U_1432] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1432),U_1433) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1432),U_1434)
| ( U_1432 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1433 != U_1434 ) )
& ( U_1432 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1433 = U_1434
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1432),U_1433) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1432),U_1434) ) ),
inference(variable_rename,[status(thm)],[f_456_1]) ).
fof(f_456_3,plain,
( ! [U_1440,U_1438,U_1436] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1436),U_1438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1436),U_1440)
| ( U_1436 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1438 != U_1440 ) )
& ! [U_1439,U_1437,U_1435] :
( U_1435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1437 = U_1439
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1435),U_1437) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1435),U_1439) ) ),
inference(miniscope,[status(thm)],[f_456_2]) ).
fof(f_456_4,plain,
( ! [U_1440,U_1438,U_1436] :
( U_1436 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP150(U_1440,U_1438,U_1436) )
& ! [U_1440,U_1438,U_1436] :
( U_1438 != U_1440
| ~ sP150(U_1440,U_1438,U_1436) )
& ! [U_1440,U_1438,U_1436] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1436),U_1438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1436),U_1440)
| sP150(U_1440,U_1438,U_1436) )
& ! [U_1437,U_1435,U_1439] :
( U_1435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1437 = U_1439
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1435),U_1437) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1435),U_1439) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150])],[f_456_3]) ).
cnf(f_456_5,plain,
( U_1435 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1437 = U_1439
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1435),U_1437) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1435),U_1439) ),
inference(clausify,[status(thm)],[f_456_4]) ).
cnf(f_456_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1436),U_1438) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1436),U_1440)
| sP150(U_1440,U_1438,U_1436) ),
inference(clausify,[status(thm)],[f_456_4]) ).
cnf(f_456_7,plain,
( U_1438 != U_1440
| ~ sP150(U_1440,U_1438,U_1436) ),
inference(clausify,[status(thm)],[f_456_4]) ).
cnf(f_456_8,plain,
( U_1436 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP150(U_1440,U_1438,U_1436) ),
inference(clausify,[status(thm)],[f_456_4]) ).
fof(f_457_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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_ma_2 != V_n_2 ) )
& ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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_457_2,plain,
! [U_1443,U_1442,U_1441] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1441),U_1442) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1443),U_1442)
| ( U_1442 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1441 != U_1443 ) )
& ( U_1442 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1441 = U_1443
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1441),U_1442) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1443),U_1442) ) ),
inference(variable_rename,[status(thm)],[f_457_1]) ).
fof(f_457_3,plain,
( ! [U_1449,U_1447,U_1445] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1445),U_1447) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1449),U_1447)
| ( U_1447 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1445 != U_1449 ) )
& ! [U_1448,U_1446,U_1444] :
( U_1446 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1444 = U_1448
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1444),U_1446) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1448),U_1446) ) ),
inference(miniscope,[status(thm)],[f_457_2]) ).
fof(f_457_4,plain,
( ! [U_1445,U_1447,U_1449] :
( U_1447 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP151(U_1445,U_1447,U_1449) )
& ! [U_1445,U_1447,U_1449] :
( U_1445 != U_1449
| ~ sP151(U_1445,U_1447,U_1449) )
& ! [U_1445,U_1447,U_1449] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1445),U_1447) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1449),U_1447)
| sP151(U_1445,U_1447,U_1449) )
& ! [U_1446,U_1444,U_1448] :
( U_1446 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1444 = U_1448
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1444),U_1446) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1448),U_1446) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP151])],[f_457_3]) ).
cnf(f_457_5,plain,
( U_1446 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1444 = U_1448
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1444),U_1446) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1448),U_1446) ),
inference(clausify,[status(thm)],[f_457_4]) ).
cnf(f_457_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1445),U_1447) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1449),U_1447)
| sP151(U_1445,U_1447,U_1449) ),
inference(clausify,[status(thm)],[f_457_4]) ).
cnf(f_457_7,plain,
( U_1445 != U_1449
| ~ sP151(U_1445,U_1447,U_1449) ),
inference(clausify,[status(thm)],[f_457_4]) ).
cnf(f_457_8,plain,
( U_1447 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP151(U_1445,U_1447,U_1449) ),
inference(clausify,[status(thm)],[f_457_4]) ).
fof(f_458_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_458_2,plain,
! [U_1452,U_1451,U_1450] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1450),U_1452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1451),U_1452))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1452)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1450,U_1451) ),
inference(variable_rename,[status(thm)],[f_458_1]) ).
fof(f_458_3,plain,
! [U_1450,U_1452,U_1451] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1450),U_1452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1451),U_1452))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1452)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1450,U_1451) ),
inference(definitional_conversion,[status(esa)],[f_458_2]) ).
cnf(f_458_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1450),U_1452),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1451),U_1452))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1452)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1450,U_1451) ),
inference(clausify,[status(thm)],[f_458_3]) ).
fof(f_459_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_459_2,plain,
! [U_1455,U_1454,U_1453] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1455),U_1453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1455),U_1454))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1455)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1453,U_1454) ),
inference(variable_rename,[status(thm)],[f_459_1]) ).
fof(f_459_3,plain,
! [U_1455,U_1454,U_1453] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1455),U_1453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1455),U_1454))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1455)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1453,U_1454) ),
inference(definitional_conversion,[status(esa)],[f_459_2]) ).
cnf(f_459_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1455),U_1453),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1455),U_1454))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1455)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1453,U_1454) ),
inference(clausify,[status(thm)],[f_459_3]) ).
fof(f_460_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_460_2,plain,
! [U_1456] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1456) = U_1456,
inference(variable_rename,[status(thm)],[f_460_1]) ).
fof(f_460_3,plain,
! [U_1456] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1456) = U_1456,
inference(definitional_conversion,[status(esa)],[f_460_2]) ).
cnf(f_460_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1456) = U_1456,
inference(clausify,[status(thm)],[f_460_3]) ).
fof(f_461_1,plain,
! [V_n_2,V_ma_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_ma_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_ma_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_ma_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_ma_2,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_add__gr__0]) ).
fof(f_461_2,plain,
! [U_1458,U_1457] :
( ( 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_1457,U_1458))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1458)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1457) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1458)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1457)
| ~ 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_1457,U_1458)) ) ),
inference(variable_rename,[status(thm)],[f_461_1]) ).
fof(f_461_3,plain,
( ! [U_1462,U_1460] :
( 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_1460,U_1462))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1462)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1460) ) )
& ! [U_1461,U_1459] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1461)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1459)
| ~ 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_1459,U_1461)) ) ),
inference(miniscope,[status(thm)],[f_461_2]) ).
fof(f_461_4,plain,
( ! [U_1460,U_1462] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1462)
| ~ sP152(U_1460,U_1462) )
& ! [U_1460,U_1462] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1460)
| ~ sP152(U_1460,U_1462) )
& ! [U_1460,U_1462] :
( 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_1460,U_1462))
| sP152(U_1460,U_1462) )
& ! [U_1461,U_1459] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1461)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1459)
| ~ 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_1459,U_1461)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_461_3]) ).
cnf(f_461_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1461)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1459)
| ~ 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_1459,U_1461)) ),
inference(clausify,[status(thm)],[f_461_4]) ).
cnf(f_461_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_1460,U_1462))
| sP152(U_1460,U_1462) ),
inference(clausify,[status(thm)],[f_461_4]) ).
cnf(f_461_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1460)
| ~ sP152(U_1460,U_1462) ),
inference(clausify,[status(thm)],[f_461_4]) ).
cnf(f_461_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1462)
| ~ sP152(U_1460,U_1462) ),
inference(clausify,[status(thm)],[f_461_4]) ).
fof(f_462_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_462_2,plain,
! [U_1463] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1463,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1463,
inference(variable_rename,[status(thm)],[f_462_1]) ).
fof(f_462_3,plain,
! [U_1463] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1463,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1463,
inference(definitional_conversion,[status(esa)],[f_462_2]) ).
cnf(f_462_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1463,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1463,
inference(clausify,[status(thm)],[f_462_3]) ).
fof(f_463_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_add__is__0]) ).
fof(f_463_2,plain,
! [U_1465,U_1464] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1464,U_1465) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1465 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1464 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( ( U_1465 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1464 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1464,U_1465) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_463_1]) ).
fof(f_463_3,plain,
( ! [U_1469,U_1467] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1467,U_1469) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1469 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1467 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1468,U_1466] :
( ( U_1468 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1466,U_1468) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_463_2]) ).
fof(f_463_4,plain,
( ! [U_1466,U_1468] :
( U_1468 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP153(U_1466,U_1468) )
& ! [U_1466,U_1468] :
( U_1466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP153(U_1466,U_1468) )
& ! [U_1469,U_1467] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1467,U_1469) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1469 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1467 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_1466,U_1468] :
( sP153(U_1466,U_1468)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1466,U_1468) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153])],[f_463_3]) ).
cnf(f_463_5,plain,
( sP153(U_1466,U_1468)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1466,U_1468) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_463_4]) ).
cnf(f_463_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1467,U_1469) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1469 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1467 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_463_4]) ).
cnf(f_463_7,plain,
( U_1466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP153(U_1466,U_1468) ),
inference(clausify,[status(thm)],[f_463_4]) ).
cnf(f_463_8,plain,
( U_1468 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP153(U_1466,U_1468) ),
inference(clausify,[status(thm)],[f_463_4]) ).
fof(f_464_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_464_2,plain,
! [U_1471,U_1470] :
( U_1471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1470,U_1471) != U_1470 ),
inference(variable_rename,[status(thm)],[f_464_1]) ).
fof(f_464_3,plain,
! [U_1471] :
( ! [U_1470] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1470,U_1471) != U_1470
| U_1471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(miniscope,[status(thm)],[f_464_2]) ).
fof(f_464_4,plain,
! [U_1471,U_1470] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1470,U_1471) != U_1470
| U_1471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_464_3]) ).
cnf(f_464_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1470,U_1471) != U_1470
| U_1471 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_464_4]) ).
fof(f_465_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_465_2,plain,
! [U_1473,U_1472] :
( U_1472 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1473 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1472 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1472),U_1473) ),
inference(variable_rename,[status(thm)],[f_465_1]) ).
fof(f_465_3,plain,
! [U_1472,U_1473] :
( U_1472 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1473 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1472 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1472),U_1473) ),
inference(definitional_conversion,[status(esa)],[f_465_2]) ).
cnf(f_465_4,plain,
( U_1472 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1473 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1472 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1472),U_1473) ),
inference(clausify,[status(thm)],[f_465_3]) ).
fof(f_466_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_466_2,plain,
! [U_1475,U_1474] :
( ( ( c_Groups_Oplus__class_Oplus(U_1474,U_1475,U_1475) = c_Groups_Ozero__class_Ozero(U_1474)
| U_1475 != c_Groups_Ozero__class_Ozero(U_1474) )
& ( U_1475 = c_Groups_Ozero__class_Ozero(U_1474)
| c_Groups_Oplus__class_Oplus(U_1474,U_1475,U_1475) != c_Groups_Ozero__class_Ozero(U_1474) ) )
| ~ class_Groups_Olinordered__ab__group__add(U_1474) ),
inference(variable_rename,[status(thm)],[f_466_1]) ).
fof(f_466_3,plain,
( ! [U_1475,U_1474] :
( c_Groups_Oplus__class_Oplus(U_1474,U_1475,U_1475) = c_Groups_Ozero__class_Ozero(U_1474)
| U_1475 != c_Groups_Ozero__class_Ozero(U_1474)
| ~ sP154(U_1475,U_1474) )
& ! [U_1475,U_1474] :
( U_1475 = c_Groups_Ozero__class_Ozero(U_1474)
| c_Groups_Oplus__class_Oplus(U_1474,U_1475,U_1475) != c_Groups_Ozero__class_Ozero(U_1474)
| ~ sP154(U_1475,U_1474) )
& ! [U_1475,U_1474] :
( sP154(U_1475,U_1474)
| ~ class_Groups_Olinordered__ab__group__add(U_1474) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP154])],[f_466_2]) ).
cnf(f_466_4,plain,
( sP154(U_1475,U_1474)
| ~ class_Groups_Olinordered__ab__group__add(U_1474) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_5,plain,
( U_1475 = c_Groups_Ozero__class_Ozero(U_1474)
| c_Groups_Oplus__class_Oplus(U_1474,U_1475,U_1475) != c_Groups_Ozero__class_Ozero(U_1474)
| ~ sP154(U_1475,U_1474) ),
inference(clausify,[status(thm)],[f_466_3]) ).
cnf(f_466_6,plain,
( c_Groups_Oplus__class_Oplus(U_1474,U_1475,U_1475) = c_Groups_Ozero__class_Ozero(U_1474)
| U_1475 != c_Groups_Ozero__class_Ozero(U_1474)
| ~ sP154(U_1475,U_1474) ),
inference(clausify,[status(thm)],[f_466_3]) ).
fof(f_467_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__le__cancel1]) ).
fof(f_467_2,plain,
! [U_1478,U_1477,U_1476] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1478))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1477,U_1478) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1477,U_1478)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1478)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1476) ),
inference(variable_rename,[status(thm)],[f_467_1]) ).
fof(f_467_3,plain,
( ! [U_1477,U_1478,U_1476] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1478))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1477,U_1478)
| ~ sP155(U_1477,U_1478,U_1476) )
& ! [U_1477,U_1478,U_1476] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1477,U_1478)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1478))
| ~ sP155(U_1477,U_1478,U_1476) )
& ! [U_1477,U_1478,U_1476] :
( sP155(U_1477,U_1478,U_1476)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1476) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155])],[f_467_2]) ).
cnf(f_467_4,plain,
( sP155(U_1477,U_1478,U_1476)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1476) ),
inference(clausify,[status(thm)],[f_467_3]) ).
cnf(f_467_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1477,U_1478)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1478))
| ~ sP155(U_1477,U_1478,U_1476) ),
inference(clausify,[status(thm)],[f_467_3]) ).
cnf(f_467_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1477),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1476),U_1478))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1477,U_1478)
| ~ sP155(U_1477,U_1478,U_1476) ),
inference(clausify,[status(thm)],[f_467_3]) ).
fof(f_468_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_k] :
( ! [B_x] :
? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,B_x))),B_k)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) ) )
& ( ? [B_k] :
( ? [B_x] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,B_x))),B_k)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) )
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__iff2]) ).
fof(f_468_2,plain,
! [U_1486,U_1485] :
( ( ( c_SEQ_OBseq(U_1485,U_1486)
| ! [U_1484] :
( ! [U_1483] :
? [U_1482] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,U_1482),c_Groups_Ouminus__class_Ouminus(U_1485,U_1483))),U_1484)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1484) ) )
& ( ? [U_1481] :
( ? [U_1480] :
! [U_1479] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,U_1479),c_Groups_Ouminus__class_Ouminus(U_1485,U_1480))),U_1481)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1481) )
| ~ c_SEQ_OBseq(U_1485,U_1486) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1485) ),
inference(variable_rename,[status(thm)],[f_468_1]) ).
fof(f_468_3,plain,
! [U_1486,U_1485] :
( ( ( c_SEQ_OBseq(U_1485,U_1486)
| ! [U_1484] :
( ! [U_1483] :
? [U_1482] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,U_1482),c_Groups_Ouminus__class_Ouminus(U_1485,U_1483))),U_1484)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1484) ) )
& ( ( ? [U_1480] :
! [U_1479] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,U_1479),c_Groups_Ouminus__class_Ouminus(U_1485,U_1480))),sK10(U_1486,U_1485))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK10(U_1486,U_1485)) )
| ~ c_SEQ_OBseq(U_1485,U_1486) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1485) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_1481,sK10(U_1486,U_1485))],[f_468_2]) ).
fof(f_468_4,plain,
! [U_1486,U_1485] :
( ( ( c_SEQ_OBseq(U_1485,U_1486)
| ! [U_1484] :
( ! [U_1483] :
? [U_1482] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,U_1482),c_Groups_Ouminus__class_Ouminus(U_1485,U_1483))),U_1484)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1484) ) )
& ( ( ! [U_1479] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,U_1479),c_Groups_Ouminus__class_Ouminus(U_1485,sK11(U_1486,U_1485)))),sK10(U_1486,U_1485))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK10(U_1486,U_1485)) )
| ~ c_SEQ_OBseq(U_1485,U_1486) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1485) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_1480,sK11(U_1486,U_1485))],[f_468_3]) ).
fof(f_468_5,plain,
! [U_1486,U_1485] :
( ( ( c_SEQ_OBseq(U_1485,U_1486)
| ! [U_1484] :
( ! [U_1483] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,sK12(U_1486,U_1485,U_1484,U_1483)),c_Groups_Ouminus__class_Ouminus(U_1485,U_1483))),U_1484)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1484) ) )
& ( ( ! [U_1479] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,U_1479),c_Groups_Ouminus__class_Ouminus(U_1485,sK11(U_1486,U_1485)))),sK10(U_1486,U_1485))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK10(U_1486,U_1485)) )
| ~ c_SEQ_OBseq(U_1485,U_1486) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1485) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_1482,sK12(U_1486,U_1485,U_1484,U_1483))],[f_468_4]) ).
fof(f_468_6,plain,
( ! [U_1479,U_1485,U_1486] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,U_1479),c_Groups_Ouminus__class_Ouminus(U_1485,sK11(U_1486,U_1485)))),sK10(U_1486,U_1485))
| ~ sP156(U_1479,U_1485,U_1486) )
& ! [U_1479,U_1485,U_1486] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK10(U_1486,U_1485))
| ~ sP156(U_1479,U_1485,U_1486) )
& ! [U_1479,U_1483,U_1484,U_1485,U_1486] :
( c_SEQ_OBseq(U_1485,U_1486)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,sK12(U_1486,U_1485,U_1484,U_1483)),c_Groups_Ouminus__class_Ouminus(U_1485,U_1483))),U_1484)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1484)
| ~ sP157(U_1479,U_1483,U_1484,U_1485,U_1486) )
& ! [U_1479,U_1483,U_1484,U_1485,U_1486] :
( sP156(U_1479,U_1485,U_1486)
| ~ c_SEQ_OBseq(U_1485,U_1486)
| ~ sP157(U_1479,U_1483,U_1484,U_1485,U_1486) )
& ! [U_1479,U_1483,U_1484,U_1485,U_1486] :
( sP157(U_1479,U_1483,U_1484,U_1485,U_1486)
| ~ class_RealVector_Oreal__normed__vector(U_1485) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156,sP157])],[f_468_5]) ).
cnf(f_468_7,plain,
( sP157(U_1479,U_1483,U_1484,U_1485,U_1486)
| ~ class_RealVector_Oreal__normed__vector(U_1485) ),
inference(clausify,[status(thm)],[f_468_6]) ).
cnf(f_468_8,plain,
( sP156(U_1479,U_1485,U_1486)
| ~ c_SEQ_OBseq(U_1485,U_1486)
| ~ sP157(U_1479,U_1483,U_1484,U_1485,U_1486) ),
inference(clausify,[status(thm)],[f_468_6]) ).
cnf(f_468_9,plain,
( c_SEQ_OBseq(U_1485,U_1486)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,sK12(U_1486,U_1485,U_1484,U_1483)),c_Groups_Ouminus__class_Ouminus(U_1485,U_1483))),U_1484)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1484)
| ~ sP157(U_1479,U_1483,U_1484,U_1485,U_1486) ),
inference(clausify,[status(thm)],[f_468_6]) ).
cnf(f_468_10,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK10(U_1486,U_1485))
| ~ sP156(U_1479,U_1485,U_1486) ),
inference(clausify,[status(thm)],[f_468_6]) ).
cnf(f_468_11,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1485,c_Groups_Oplus__class_Oplus(U_1485,hAPP(U_1486,U_1479),c_Groups_Ouminus__class_Ouminus(U_1485,sK11(U_1486,U_1485)))),sK10(U_1486,U_1485))
| ~ sP156(U_1479,U_1485,U_1486) ),
inference(clausify,[status(thm)],[f_468_6]) ).
fof(f_469_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_k] :
( ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,B_N)))),B_k)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) ) )
& ( ? [B_k] :
( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Oplus__class_Oplus(T_a,hAPP(V_X_2,B_n),c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_X_2,B_N)))),B_k)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_k) )
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__iff3]) ).
fof(f_469_2,plain,
! [U_1494,U_1493] :
( ( ( c_SEQ_OBseq(U_1493,U_1494)
| ! [U_1492] :
( ! [U_1491] :
? [U_1490] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,U_1490),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,U_1491)))),U_1492)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1492) ) )
& ( ? [U_1489] :
( ? [U_1488] :
! [U_1487] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,U_1487),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,U_1488)))),U_1489)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1489) )
| ~ c_SEQ_OBseq(U_1493,U_1494) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1493) ),
inference(variable_rename,[status(thm)],[f_469_1]) ).
fof(f_469_3,plain,
! [U_1494,U_1493] :
( ( ( c_SEQ_OBseq(U_1493,U_1494)
| ! [U_1492] :
( ! [U_1491] :
? [U_1490] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,U_1490),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,U_1491)))),U_1492)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1492) ) )
& ( ( ? [U_1488] :
! [U_1487] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,U_1487),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,U_1488)))),sK13(U_1494,U_1493))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK13(U_1494,U_1493)) )
| ~ c_SEQ_OBseq(U_1493,U_1494) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1493) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_1489,sK13(U_1494,U_1493))],[f_469_2]) ).
fof(f_469_4,plain,
! [U_1494,U_1493] :
( ( ( c_SEQ_OBseq(U_1493,U_1494)
| ! [U_1492] :
( ! [U_1491] :
? [U_1490] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,U_1490),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,U_1491)))),U_1492)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1492) ) )
& ( ( ! [U_1487] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,U_1487),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,sK14(U_1494,U_1493))))),sK13(U_1494,U_1493))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK13(U_1494,U_1493)) )
| ~ c_SEQ_OBseq(U_1493,U_1494) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1493) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_1488,sK14(U_1494,U_1493))],[f_469_3]) ).
fof(f_469_5,plain,
! [U_1494,U_1493] :
( ( ( c_SEQ_OBseq(U_1493,U_1494)
| ! [U_1492] :
( ! [U_1491] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,sK15(U_1494,U_1493,U_1492,U_1491)),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,U_1491)))),U_1492)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1492) ) )
& ( ( ! [U_1487] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,U_1487),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,sK14(U_1494,U_1493))))),sK13(U_1494,U_1493))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK13(U_1494,U_1493)) )
| ~ c_SEQ_OBseq(U_1493,U_1494) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1493) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_1490,sK15(U_1494,U_1493,U_1492,U_1491))],[f_469_4]) ).
fof(f_469_6,plain,
( ! [U_1487,U_1493,U_1494] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,U_1487),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,sK14(U_1494,U_1493))))),sK13(U_1494,U_1493))
| ~ sP158(U_1487,U_1493,U_1494) )
& ! [U_1487,U_1493,U_1494] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK13(U_1494,U_1493))
| ~ sP158(U_1487,U_1493,U_1494) )
& ! [U_1487,U_1492,U_1491,U_1493,U_1494] :
( c_SEQ_OBseq(U_1493,U_1494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,sK15(U_1494,U_1493,U_1492,U_1491)),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,U_1491)))),U_1492)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1492)
| ~ sP159(U_1487,U_1492,U_1491,U_1493,U_1494) )
& ! [U_1487,U_1492,U_1491,U_1493,U_1494] :
( sP158(U_1487,U_1493,U_1494)
| ~ c_SEQ_OBseq(U_1493,U_1494)
| ~ sP159(U_1487,U_1492,U_1491,U_1493,U_1494) )
& ! [U_1487,U_1492,U_1491,U_1493,U_1494] :
( sP159(U_1487,U_1492,U_1491,U_1493,U_1494)
| ~ class_RealVector_Oreal__normed__vector(U_1493) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP158,sP159])],[f_469_5]) ).
cnf(f_469_7,plain,
( sP159(U_1487,U_1492,U_1491,U_1493,U_1494)
| ~ class_RealVector_Oreal__normed__vector(U_1493) ),
inference(clausify,[status(thm)],[f_469_6]) ).
cnf(f_469_8,plain,
( sP158(U_1487,U_1493,U_1494)
| ~ c_SEQ_OBseq(U_1493,U_1494)
| ~ sP159(U_1487,U_1492,U_1491,U_1493,U_1494) ),
inference(clausify,[status(thm)],[f_469_6]) ).
cnf(f_469_9,plain,
( c_SEQ_OBseq(U_1493,U_1494)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,sK15(U_1494,U_1493,U_1492,U_1491)),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,U_1491)))),U_1492)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1492)
| ~ sP159(U_1487,U_1492,U_1491,U_1493,U_1494) ),
inference(clausify,[status(thm)],[f_469_6]) ).
cnf(f_469_10,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK13(U_1494,U_1493))
| ~ sP158(U_1487,U_1493,U_1494) ),
inference(clausify,[status(thm)],[f_469_6]) ).
cnf(f_469_11,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1493,c_Groups_Oplus__class_Oplus(U_1493,hAPP(U_1494,U_1487),c_Groups_Ouminus__class_Ouminus(U_1493,hAPP(U_1494,sK14(U_1494,U_1493))))),sK13(U_1494,U_1493))
| ~ sP158(U_1487,U_1493,U_1494) ),
inference(clausify,[status(thm)],[f_469_6]) ).
fof(f_470_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,V_x)),
inference(fof_nnf,[status(thm)],[fact_complex__mod__minus__le__complex__mod]) ).
fof(f_470_2,plain,
! [U_1495] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1495)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1495)),
inference(variable_rename,[status(thm)],[f_470_1]) ).
fof(f_470_3,plain,
! [U_1495] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1495)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1495)),
inference(definitional_conversion,[status(esa)],[f_470_2]) ).
cnf(f_470_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1495)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_1495)),
inference(clausify,[status(thm)],[f_470_3]) ).
fof(f_471_1,plain,
! [T_a] :
( ? [B_K] :
( ! [B_a,B_b] : 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),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Opos__bounded]) ).
fof(f_471_2,plain,
! [U_1499] :
( ? [U_1498] :
( ! [U_1497,U_1496] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1499),U_1497),U_1496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1499,U_1497)),c_RealVector_Onorm__class_Onorm(U_1499,U_1496))),U_1498))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1498) )
| ~ class_RealVector_Oreal__normed__algebra(U_1499) ),
inference(variable_rename,[status(thm)],[f_471_1]) ).
fof(f_471_3,plain,
! [U_1499] :
( ( ! [U_1497,U_1496] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1499),U_1497),U_1496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1499,U_1497)),c_RealVector_Onorm__class_Onorm(U_1499,U_1496))),sK16(U_1499)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK16(U_1499)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1499) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_1498,sK16(U_1499))],[f_471_2]) ).
fof(f_471_4,plain,
( ! [U_1496,U_1497,U_1499] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1499),U_1497),U_1496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1499,U_1497)),c_RealVector_Onorm__class_Onorm(U_1499,U_1496))),sK16(U_1499)))
| ~ sP160(U_1496,U_1497,U_1499) )
& ! [U_1496,U_1497,U_1499] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK16(U_1499))
| ~ sP160(U_1496,U_1497,U_1499) )
& ! [U_1496,U_1497,U_1499] :
( sP160(U_1496,U_1497,U_1499)
| ~ class_RealVector_Oreal__normed__algebra(U_1499) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_471_3]) ).
cnf(f_471_5,plain,
( sP160(U_1496,U_1497,U_1499)
| ~ class_RealVector_Oreal__normed__algebra(U_1499) ),
inference(clausify,[status(thm)],[f_471_4]) ).
cnf(f_471_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK16(U_1499))
| ~ sP160(U_1496,U_1497,U_1499) ),
inference(clausify,[status(thm)],[f_471_4]) ).
cnf(f_471_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1499,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1499),U_1497),U_1496)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1499,U_1497)),c_RealVector_Onorm__class_Onorm(U_1499,U_1496))),sK16(U_1499)))
| ~ sP160(U_1496,U_1497,U_1499) ),
inference(clausify,[status(thm)],[f_471_4]) ).
fof(f_472_1,plain,
! [V_x,T_a] :
( ? [B_K] :
( ! [B_x] : 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),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Opos__bounded]) ).
fof(f_472_2,plain,
! [U_1503,U_1502] :
( ? [U_1501] :
( ! [U_1500] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1502),U_1503),U_1500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1502,U_1500)),U_1501))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1501) )
| ~ class_RealVector_Oreal__normed__algebra(U_1502) ),
inference(variable_rename,[status(thm)],[f_472_1]) ).
fof(f_472_3,plain,
! [U_1503,U_1502] :
( ( ! [U_1500] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1502),U_1503),U_1500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1502,U_1500)),sK17(U_1503,U_1502)))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK17(U_1503,U_1502)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1502) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_1501,sK17(U_1503,U_1502))],[f_472_2]) ).
fof(f_472_4,plain,
( ! [U_1500,U_1502,U_1503] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1502),U_1503),U_1500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1502,U_1500)),sK17(U_1503,U_1502)))
| ~ sP161(U_1500,U_1502,U_1503) )
& ! [U_1500,U_1502,U_1503] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK17(U_1503,U_1502))
| ~ sP161(U_1500,U_1502,U_1503) )
& ! [U_1500,U_1502,U_1503] :
( sP161(U_1500,U_1502,U_1503)
| ~ class_RealVector_Oreal__normed__algebra(U_1502) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161])],[f_472_3]) ).
cnf(f_472_5,plain,
( sP161(U_1500,U_1502,U_1503)
| ~ class_RealVector_Oreal__normed__algebra(U_1502) ),
inference(clausify,[status(thm)],[f_472_4]) ).
cnf(f_472_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK17(U_1503,U_1502))
| ~ sP161(U_1500,U_1502,U_1503) ),
inference(clausify,[status(thm)],[f_472_4]) ).
cnf(f_472_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1502,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1502),U_1503),U_1500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1502,U_1500)),sK17(U_1503,U_1502)))
| ~ sP161(U_1500,U_1502,U_1503) ),
inference(clausify,[status(thm)],[f_472_4]) ).
fof(f_473_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_473_2,plain,
! [U_1507,U_1506,U_1505,U_1504] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1504),U_1505),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1506),U_1505),U_1507)) = 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_1504,U_1506)),U_1505),U_1507),
inference(variable_rename,[status(thm)],[f_473_1]) ).
fof(f_473_3,plain,
! [U_1504,U_1505,U_1506,U_1507] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1504),U_1505),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1506),U_1505),U_1507)) = 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_1504,U_1506)),U_1505),U_1507),
inference(definitional_conversion,[status(esa)],[f_473_2]) ).
cnf(f_473_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1504),U_1505),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1506),U_1505),U_1507)) = 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_1504,U_1506)),U_1505),U_1507),
inference(clausify,[status(thm)],[f_473_3]) ).
fof(f_474_1,plain,
! [V_n_2,V_k_2,V_ma_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_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_474_2,plain,
! [U_1510,U_1509,U_1508] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1508,U_1509) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1510,U_1509)
| U_1508 != U_1510 )
& ( U_1508 = U_1510
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1508,U_1509) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1510,U_1509) ) ),
inference(variable_rename,[status(thm)],[f_474_1]) ).
fof(f_474_3,plain,
( ! [U_1516,U_1514,U_1512] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1512,U_1514) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1516,U_1514)
| U_1512 != U_1516 )
& ! [U_1515,U_1513,U_1511] :
( U_1511 = U_1515
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1511,U_1513) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1515,U_1513) ) ),
inference(miniscope,[status(thm)],[f_474_2]) ).
fof(f_474_4,plain,
( ! [U_1514,U_1516,U_1512] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1512,U_1514) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1516,U_1514)
| U_1512 != U_1516 )
& ! [U_1511,U_1513,U_1515] :
( U_1511 = U_1515
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1511,U_1513) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1515,U_1513) ) ),
inference(definitional_conversion,[status(esa)],[f_474_3]) ).
cnf(f_474_5,plain,
( U_1511 = U_1515
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1511,U_1513) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1515,U_1513) ),
inference(clausify,[status(thm)],[f_474_4]) ).
cnf(f_474_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1512,U_1514) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1516,U_1514)
| U_1512 != U_1516 ),
inference(clausify,[status(thm)],[f_474_4]) ).
fof(f_475_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_2) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_n_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_k_2,V_ma_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_475_2,plain,
! [U_1519,U_1518,U_1517] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1517,U_1518) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1517,U_1519)
| U_1518 != U_1519 )
& ( U_1518 = U_1519
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1517,U_1518) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1517,U_1519) ) ),
inference(variable_rename,[status(thm)],[f_475_1]) ).
fof(f_475_3,plain,
( ! [U_1525,U_1523] :
( ! [U_1521] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1521,U_1523) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1521,U_1525)
| U_1523 != U_1525 )
& ! [U_1524,U_1522] :
( ! [U_1520] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1522) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1524)
| U_1522 = U_1524 ) ),
inference(miniscope,[status(thm)],[f_475_2]) ).
fof(f_475_4,plain,
( ! [U_1523,U_1521,U_1525] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1521,U_1523) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1521,U_1525)
| U_1523 != U_1525 )
& ! [U_1520,U_1522,U_1524] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1522) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1524)
| U_1522 = U_1524 ) ),
inference(definitional_conversion,[status(esa)],[f_475_3]) ).
cnf(f_475_5,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1522) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1520,U_1524)
| U_1522 = U_1524 ),
inference(clausify,[status(thm)],[f_475_4]) ).
cnf(f_475_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1521,U_1523) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1521,U_1525)
| U_1523 != U_1525 ),
inference(clausify,[status(thm)],[f_475_4]) ).
fof(f_476_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_476_2,plain,
! [U_1528,U_1527,U_1526] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1526,U_1527)),U_1528) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1526),U_1528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1527),U_1528)),
inference(variable_rename,[status(thm)],[f_476_1]) ).
fof(f_476_3,plain,
! [U_1526,U_1527,U_1528] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1526,U_1527)),U_1528) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1526),U_1528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1527),U_1528)),
inference(definitional_conversion,[status(esa)],[f_476_2]) ).
cnf(f_476_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1526,U_1527)),U_1528) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1526),U_1528),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1527),U_1528)),
inference(clausify,[status(thm)],[f_476_3]) ).
fof(f_477_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_477_2,plain,
! [U_1531,U_1530,U_1529] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1529),U_1530)),U_1531) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1529),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1530),U_1531)),
inference(variable_rename,[status(thm)],[f_477_1]) ).
fof(f_477_3,plain,
! [U_1529,U_1530,U_1531] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1529),U_1530)),U_1531) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1529),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1530),U_1531)),
inference(definitional_conversion,[status(esa)],[f_477_2]) ).
cnf(f_477_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1529),U_1530)),U_1531) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1529),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1530),U_1531)),
inference(clausify,[status(thm)],[f_477_3]) ).
fof(f_478_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_478_2,plain,
! [U_1534,U_1533,U_1532] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1532,U_1533),U_1534) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1532,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1533,U_1534)),
inference(variable_rename,[status(thm)],[f_478_1]) ).
fof(f_478_3,plain,
! [U_1533,U_1532,U_1534] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1532,U_1533),U_1534) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1532,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1533,U_1534)),
inference(definitional_conversion,[status(esa)],[f_478_2]) ).
cnf(f_478_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1532,U_1533),U_1534) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1532,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1533,U_1534)),
inference(clausify,[status(thm)],[f_478_3]) ).
fof(f_479_1,plain,
! [V_n_2,V_ma_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_ma_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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_479_2,plain,
! [U_1536,U_1535] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1535),U_1536) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1536 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1535 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( U_1536 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1535 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1535),U_1536) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_479_1]) ).
fof(f_479_3,plain,
( ! [U_1540,U_1538] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1538),U_1540) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1540 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1538 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1539,U_1537] :
( ( U_1539 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& U_1537 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1537),U_1539) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_479_2]) ).
fof(f_479_4,plain,
( ! [U_1539,U_1537] :
( U_1539 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP162(U_1539,U_1537) )
& ! [U_1539,U_1537] :
( U_1537 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP162(U_1539,U_1537) )
& ! [U_1540,U_1538] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1538),U_1540) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1540 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1538 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1539,U_1537] :
( sP162(U_1539,U_1537)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1537),U_1539) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP162])],[f_479_3]) ).
cnf(f_479_5,plain,
( sP162(U_1539,U_1537)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1537),U_1539) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_479_4]) ).
cnf(f_479_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1538),U_1540) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1540 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| U_1538 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_479_4]) ).
cnf(f_479_7,plain,
( U_1537 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP162(U_1539,U_1537) ),
inference(clausify,[status(thm)],[f_479_4]) ).
cnf(f_479_8,plain,
( U_1539 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP162(U_1539,U_1537) ),
inference(clausify,[status(thm)],[f_479_4]) ).
fof(f_480_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_480_2,plain,
! [U_1543,U_1542,U_1541] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1541),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1542,U_1543)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1541),U_1542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1541),U_1543)),
inference(variable_rename,[status(thm)],[f_480_1]) ).
fof(f_480_3,plain,
! [U_1541,U_1542,U_1543] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1541),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1542,U_1543)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1541),U_1542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1541),U_1543)),
inference(definitional_conversion,[status(esa)],[f_480_2]) ).
cnf(f_480_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1541),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1542,U_1543)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1541),U_1542),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1541),U_1543)),
inference(clausify,[status(thm)],[f_480_3]) ).
fof(f_481_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_481_2,plain,
! [U_1546,U_1545,U_1544] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1544,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1545,U_1546)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1545,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1544,U_1546)),
inference(variable_rename,[status(thm)],[f_481_1]) ).
fof(f_481_3,plain,
! [U_1544,U_1545,U_1546] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1544,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1545,U_1546)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1545,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1544,U_1546)),
inference(definitional_conversion,[status(esa)],[f_481_2]) ).
cnf(f_481_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1544,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1545,U_1546)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1545,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1544,U_1546)),
inference(clausify,[status(thm)],[f_481_3]) ).
fof(f_482_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_482_2,plain,
! [U_1548,U_1547] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1547),U_1548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1548),U_1547),
inference(variable_rename,[status(thm)],[f_482_1]) ).
fof(f_482_3,plain,
! [U_1547,U_1548] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1547),U_1548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1548),U_1547),
inference(definitional_conversion,[status(esa)],[f_482_2]) ).
cnf(f_482_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1547),U_1548) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1548),U_1547),
inference(clausify,[status(thm)],[f_482_3]) ).
fof(f_483_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_483_2,plain,
! [U_1550,U_1549] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1549,U_1550) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1550,U_1549),
inference(variable_rename,[status(thm)],[f_483_1]) ).
fof(f_483_3,plain,
! [U_1550,U_1549] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1549,U_1550) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1550,U_1549),
inference(definitional_conversion,[status(esa)],[f_483_2]) ).
cnf(f_483_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1549,U_1550) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1550,U_1549),
inference(clausify,[status(thm)],[f_483_3]) ).
fof(f_484_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_484_2,plain,
! [U_1551] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1551),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1551,
inference(variable_rename,[status(thm)],[f_484_1]) ).
fof(f_484_3,plain,
! [U_1551] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1551),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1551,
inference(definitional_conversion,[status(esa)],[f_484_2]) ).
cnf(f_484_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1551),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1551,
inference(clausify,[status(thm)],[f_484_3]) ).
fof(f_485_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| V_ma_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
& V_ma_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_ma_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__1__eq__mult__iff]) ).
fof(f_485_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_485_1]) ).
fof(f_485_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_485_2]) ).
fof(f_485_4,plain,
( ! [U_1556,U_1554] :
( U_1556 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP163(U_1556,U_1554) )
& ! [U_1556,U_1554] :
( U_1554 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP163(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] :
( sP163(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,[sP163])],[f_485_3]) ).
cnf(f_485_5,plain,
( sP163(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_485_4]) ).
cnf(f_485_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_485_4]) ).
cnf(f_485_7,plain,
( U_1554 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP163(U_1556,U_1554) ),
inference(clausify,[status(thm)],[f_485_4]) ).
cnf(f_485_8,plain,
( U_1556 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP163(U_1556,U_1554) ),
inference(clausify,[status(thm)],[f_485_4]) ).
fof(f_486_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_486_2,plain,
! [U_1558] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1558) = U_1558,
inference(variable_rename,[status(thm)],[f_486_1]) ).
fof(f_486_3,plain,
! [U_1558] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1558) = U_1558,
inference(definitional_conversion,[status(esa)],[f_486_2]) ).
cnf(f_486_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_1558) = U_1558,
inference(clausify,[status(thm)],[f_486_3]) ).
fof(f_487_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| ( V_ma_2 != V_n_2
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_ma_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_ma_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_487_2,plain,
! [U_1561,U_1560,U_1559] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1559),U_1560) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1559),U_1561)
| ( U_1560 != U_1561
& U_1559 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_1560 = U_1561
| U_1559 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1559),U_1560) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1559),U_1561) ) ),
inference(variable_rename,[status(thm)],[f_487_1]) ).
fof(f_487_3,plain,
( ! [U_1567,U_1565,U_1563] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1563),U_1565) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1563),U_1567)
| ( U_1565 != U_1567
& U_1563 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1566,U_1564,U_1562] :
( U_1564 = U_1566
| U_1562 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1562),U_1564) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1562),U_1566) ) ),
inference(miniscope,[status(thm)],[f_487_2]) ).
fof(f_487_4,plain,
( ! [U_1567,U_1565,U_1563] :
( U_1565 != U_1567
| ~ sP164(U_1567,U_1565,U_1563) )
& ! [U_1567,U_1565,U_1563] :
( U_1563 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP164(U_1567,U_1565,U_1563) )
& ! [U_1567,U_1565,U_1563] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1563),U_1565) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1563),U_1567)
| sP164(U_1567,U_1565,U_1563) )
& ! [U_1564,U_1562,U_1566] :
( U_1564 = U_1566
| U_1562 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1562),U_1564) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1562),U_1566) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164])],[f_487_3]) ).
cnf(f_487_5,plain,
( U_1564 = U_1566
| U_1562 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1562),U_1564) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1562),U_1566) ),
inference(clausify,[status(thm)],[f_487_4]) ).
cnf(f_487_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1563),U_1565) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1563),U_1567)
| sP164(U_1567,U_1565,U_1563) ),
inference(clausify,[status(thm)],[f_487_4]) ).
cnf(f_487_7,plain,
( U_1563 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP164(U_1567,U_1565,U_1563) ),
inference(clausify,[status(thm)],[f_487_4]) ).
cnf(f_487_8,plain,
( U_1565 != U_1567
| ~ sP164(U_1567,U_1565,U_1563) ),
inference(clausify,[status(thm)],[f_487_4]) ).
fof(f_488_1,plain,
! [V_n_2,V_ma_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_ma_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_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__less__cancel1]) ).
fof(f_488_2,plain,
! [U_1570,U_1569,U_1568] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1570))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1569,U_1570) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1569,U_1570)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1570)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1568) ),
inference(variable_rename,[status(thm)],[f_488_1]) ).
fof(f_488_3,plain,
( ! [U_1569,U_1570,U_1568] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1570))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1569,U_1570)
| ~ sP165(U_1569,U_1570,U_1568) )
& ! [U_1569,U_1570,U_1568] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1569,U_1570)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1570))
| ~ sP165(U_1569,U_1570,U_1568) )
& ! [U_1569,U_1570,U_1568] :
( sP165(U_1569,U_1570,U_1568)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1568) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_488_2]) ).
cnf(f_488_4,plain,
( sP165(U_1569,U_1570,U_1568)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1568) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1569,U_1570)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1570))
| ~ sP165(U_1569,U_1570,U_1568) ),
inference(clausify,[status(thm)],[f_488_3]) ).
cnf(f_488_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1569),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1568),U_1570))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1569,U_1570)
| ~ sP165(U_1569,U_1570,U_1568) ),
inference(clausify,[status(thm)],[f_488_3]) ).
fof(f_489_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__eq__cancel1]) ).
fof(f_489_2,plain,
! [U_1573,U_1572,U_1571] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1572) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1573)
| U_1572 != U_1573 )
& ( U_1572 = U_1573
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1572) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1573) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1571) ),
inference(variable_rename,[status(thm)],[f_489_1]) ).
fof(f_489_3,plain,
( ! [U_1573,U_1572,U_1571] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1572) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1573)
| U_1572 != U_1573
| ~ sP166(U_1573,U_1572,U_1571) )
& ! [U_1573,U_1572,U_1571] :
( U_1572 = U_1573
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1572) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1573)
| ~ sP166(U_1573,U_1572,U_1571) )
& ! [U_1573,U_1572,U_1571] :
( sP166(U_1573,U_1572,U_1571)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1571) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_489_2]) ).
cnf(f_489_4,plain,
( sP166(U_1573,U_1572,U_1571)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1571) ),
inference(clausify,[status(thm)],[f_489_3]) ).
cnf(f_489_5,plain,
( U_1572 = U_1573
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1572) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1573)
| ~ sP166(U_1573,U_1572,U_1571) ),
inference(clausify,[status(thm)],[f_489_3]) ).
cnf(f_489_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1572) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1571),U_1573)
| U_1572 != U_1573
| ~ sP166(U_1573,U_1572,U_1571) ),
inference(clausify,[status(thm)],[f_489_3]) ).
fof(f_490_1,plain,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_z) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I4_J]) ).
fof(f_490_2,plain,
! [U_1576,U_1575,U_1574] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1574,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1576,U_1575))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1574,U_1575) ),
inference(variable_rename,[status(thm)],[f_490_1]) ).
fof(f_490_3,plain,
! [U_1576,U_1575,U_1574] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1574,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1576,U_1575))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1574,U_1575) ),
inference(definitional_conversion,[status(esa)],[f_490_2]) ).
cnf(f_490_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1574,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1576,U_1575))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1574,U_1575) ),
inference(clausify,[status(thm)],[f_490_3]) ).
fof(f_491_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I3_J]) ).
fof(f_491_2,plain,
! [U_1579,U_1578,U_1577] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1577,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1578,U_1579))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1577,U_1578) ),
inference(variable_rename,[status(thm)],[f_491_1]) ).
fof(f_491_3,plain,
! [U_1578,U_1577,U_1579] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1577,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1578,U_1579))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1577,U_1578) ),
inference(definitional_conversion,[status(esa)],[f_491_2]) ).
cnf(f_491_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1577,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1578,U_1579))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1577,U_1578) ),
inference(clausify,[status(thm)],[f_491_3]) ).
fof(f_492_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I5_J]) ).
fof(f_492_2,plain,
! [U_1581,U_1580] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1580,U_1581)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1580,U_1581) ),
inference(variable_rename,[status(thm)],[f_492_1]) ).
fof(f_492_3,plain,
! [U_1580,U_1581] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1580,U_1581)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1580,U_1581) ),
inference(definitional_conversion,[status(esa)],[f_492_2]) ).
cnf(f_492_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1580,U_1581)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1580,U_1581) ),
inference(clausify,[status(thm)],[f_492_3]) ).
fof(f_493_1,plain,
! [V_z,V_y,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I1_J]) ).
fof(f_493_2,plain,
! [U_1584,U_1583,U_1582] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1582,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1583,U_1584))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1582,U_1583) ),
inference(variable_rename,[status(thm)],[f_493_1]) ).
fof(f_493_3,plain,
! [U_1584,U_1583,U_1582] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1582,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1583,U_1584))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1582,U_1583) ),
inference(definitional_conversion,[status(esa)],[f_493_2]) ).
cnf(f_493_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1582,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1583,U_1584))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1582,U_1583) ),
inference(clausify,[status(thm)],[f_493_3]) ).
fof(f_494_1,plain,
! [V_y,V_z,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_y,V_z))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x,V_z) ),
inference(fof_nnf,[status(thm)],[fact_termination__basic__simps_I2_J]) ).
fof(f_494_2,plain,
! [U_1587,U_1586,U_1585] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1585,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1587,U_1586))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1585,U_1586) ),
inference(variable_rename,[status(thm)],[f_494_1]) ).
fof(f_494_3,plain,
! [U_1587,U_1586,U_1585] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1585,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1587,U_1586))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1585,U_1586) ),
inference(definitional_conversion,[status(esa)],[f_494_2]) ).
cnf(f_494_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1585,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1587,U_1586))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1585,U_1586) ),
inference(clausify,[status(thm)],[f_494_3]) ).
fof(f_495_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_Odecseq(T_a,V_X_2)
| ? [B_m,B_n] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) ) )
& ( ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_n),hAPP(V_X_2,B_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
| ~ c_SEQ_Odecseq(T_a,V_X_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_decseq__def]) ).
fof(f_495_2,plain,
! [U_1593,U_1592] :
( ( ( c_SEQ_Odecseq(U_1592,U_1593)
| ? [U_1591,U_1590] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,U_1590),hAPP(U_1593,U_1591))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1591,U_1590) ) )
& ( ! [U_1589,U_1588] :
( c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,U_1588),hAPP(U_1593,U_1589))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1589,U_1588) )
| ~ c_SEQ_Odecseq(U_1592,U_1593) ) )
| ~ class_Orderings_Oorder(U_1592) ),
inference(variable_rename,[status(thm)],[f_495_1]) ).
fof(f_495_3,plain,
! [U_1593,U_1592] :
( ( ( c_SEQ_Odecseq(U_1592,U_1593)
| ? [U_1590] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,U_1590),hAPP(U_1593,sK18(U_1593,U_1592)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK18(U_1593,U_1592),U_1590) ) )
& ( ! [U_1589,U_1588] :
( c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,U_1588),hAPP(U_1593,U_1589))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1589,U_1588) )
| ~ c_SEQ_Odecseq(U_1592,U_1593) ) )
| ~ class_Orderings_Oorder(U_1592) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_1591,sK18(U_1593,U_1592))],[f_495_2]) ).
fof(f_495_4,plain,
! [U_1593,U_1592] :
( ( ( c_SEQ_Odecseq(U_1592,U_1593)
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,sK19(U_1593,U_1592)),hAPP(U_1593,sK18(U_1593,U_1592)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK18(U_1593,U_1592),sK19(U_1593,U_1592)) ) )
& ( ! [U_1589,U_1588] :
( c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,U_1588),hAPP(U_1593,U_1589))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1589,U_1588) )
| ~ c_SEQ_Odecseq(U_1592,U_1593) ) )
| ~ class_Orderings_Oorder(U_1592) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_1590,sK19(U_1593,U_1592))],[f_495_3]) ).
fof(f_495_5,plain,
( ! [U_1592,U_1593] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,sK19(U_1593,U_1592)),hAPP(U_1593,sK18(U_1593,U_1592)))
| ~ sP167(U_1592,U_1593) )
& ! [U_1592,U_1593] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK18(U_1593,U_1592),sK19(U_1593,U_1592))
| ~ sP167(U_1592,U_1593) )
& ! [U_1588,U_1589,U_1592,U_1593] :
( c_SEQ_Odecseq(U_1592,U_1593)
| sP167(U_1592,U_1593)
| ~ sP168(U_1588,U_1589,U_1592,U_1593) )
& ! [U_1588,U_1589,U_1592,U_1593] :
( c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,U_1588),hAPP(U_1593,U_1589))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1589,U_1588)
| ~ c_SEQ_Odecseq(U_1592,U_1593)
| ~ sP168(U_1588,U_1589,U_1592,U_1593) )
& ! [U_1588,U_1589,U_1592,U_1593] :
( sP168(U_1588,U_1589,U_1592,U_1593)
| ~ class_Orderings_Oorder(U_1592) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167,sP168])],[f_495_4]) ).
cnf(f_495_6,plain,
( sP168(U_1588,U_1589,U_1592,U_1593)
| ~ class_Orderings_Oorder(U_1592) ),
inference(clausify,[status(thm)],[f_495_5]) ).
cnf(f_495_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,U_1588),hAPP(U_1593,U_1589))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1589,U_1588)
| ~ c_SEQ_Odecseq(U_1592,U_1593)
| ~ sP168(U_1588,U_1589,U_1592,U_1593) ),
inference(clausify,[status(thm)],[f_495_5]) ).
cnf(f_495_8,plain,
( c_SEQ_Odecseq(U_1592,U_1593)
| sP167(U_1592,U_1593)
| ~ sP168(U_1588,U_1589,U_1592,U_1593) ),
inference(clausify,[status(thm)],[f_495_5]) ).
cnf(f_495_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK18(U_1593,U_1592),sK19(U_1593,U_1592))
| ~ sP167(U_1592,U_1593) ),
inference(clausify,[status(thm)],[f_495_5]) ).
cnf(f_495_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1592,hAPP(U_1593,sK19(U_1593,U_1592)),hAPP(U_1593,sK18(U_1593,U_1592)))
| ~ sP167(U_1592,U_1593) ),
inference(clausify,[status(thm)],[f_495_5]) ).
fof(f_496_1,plain,
! [V_y,V_x,T_a] :
( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_y),c_Groups_Ouminus__class_Ouminus(T_a,V_x))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_x,V_y)
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__mono]) ).
fof(f_496_2,plain,
! [U_1596,U_1595,U_1594] :
( c_Orderings_Oord__class_Oless__eq(U_1594,c_Groups_Ouminus__class_Ouminus(U_1594,U_1596),c_Groups_Ouminus__class_Ouminus(U_1594,U_1595))
| ~ c_Orderings_Oord__class_Oless__eq(U_1594,U_1595,U_1596)
| ~ class_Lattices_Oboolean__algebra(U_1594) ),
inference(variable_rename,[status(thm)],[f_496_1]) ).
fof(f_496_3,plain,
! [U_1596,U_1594,U_1595] :
( c_Orderings_Oord__class_Oless__eq(U_1594,c_Groups_Ouminus__class_Ouminus(U_1594,U_1596),c_Groups_Ouminus__class_Ouminus(U_1594,U_1595))
| ~ c_Orderings_Oord__class_Oless__eq(U_1594,U_1595,U_1596)
| ~ class_Lattices_Oboolean__algebra(U_1594) ),
inference(definitional_conversion,[status(esa)],[f_496_2]) ).
cnf(f_496_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1594,c_Groups_Ouminus__class_Ouminus(U_1594,U_1596),c_Groups_Ouminus__class_Ouminus(U_1594,U_1595))
| ~ c_Orderings_Oord__class_Oless__eq(U_1594,U_1595,U_1596)
| ~ class_Lattices_Oboolean__algebra(U_1594) ),
inference(clausify,[status(thm)],[f_496_3]) ).
fof(f_497_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_y_2,V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)) ) )
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__le__compl__iff]) ).
fof(f_497_2,plain,
! [U_1599,U_1598,U_1597] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_1597,c_Groups_Ouminus__class_Ouminus(U_1597,U_1598),c_Groups_Ouminus__class_Ouminus(U_1597,U_1599))
| ~ c_Orderings_Oord__class_Oless__eq(U_1597,U_1599,U_1598) )
& ( c_Orderings_Oord__class_Oless__eq(U_1597,U_1599,U_1598)
| ~ c_Orderings_Oord__class_Oless__eq(U_1597,c_Groups_Ouminus__class_Ouminus(U_1597,U_1598),c_Groups_Ouminus__class_Ouminus(U_1597,U_1599)) ) )
| ~ class_Lattices_Oboolean__algebra(U_1597) ),
inference(variable_rename,[status(thm)],[f_497_1]) ).
fof(f_497_3,plain,
( ! [U_1598,U_1597,U_1599] :
( c_Orderings_Oord__class_Oless__eq(U_1597,c_Groups_Ouminus__class_Ouminus(U_1597,U_1598),c_Groups_Ouminus__class_Ouminus(U_1597,U_1599))
| ~ c_Orderings_Oord__class_Oless__eq(U_1597,U_1599,U_1598)
| ~ sP169(U_1598,U_1597,U_1599) )
& ! [U_1598,U_1597,U_1599] :
( c_Orderings_Oord__class_Oless__eq(U_1597,U_1599,U_1598)
| ~ c_Orderings_Oord__class_Oless__eq(U_1597,c_Groups_Ouminus__class_Ouminus(U_1597,U_1598),c_Groups_Ouminus__class_Ouminus(U_1597,U_1599))
| ~ sP169(U_1598,U_1597,U_1599) )
& ! [U_1598,U_1597,U_1599] :
( sP169(U_1598,U_1597,U_1599)
| ~ class_Lattices_Oboolean__algebra(U_1597) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP169])],[f_497_2]) ).
cnf(f_497_4,plain,
( sP169(U_1598,U_1597,U_1599)
| ~ class_Lattices_Oboolean__algebra(U_1597) ),
inference(clausify,[status(thm)],[f_497_3]) ).
cnf(f_497_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_1597,U_1599,U_1598)
| ~ c_Orderings_Oord__class_Oless__eq(U_1597,c_Groups_Ouminus__class_Ouminus(U_1597,U_1598),c_Groups_Ouminus__class_Ouminus(U_1597,U_1599))
| ~ sP169(U_1598,U_1597,U_1599) ),
inference(clausify,[status(thm)],[f_497_3]) ).
cnf(f_497_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_1597,c_Groups_Ouminus__class_Ouminus(U_1597,U_1598),c_Groups_Ouminus__class_Ouminus(U_1597,U_1599))
| ~ c_Orderings_Oord__class_Oless__eq(U_1597,U_1599,U_1598)
| ~ sP169(U_1598,U_1597,U_1599) ),
inference(clausify,[status(thm)],[f_497_3]) ).
fof(f_498_1,plain,
! [V_x,T_a] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(T_a))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_x) ) )
| V_x = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(T_a),V_x) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| V_x != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__poly__def]) ).
fof(f_498_2,plain,
! [U_1601,U_1600] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1600),U_1601) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1600),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1600)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1600),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600)),U_1601) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1600),U_1601) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1600))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1600),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600)),U_1601) ) )
| U_1601 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600)) )
& ( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1600),U_1601) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600))
| U_1601 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600)) ) )
| ~ class_Rings_Olinordered__idom(U_1600) ),
inference(variable_rename,[status(thm)],[f_498_1]) ).
fof(f_498_3,plain,
( ! [U_1601,U_1600] :
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1600),U_1601) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1600),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1600)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1600),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600)),U_1601)
| ~ sP170(U_1601,U_1600) )
& ! [U_1601,U_1600] :
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1600),U_1601) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1600))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1600),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600)),U_1601)
| ~ sP170(U_1601,U_1600) )
& ! [U_1601,U_1600] :
( sP170(U_1601,U_1600)
| U_1601 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600))
| ~ sP171(U_1601,U_1600) )
& ! [U_1601,U_1600] :
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1600),U_1601) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600))
| U_1601 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600))
| ~ sP171(U_1601,U_1600) )
& ! [U_1601,U_1600] :
( sP171(U_1601,U_1600)
| ~ class_Rings_Olinordered__idom(U_1600) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170,sP171])],[f_498_2]) ).
cnf(f_498_4,plain,
( sP171(U_1601,U_1600)
| ~ class_Rings_Olinordered__idom(U_1600) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1600),U_1601) = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600))
| U_1601 != c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600))
| ~ sP171(U_1601,U_1600) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_6,plain,
( sP170(U_1601,U_1600)
| U_1601 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600))
| ~ sP171(U_1601,U_1600) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_7,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1600),U_1601) = c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1600))
| ~ c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1600),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600)),U_1601)
| ~ sP170(U_1601,U_1600) ),
inference(clausify,[status(thm)],[f_498_3]) ).
cnf(f_498_8,plain,
( c_Groups_Osgn__class_Osgn(tc_Polynomial_Opoly(U_1600),U_1601) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_1600),c_Groups_Oone__class_Oone(tc_Polynomial_Opoly(U_1600)))
| c_Orderings_Oord__class_Oless(tc_Polynomial_Opoly(U_1600),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1600)),U_1601)
| ~ sP170(U_1601,U_1600) ),
inference(clausify,[status(thm)],[f_498_3]) ).
fof(f_499_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a)) = c_Groups_Osgn__class_Osgn(T_a,V_a)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__sgn]) ).
fof(f_499_2,plain,
! [U_1603,U_1602] :
( c_Groups_Osgn__class_Osgn(U_1602,c_Groups_Osgn__class_Osgn(U_1602,U_1603)) = c_Groups_Osgn__class_Osgn(U_1602,U_1603)
| ~ class_Rings_Olinordered__idom(U_1602) ),
inference(variable_rename,[status(thm)],[f_499_1]) ).
fof(f_499_3,plain,
! [U_1603,U_1602] :
( c_Groups_Osgn__class_Osgn(U_1602,c_Groups_Osgn__class_Osgn(U_1602,U_1603)) = c_Groups_Osgn__class_Osgn(U_1602,U_1603)
| ~ class_Rings_Olinordered__idom(U_1602) ),
inference(definitional_conversion,[status(esa)],[f_499_2]) ).
cnf(f_499_4,plain,
( c_Groups_Osgn__class_Osgn(U_1602,c_Groups_Osgn__class_Osgn(U_1602,U_1603)) = c_Groups_Osgn__class_Osgn(U_1602,U_1603)
| ~ class_Rings_Olinordered__idom(U_1602) ),
inference(clausify,[status(thm)],[f_499_3]) ).
fof(f_500_1,plain,
! [V_x,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x))
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__minus]) ).
fof(f_500_2,plain,
! [U_1605,U_1604] :
( c_Groups_Osgn__class_Osgn(U_1604,c_Groups_Ouminus__class_Ouminus(U_1604,U_1605)) = c_Groups_Ouminus__class_Ouminus(U_1604,c_Groups_Osgn__class_Osgn(U_1604,U_1605))
| ~ class_RealVector_Oreal__normed__vector(U_1604) ),
inference(variable_rename,[status(thm)],[f_500_1]) ).
fof(f_500_3,plain,
! [U_1605,U_1604] :
( c_Groups_Osgn__class_Osgn(U_1604,c_Groups_Ouminus__class_Ouminus(U_1604,U_1605)) = c_Groups_Ouminus__class_Ouminus(U_1604,c_Groups_Osgn__class_Osgn(U_1604,U_1605))
| ~ class_RealVector_Oreal__normed__vector(U_1604) ),
inference(definitional_conversion,[status(esa)],[f_500_2]) ).
cnf(f_500_4,plain,
( c_Groups_Osgn__class_Osgn(U_1604,c_Groups_Ouminus__class_Ouminus(U_1604,U_1605)) = c_Groups_Ouminus__class_Ouminus(U_1604,c_Groups_Osgn__class_Osgn(U_1604,U_1605))
| ~ class_RealVector_Oreal__normed__vector(U_1604) ),
inference(clausify,[status(thm)],[f_500_3]) ).
fof(f_501_1,plain,
! [T_a] :
( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a)
| ~ class_RealVector_Oreal__normed__algebra__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__one]) ).
fof(f_501_2,plain,
! [U_1606] :
( c_Groups_Osgn__class_Osgn(U_1606,c_Groups_Oone__class_Oone(U_1606)) = c_Groups_Oone__class_Oone(U_1606)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1606) ),
inference(variable_rename,[status(thm)],[f_501_1]) ).
fof(f_501_3,plain,
! [U_1606] :
( c_Groups_Osgn__class_Osgn(U_1606,c_Groups_Oone__class_Oone(U_1606)) = c_Groups_Oone__class_Oone(U_1606)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1606) ),
inference(definitional_conversion,[status(esa)],[f_501_2]) ).
cnf(f_501_4,plain,
( c_Groups_Osgn__class_Osgn(U_1606,c_Groups_Oone__class_Oone(U_1606)) = c_Groups_Oone__class_Oone(U_1606)
| ~ class_RealVector_Oreal__normed__algebra__1(U_1606) ),
inference(clausify,[status(thm)],[f_501_3]) ).
fof(f_502_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Osgn__class_Osgn(T_a,V_y))
| ~ class_RealVector_Oreal__normed__div__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__mult]) ).
fof(f_502_2,plain,
! [U_1609,U_1608,U_1607] :
( c_Groups_Osgn__class_Osgn(U_1607,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1607),U_1608),U_1609)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1607),c_Groups_Osgn__class_Osgn(U_1607,U_1608)),c_Groups_Osgn__class_Osgn(U_1607,U_1609))
| ~ class_RealVector_Oreal__normed__div__algebra(U_1607) ),
inference(variable_rename,[status(thm)],[f_502_1]) ).
fof(f_502_3,plain,
! [U_1607,U_1608,U_1609] :
( c_Groups_Osgn__class_Osgn(U_1607,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1607),U_1608),U_1609)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1607),c_Groups_Osgn__class_Osgn(U_1607,U_1608)),c_Groups_Osgn__class_Osgn(U_1607,U_1609))
| ~ class_RealVector_Oreal__normed__div__algebra(U_1607) ),
inference(definitional_conversion,[status(esa)],[f_502_2]) ).
cnf(f_502_4,plain,
( c_Groups_Osgn__class_Osgn(U_1607,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1607),U_1608),U_1609)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1607),c_Groups_Osgn__class_Osgn(U_1607,U_1608)),c_Groups_Osgn__class_Osgn(U_1607,U_1609))
| ~ class_RealVector_Oreal__normed__div__algebra(U_1607) ),
inference(clausify,[status(thm)],[f_502_3]) ).
fof(f_503_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Osgn__class_Osgn(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_Osgn__class_Osgn(T_a,V_a)),c_Groups_Osgn__class_Osgn(T_a,V_b))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__times]) ).
fof(f_503_2,plain,
! [U_1612,U_1611,U_1610] :
( c_Groups_Osgn__class_Osgn(U_1610,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1610),U_1611),U_1612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1610),c_Groups_Osgn__class_Osgn(U_1610,U_1611)),c_Groups_Osgn__class_Osgn(U_1610,U_1612))
| ~ class_Rings_Olinordered__idom(U_1610) ),
inference(variable_rename,[status(thm)],[f_503_1]) ).
fof(f_503_3,plain,
! [U_1610,U_1611,U_1612] :
( c_Groups_Osgn__class_Osgn(U_1610,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1610),U_1611),U_1612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1610),c_Groups_Osgn__class_Osgn(U_1610,U_1611)),c_Groups_Osgn__class_Osgn(U_1610,U_1612))
| ~ class_Rings_Olinordered__idom(U_1610) ),
inference(definitional_conversion,[status(esa)],[f_503_2]) ).
cnf(f_503_4,plain,
( c_Groups_Osgn__class_Osgn(U_1610,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1610),U_1611),U_1612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1610),c_Groups_Osgn__class_Osgn(U_1610,U_1611)),c_Groups_Osgn__class_Osgn(U_1610,U_1612))
| ~ class_Rings_Olinordered__idom(U_1610) ),
inference(clausify,[status(thm)],[f_503_3]) ).
fof(f_504_1,plain,
! [T_a] :
( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_Groups_Osgn__if(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn0]) ).
fof(f_504_2,plain,
! [U_1613] :
( c_Groups_Osgn__class_Osgn(U_1613,c_Groups_Ozero__class_Ozero(U_1613)) = c_Groups_Ozero__class_Ozero(U_1613)
| ~ class_Groups_Osgn__if(U_1613) ),
inference(variable_rename,[status(thm)],[f_504_1]) ).
fof(f_504_3,plain,
! [U_1613] :
( c_Groups_Osgn__class_Osgn(U_1613,c_Groups_Ozero__class_Ozero(U_1613)) = c_Groups_Ozero__class_Ozero(U_1613)
| ~ class_Groups_Osgn__if(U_1613) ),
inference(definitional_conversion,[status(esa)],[f_504_2]) ).
cnf(f_504_4,plain,
( c_Groups_Osgn__class_Osgn(U_1613,c_Groups_Ozero__class_Ozero(U_1613)) = c_Groups_Ozero__class_Ozero(U_1613)
| ~ class_Groups_Osgn__if(U_1613) ),
inference(clausify,[status(thm)],[f_504_3]) ).
fof(f_505_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(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_Osgn__class_Osgn(T_a,V_a_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__0__0]) ).
fof(f_505_2,plain,
! [U_1615,U_1614] :
( ( ( c_Groups_Osgn__class_Osgn(U_1614,U_1615) = c_Groups_Ozero__class_Ozero(U_1614)
| U_1615 != c_Groups_Ozero__class_Ozero(U_1614) )
& ( U_1615 = c_Groups_Ozero__class_Ozero(U_1614)
| c_Groups_Osgn__class_Osgn(U_1614,U_1615) != c_Groups_Ozero__class_Ozero(U_1614) ) )
| ~ class_Rings_Olinordered__idom(U_1614) ),
inference(variable_rename,[status(thm)],[f_505_1]) ).
fof(f_505_3,plain,
( ! [U_1614,U_1615] :
( c_Groups_Osgn__class_Osgn(U_1614,U_1615) = c_Groups_Ozero__class_Ozero(U_1614)
| U_1615 != c_Groups_Ozero__class_Ozero(U_1614)
| ~ sP172(U_1614,U_1615) )
& ! [U_1614,U_1615] :
( U_1615 = c_Groups_Ozero__class_Ozero(U_1614)
| c_Groups_Osgn__class_Osgn(U_1614,U_1615) != c_Groups_Ozero__class_Ozero(U_1614)
| ~ sP172(U_1614,U_1615) )
& ! [U_1614,U_1615] :
( sP172(U_1614,U_1615)
| ~ class_Rings_Olinordered__idom(U_1614) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP172])],[f_505_2]) ).
cnf(f_505_4,plain,
( sP172(U_1614,U_1615)
| ~ class_Rings_Olinordered__idom(U_1614) ),
inference(clausify,[status(thm)],[f_505_3]) ).
cnf(f_505_5,plain,
( U_1615 = c_Groups_Ozero__class_Ozero(U_1614)
| c_Groups_Osgn__class_Osgn(U_1614,U_1615) != c_Groups_Ozero__class_Ozero(U_1614)
| ~ sP172(U_1614,U_1615) ),
inference(clausify,[status(thm)],[f_505_3]) ).
cnf(f_505_6,plain,
( c_Groups_Osgn__class_Osgn(U_1614,U_1615) = c_Groups_Ozero__class_Ozero(U_1614)
| U_1615 != c_Groups_Ozero__class_Ozero(U_1614)
| ~ sP172(U_1614,U_1615) ),
inference(clausify,[status(thm)],[f_505_3]) ).
fof(f_506_1,plain,
! [T_a] :
( c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__zero]) ).
fof(f_506_2,plain,
! [U_1616] :
( c_Groups_Osgn__class_Osgn(U_1616,c_Groups_Ozero__class_Ozero(U_1616)) = c_Groups_Ozero__class_Ozero(U_1616)
| ~ class_RealVector_Oreal__normed__vector(U_1616) ),
inference(variable_rename,[status(thm)],[f_506_1]) ).
fof(f_506_3,plain,
! [U_1616] :
( c_Groups_Osgn__class_Osgn(U_1616,c_Groups_Ozero__class_Ozero(U_1616)) = c_Groups_Ozero__class_Ozero(U_1616)
| ~ class_RealVector_Oreal__normed__vector(U_1616) ),
inference(definitional_conversion,[status(esa)],[f_506_2]) ).
cnf(f_506_4,plain,
( c_Groups_Osgn__class_Osgn(U_1616,c_Groups_Ozero__class_Ozero(U_1616)) = c_Groups_Ozero__class_Ozero(U_1616)
| ~ class_RealVector_Oreal__normed__vector(U_1616) ),
inference(clausify,[status(thm)],[f_506_3]) ).
fof(f_507_1,plain,
! [V_x_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_x_2) = c_Groups_Ozero__class_Ozero(T_a)
| V_x_2 != c_Groups_Ozero__class_Ozero(T_a) )
& ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a)
| c_Groups_Osgn__class_Osgn(T_a,V_x_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__zero__iff]) ).
fof(f_507_2,plain,
! [U_1618,U_1617] :
( ( ( c_Groups_Osgn__class_Osgn(U_1617,U_1618) = c_Groups_Ozero__class_Ozero(U_1617)
| U_1618 != c_Groups_Ozero__class_Ozero(U_1617) )
& ( U_1618 = c_Groups_Ozero__class_Ozero(U_1617)
| c_Groups_Osgn__class_Osgn(U_1617,U_1618) != c_Groups_Ozero__class_Ozero(U_1617) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1617) ),
inference(variable_rename,[status(thm)],[f_507_1]) ).
fof(f_507_3,plain,
( ! [U_1617,U_1618] :
( c_Groups_Osgn__class_Osgn(U_1617,U_1618) = c_Groups_Ozero__class_Ozero(U_1617)
| U_1618 != c_Groups_Ozero__class_Ozero(U_1617)
| ~ sP173(U_1617,U_1618) )
& ! [U_1617,U_1618] :
( U_1618 = c_Groups_Ozero__class_Ozero(U_1617)
| c_Groups_Osgn__class_Osgn(U_1617,U_1618) != c_Groups_Ozero__class_Ozero(U_1617)
| ~ sP173(U_1617,U_1618) )
& ! [U_1617,U_1618] :
( sP173(U_1617,U_1618)
| ~ class_RealVector_Oreal__normed__vector(U_1617) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173])],[f_507_2]) ).
cnf(f_507_4,plain,
( sP173(U_1617,U_1618)
| ~ class_RealVector_Oreal__normed__vector(U_1617) ),
inference(clausify,[status(thm)],[f_507_3]) ).
cnf(f_507_5,plain,
( U_1618 = c_Groups_Ozero__class_Ozero(U_1617)
| c_Groups_Osgn__class_Osgn(U_1617,U_1618) != c_Groups_Ozero__class_Ozero(U_1617)
| ~ sP173(U_1617,U_1618) ),
inference(clausify,[status(thm)],[f_507_3]) ).
cnf(f_507_6,plain,
( c_Groups_Osgn__class_Osgn(U_1617,U_1618) = c_Groups_Ozero__class_Ozero(U_1617)
| U_1618 != c_Groups_Ozero__class_Ozero(U_1617)
| ~ sP173(U_1617,U_1618) ),
inference(clausify,[status(thm)],[f_507_3]) ).
fof(f_508_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a)) )
& ( c_Orderings_Oord__class_Oless(T_a,V_a_2,c_Groups_Ozero__class_Ozero(T_a))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Osgn__class_Osgn(T_a,V_a_2),c_Groups_Ozero__class_Ozero(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__less]) ).
fof(f_508_2,plain,
! [U_1620,U_1619] :
( ( ( c_Orderings_Oord__class_Oless(U_1619,c_Groups_Osgn__class_Osgn(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619))
| ~ c_Orderings_Oord__class_Oless(U_1619,U_1620,c_Groups_Ozero__class_Ozero(U_1619)) )
& ( c_Orderings_Oord__class_Oless(U_1619,U_1620,c_Groups_Ozero__class_Ozero(U_1619))
| ~ c_Orderings_Oord__class_Oless(U_1619,c_Groups_Osgn__class_Osgn(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619)) ) )
| ~ class_Rings_Olinordered__idom(U_1619) ),
inference(variable_rename,[status(thm)],[f_508_1]) ).
fof(f_508_3,plain,
( ! [U_1620,U_1619] :
( c_Orderings_Oord__class_Oless(U_1619,c_Groups_Osgn__class_Osgn(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619))
| ~ c_Orderings_Oord__class_Oless(U_1619,U_1620,c_Groups_Ozero__class_Ozero(U_1619))
| ~ sP174(U_1620,U_1619) )
& ! [U_1620,U_1619] :
( c_Orderings_Oord__class_Oless(U_1619,U_1620,c_Groups_Ozero__class_Ozero(U_1619))
| ~ c_Orderings_Oord__class_Oless(U_1619,c_Groups_Osgn__class_Osgn(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619))
| ~ sP174(U_1620,U_1619) )
& ! [U_1620,U_1619] :
( sP174(U_1620,U_1619)
| ~ class_Rings_Olinordered__idom(U_1619) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP174])],[f_508_2]) ).
cnf(f_508_4,plain,
( sP174(U_1620,U_1619)
| ~ class_Rings_Olinordered__idom(U_1619) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_5,plain,
( c_Orderings_Oord__class_Oless(U_1619,U_1620,c_Groups_Ozero__class_Ozero(U_1619))
| ~ c_Orderings_Oord__class_Oless(U_1619,c_Groups_Osgn__class_Osgn(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619))
| ~ sP174(U_1620,U_1619) ),
inference(clausify,[status(thm)],[f_508_3]) ).
cnf(f_508_6,plain,
( c_Orderings_Oord__class_Oless(U_1619,c_Groups_Osgn__class_Osgn(U_1619,U_1620),c_Groups_Ozero__class_Ozero(U_1619))
| ~ c_Orderings_Oord__class_Oless(U_1619,U_1620,c_Groups_Ozero__class_Ozero(U_1619))
| ~ sP174(U_1620,U_1619) ),
inference(clausify,[status(thm)],[f_508_3]) ).
fof(f_509_1,plain,
! [V_a_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(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),V_a_2)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),c_Groups_Osgn__class_Osgn(T_a,V_a_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__greater]) ).
fof(f_509_2,plain,
! [U_1622,U_1621] :
( ( ( c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Osgn__class_Osgn(U_1621,U_1622))
| ~ c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),U_1622) )
& ( c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),U_1622)
| ~ c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Osgn__class_Osgn(U_1621,U_1622)) ) )
| ~ class_Rings_Olinordered__idom(U_1621) ),
inference(variable_rename,[status(thm)],[f_509_1]) ).
fof(f_509_3,plain,
( ! [U_1622,U_1621] :
( c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Osgn__class_Osgn(U_1621,U_1622))
| ~ c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),U_1622)
| ~ sP175(U_1622,U_1621) )
& ! [U_1622,U_1621] :
( c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),U_1622)
| ~ c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Osgn__class_Osgn(U_1621,U_1622))
| ~ sP175(U_1622,U_1621) )
& ! [U_1622,U_1621] :
( sP175(U_1622,U_1621)
| ~ class_Rings_Olinordered__idom(U_1621) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP175])],[f_509_2]) ).
cnf(f_509_4,plain,
( sP175(U_1622,U_1621)
| ~ class_Rings_Olinordered__idom(U_1621) ),
inference(clausify,[status(thm)],[f_509_3]) ).
cnf(f_509_5,plain,
( c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),U_1622)
| ~ c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Osgn__class_Osgn(U_1621,U_1622))
| ~ sP175(U_1622,U_1621) ),
inference(clausify,[status(thm)],[f_509_3]) ).
cnf(f_509_6,plain,
( c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),c_Groups_Osgn__class_Osgn(U_1621,U_1622))
| ~ c_Orderings_Oord__class_Oless(U_1621,c_Groups_Ozero__class_Ozero(U_1621),U_1622)
| ~ sP175(U_1622,U_1621) ),
inference(clausify,[status(thm)],[f_509_3]) ).
fof(f_510_1,plain,
! [V_k,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__sgn]) ).
fof(f_510_2,plain,
! [U_1624,U_1623] :
( c_Groups_Oabs__class_Oabs(U_1623,U_1624) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1623),U_1624),c_Groups_Osgn__class_Osgn(U_1623,U_1624))
| ~ class_Rings_Olinordered__idom(U_1623) ),
inference(variable_rename,[status(thm)],[f_510_1]) ).
fof(f_510_3,plain,
! [U_1624,U_1623] :
( c_Groups_Oabs__class_Oabs(U_1623,U_1624) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1623),U_1624),c_Groups_Osgn__class_Osgn(U_1623,U_1624))
| ~ class_Rings_Olinordered__idom(U_1623) ),
inference(definitional_conversion,[status(esa)],[f_510_2]) ).
cnf(f_510_4,plain,
( c_Groups_Oabs__class_Oabs(U_1623,U_1624) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1623),U_1624),c_Groups_Osgn__class_Osgn(U_1623,U_1624))
| ~ class_Rings_Olinordered__idom(U_1623) ),
inference(clausify,[status(thm)],[f_510_3]) ).
fof(f_511_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),c_Groups_Oabs__class_Oabs(T_a,V_x)) = V_x
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__sgn__abs]) ).
fof(f_511_2,plain,
! [U_1626,U_1625] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1625),c_Groups_Osgn__class_Osgn(U_1625,U_1626)),c_Groups_Oabs__class_Oabs(U_1625,U_1626)) = U_1626
| ~ class_Rings_Olinordered__idom(U_1625) ),
inference(variable_rename,[status(thm)],[f_511_1]) ).
fof(f_511_3,plain,
! [U_1625,U_1626] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1625),c_Groups_Osgn__class_Osgn(U_1625,U_1626)),c_Groups_Oabs__class_Oabs(U_1625,U_1626)) = U_1626
| ~ class_Rings_Olinordered__idom(U_1625) ),
inference(definitional_conversion,[status(esa)],[f_511_2]) ).
cnf(f_511_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1625),c_Groups_Osgn__class_Osgn(U_1625,U_1626)),c_Groups_Oabs__class_Oabs(U_1625,U_1626)) = U_1626
| ~ class_Rings_Olinordered__idom(U_1625) ),
inference(clausify,[status(thm)],[f_511_3]) ).
fof(f_512_1,plain,
! [V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_times_Oidem]) ).
fof(f_512_2,plain,
! [U_1628,U_1627] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1627),U_1628),U_1628) = U_1628
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1627) ),
inference(variable_rename,[status(thm)],[f_512_1]) ).
fof(f_512_3,plain,
! [U_1627,U_1628] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1627),U_1628),U_1628) = U_1628
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1627) ),
inference(definitional_conversion,[status(esa)],[f_512_2]) ).
cnf(f_512_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1627),U_1628),U_1628) = U_1628
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1627) ),
inference(clausify,[status(thm)],[f_512_3]) ).
fof(f_513_1,plain,
! [V_x,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__idem]) ).
fof(f_513_2,plain,
! [U_1630,U_1629] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1629),U_1630),U_1630) = U_1630
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1629) ),
inference(variable_rename,[status(thm)],[f_513_1]) ).
fof(f_513_3,plain,
! [U_1629,U_1630] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1629),U_1630),U_1630) = U_1630
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1629) ),
inference(definitional_conversion,[status(esa)],[f_513_2]) ).
cnf(f_513_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1629),U_1630),U_1630) = U_1630
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1629) ),
inference(clausify,[status(thm)],[f_513_3]) ).
fof(f_514_1,plain,
! [V_b,V_a,T_a] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_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)
| ~ class_Lattices_Oab__semigroup__idem__mult(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left__idem]) ).
fof(f_514_2,plain,
! [U_1633,U_1632,U_1631] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1633)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1633)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1631) ),
inference(variable_rename,[status(thm)],[f_514_1]) ).
fof(f_514_3,plain,
! [U_1632,U_1633,U_1631] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1633)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1633)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1631) ),
inference(definitional_conversion,[status(esa)],[f_514_2]) ).
cnf(f_514_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1633)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1631),U_1632),U_1633)
| ~ class_Lattices_Oab__semigroup__idem__mult(U_1631) ),
inference(clausify,[status(thm)],[f_514_3]) ).
fof(f_515_1,plain,
! [V_x,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x)) = V_x
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_double__compl]) ).
fof(f_515_2,plain,
! [U_1635,U_1634] :
( c_Groups_Ouminus__class_Ouminus(U_1634,c_Groups_Ouminus__class_Ouminus(U_1634,U_1635)) = U_1635
| ~ class_Lattices_Oboolean__algebra(U_1634) ),
inference(variable_rename,[status(thm)],[f_515_1]) ).
fof(f_515_3,plain,
! [U_1634,U_1635] :
( c_Groups_Ouminus__class_Ouminus(U_1634,c_Groups_Ouminus__class_Ouminus(U_1634,U_1635)) = U_1635
| ~ class_Lattices_Oboolean__algebra(U_1634) ),
inference(definitional_conversion,[status(esa)],[f_515_2]) ).
cnf(f_515_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_1634,c_Groups_Ouminus__class_Ouminus(U_1634,U_1635)) = U_1635
| ~ class_Lattices_Oboolean__algebra(U_1634) ),
inference(clausify,[status(thm)],[f_515_3]) ).
fof(f_516_1,plain,
! [V_x_2,V_A_2,T_b,T_a] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,T_a),V_A_2),V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,hAPP(V_A_2,V_x_2))
| ~ class_Groups_Ouminus(T_a) ),
inference(fof_nnf,[status(thm)],[fact_uminus__apply]) ).
fof(f_516_2,plain,
! [U_1639,U_1638,U_1637,U_1636] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1637,U_1636),U_1638),U_1639) = c_Groups_Ouminus__class_Ouminus(U_1636,hAPP(U_1638,U_1639))
| ~ class_Groups_Ouminus(U_1636) ),
inference(variable_rename,[status(thm)],[f_516_1]) ).
fof(f_516_3,plain,
! [U_1636,U_1637,U_1638,U_1639] :
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1637,U_1636),U_1638),U_1639) = c_Groups_Ouminus__class_Ouminus(U_1636,hAPP(U_1638,U_1639))
| ~ class_Groups_Ouminus(U_1636) ),
inference(definitional_conversion,[status(esa)],[f_516_2]) ).
cnf(f_516_4,plain,
( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1637,U_1636),U_1638),U_1639) = c_Groups_Ouminus__class_Ouminus(U_1636,hAPP(U_1638,U_1639))
| ~ class_Groups_Ouminus(U_1636) ),
inference(clausify,[status(thm)],[f_516_3]) ).
fof(f_517_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| c_Groups_Ouminus__class_Ouminus(T_a,V_x_2) != c_Groups_Ouminus__class_Ouminus(T_a,V_y_2) ) )
| ~ class_Lattices_Oboolean__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_compl__eq__compl__iff]) ).
fof(f_517_2,plain,
! [U_1642,U_1641,U_1640] :
( ( ( c_Groups_Ouminus__class_Ouminus(U_1640,U_1641) = c_Groups_Ouminus__class_Ouminus(U_1640,U_1642)
| U_1641 != U_1642 )
& ( U_1641 = U_1642
| c_Groups_Ouminus__class_Ouminus(U_1640,U_1641) != c_Groups_Ouminus__class_Ouminus(U_1640,U_1642) ) )
| ~ class_Lattices_Oboolean__algebra(U_1640) ),
inference(variable_rename,[status(thm)],[f_517_1]) ).
fof(f_517_3,plain,
( ! [U_1640,U_1641,U_1642] :
( c_Groups_Ouminus__class_Ouminus(U_1640,U_1641) = c_Groups_Ouminus__class_Ouminus(U_1640,U_1642)
| U_1641 != U_1642
| ~ sP176(U_1640,U_1641,U_1642) )
& ! [U_1640,U_1641,U_1642] :
( U_1641 = U_1642
| c_Groups_Ouminus__class_Ouminus(U_1640,U_1641) != c_Groups_Ouminus__class_Ouminus(U_1640,U_1642)
| ~ sP176(U_1640,U_1641,U_1642) )
& ! [U_1640,U_1641,U_1642] :
( sP176(U_1640,U_1641,U_1642)
| ~ class_Lattices_Oboolean__algebra(U_1640) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176])],[f_517_2]) ).
cnf(f_517_4,plain,
( sP176(U_1640,U_1641,U_1642)
| ~ class_Lattices_Oboolean__algebra(U_1640) ),
inference(clausify,[status(thm)],[f_517_3]) ).
cnf(f_517_5,plain,
( U_1641 = U_1642
| c_Groups_Ouminus__class_Ouminus(U_1640,U_1641) != c_Groups_Ouminus__class_Ouminus(U_1640,U_1642)
| ~ sP176(U_1640,U_1641,U_1642) ),
inference(clausify,[status(thm)],[f_517_3]) ).
cnf(f_517_6,plain,
( c_Groups_Ouminus__class_Ouminus(U_1640,U_1641) = c_Groups_Ouminus__class_Ouminus(U_1640,U_1642)
| U_1641 != U_1642
| ~ sP176(U_1640,U_1641,U_1642) ),
inference(clausify,[status(thm)],[f_517_3]) ).
fof(f_518_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(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__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__pos]) ).
fof(f_518_2,plain,
! [U_1644,U_1643] :
( c_Groups_Osgn__class_Osgn(U_1643,U_1644) = c_Groups_Oone__class_Oone(U_1643)
| ~ c_Orderings_Oord__class_Oless(U_1643,c_Groups_Ozero__class_Ozero(U_1643),U_1644)
| ~ class_Rings_Olinordered__idom(U_1643) ),
inference(variable_rename,[status(thm)],[f_518_1]) ).
fof(f_518_3,plain,
! [U_1644,U_1643] :
( c_Groups_Osgn__class_Osgn(U_1643,U_1644) = c_Groups_Oone__class_Oone(U_1643)
| ~ c_Orderings_Oord__class_Oless(U_1643,c_Groups_Ozero__class_Ozero(U_1643),U_1644)
| ~ class_Rings_Olinordered__idom(U_1643) ),
inference(definitional_conversion,[status(esa)],[f_518_2]) ).
cnf(f_518_4,plain,
( c_Groups_Osgn__class_Osgn(U_1643,U_1644) = c_Groups_Oone__class_Oone(U_1643)
| ~ c_Orderings_Oord__class_Oless(U_1643,c_Groups_Ozero__class_Ozero(U_1643),U_1644)
| ~ class_Rings_Olinordered__idom(U_1643) ),
inference(clausify,[status(thm)],[f_518_3]) ).
fof(f_519_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2) )
& ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a_2)
| c_Groups_Osgn__class_Osgn(T_a,V_a_2) != c_Groups_Oone__class_Oone(T_a) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__pos]) ).
fof(f_519_2,plain,
! [U_1646,U_1645] :
( ( ( c_Groups_Osgn__class_Osgn(U_1645,U_1646) = c_Groups_Oone__class_Oone(U_1645)
| ~ c_Orderings_Oord__class_Oless(U_1645,c_Groups_Ozero__class_Ozero(U_1645),U_1646) )
& ( c_Orderings_Oord__class_Oless(U_1645,c_Groups_Ozero__class_Ozero(U_1645),U_1646)
| c_Groups_Osgn__class_Osgn(U_1645,U_1646) != c_Groups_Oone__class_Oone(U_1645) ) )
| ~ class_Rings_Olinordered__idom(U_1645) ),
inference(variable_rename,[status(thm)],[f_519_1]) ).
fof(f_519_3,plain,
( ! [U_1646,U_1645] :
( c_Groups_Osgn__class_Osgn(U_1645,U_1646) = c_Groups_Oone__class_Oone(U_1645)
| ~ c_Orderings_Oord__class_Oless(U_1645,c_Groups_Ozero__class_Ozero(U_1645),U_1646)
| ~ sP177(U_1646,U_1645) )
& ! [U_1646,U_1645] :
( c_Orderings_Oord__class_Oless(U_1645,c_Groups_Ozero__class_Ozero(U_1645),U_1646)
| c_Groups_Osgn__class_Osgn(U_1645,U_1646) != c_Groups_Oone__class_Oone(U_1645)
| ~ sP177(U_1646,U_1645) )
& ! [U_1646,U_1645] :
( sP177(U_1646,U_1645)
| ~ class_Rings_Olinordered__idom(U_1645) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP177])],[f_519_2]) ).
cnf(f_519_4,plain,
( sP177(U_1646,U_1645)
| ~ class_Rings_Olinordered__idom(U_1645) ),
inference(clausify,[status(thm)],[f_519_3]) ).
cnf(f_519_5,plain,
( c_Orderings_Oord__class_Oless(U_1645,c_Groups_Ozero__class_Ozero(U_1645),U_1646)
| c_Groups_Osgn__class_Osgn(U_1645,U_1646) != c_Groups_Oone__class_Oone(U_1645)
| ~ sP177(U_1646,U_1645) ),
inference(clausify,[status(thm)],[f_519_3]) ).
cnf(f_519_6,plain,
( c_Groups_Osgn__class_Osgn(U_1645,U_1646) = c_Groups_Oone__class_Oone(U_1645)
| ~ c_Orderings_Oord__class_Oless(U_1645,c_Groups_Ozero__class_Ozero(U_1645),U_1646)
| ~ sP177(U_1646,U_1645) ),
inference(clausify,[status(thm)],[f_519_3]) ).
fof(f_520_1,plain,
! [V_a,T_a] :
( c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(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_sgn__neg]) ).
fof(f_520_2,plain,
! [U_1648,U_1647] :
( c_Groups_Osgn__class_Osgn(U_1647,U_1648) = c_Groups_Ouminus__class_Ouminus(U_1647,c_Groups_Oone__class_Oone(U_1647))
| ~ c_Orderings_Oord__class_Oless(U_1647,U_1648,c_Groups_Ozero__class_Ozero(U_1647))
| ~ class_Rings_Olinordered__idom(U_1647) ),
inference(variable_rename,[status(thm)],[f_520_1]) ).
fof(f_520_3,plain,
! [U_1647,U_1648] :
( c_Groups_Osgn__class_Osgn(U_1647,U_1648) = c_Groups_Ouminus__class_Ouminus(U_1647,c_Groups_Oone__class_Oone(U_1647))
| ~ c_Orderings_Oord__class_Oless(U_1647,U_1648,c_Groups_Ozero__class_Ozero(U_1647))
| ~ class_Rings_Olinordered__idom(U_1647) ),
inference(definitional_conversion,[status(esa)],[f_520_2]) ).
cnf(f_520_4,plain,
( c_Groups_Osgn__class_Osgn(U_1647,U_1648) = c_Groups_Ouminus__class_Ouminus(U_1647,c_Groups_Oone__class_Oone(U_1647))
| ~ c_Orderings_Oord__class_Oless(U_1647,U_1648,c_Groups_Ozero__class_Ozero(U_1647))
| ~ class_Rings_Olinordered__idom(U_1647) ),
inference(clausify,[status(thm)],[f_520_3]) ).
fof(f_521_1,plain,
! [V_a_2,T_a] :
( ( ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(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_Groups_Osgn__class_Osgn(T_a,V_a_2) != c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__1__neg]) ).
fof(f_521_2,plain,
! [U_1650,U_1649] :
( ( ( c_Groups_Osgn__class_Osgn(U_1649,U_1650) = c_Groups_Ouminus__class_Ouminus(U_1649,c_Groups_Oone__class_Oone(U_1649))
| ~ c_Orderings_Oord__class_Oless(U_1649,U_1650,c_Groups_Ozero__class_Ozero(U_1649)) )
& ( c_Orderings_Oord__class_Oless(U_1649,U_1650,c_Groups_Ozero__class_Ozero(U_1649))
| c_Groups_Osgn__class_Osgn(U_1649,U_1650) != c_Groups_Ouminus__class_Ouminus(U_1649,c_Groups_Oone__class_Oone(U_1649)) ) )
| ~ class_Rings_Olinordered__idom(U_1649) ),
inference(variable_rename,[status(thm)],[f_521_1]) ).
fof(f_521_3,plain,
( ! [U_1649,U_1650] :
( c_Groups_Osgn__class_Osgn(U_1649,U_1650) = c_Groups_Ouminus__class_Ouminus(U_1649,c_Groups_Oone__class_Oone(U_1649))
| ~ c_Orderings_Oord__class_Oless(U_1649,U_1650,c_Groups_Ozero__class_Ozero(U_1649))
| ~ sP178(U_1649,U_1650) )
& ! [U_1649,U_1650] :
( c_Orderings_Oord__class_Oless(U_1649,U_1650,c_Groups_Ozero__class_Ozero(U_1649))
| c_Groups_Osgn__class_Osgn(U_1649,U_1650) != c_Groups_Ouminus__class_Ouminus(U_1649,c_Groups_Oone__class_Oone(U_1649))
| ~ sP178(U_1649,U_1650) )
& ! [U_1649,U_1650] :
( sP178(U_1649,U_1650)
| ~ class_Rings_Olinordered__idom(U_1649) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP178])],[f_521_2]) ).
cnf(f_521_4,plain,
( sP178(U_1649,U_1650)
| ~ class_Rings_Olinordered__idom(U_1649) ),
inference(clausify,[status(thm)],[f_521_3]) ).
cnf(f_521_5,plain,
( c_Orderings_Oord__class_Oless(U_1649,U_1650,c_Groups_Ozero__class_Ozero(U_1649))
| c_Groups_Osgn__class_Osgn(U_1649,U_1650) != c_Groups_Ouminus__class_Ouminus(U_1649,c_Groups_Oone__class_Oone(U_1649))
| ~ sP178(U_1649,U_1650) ),
inference(clausify,[status(thm)],[f_521_3]) ).
cnf(f_521_6,plain,
( c_Groups_Osgn__class_Osgn(U_1649,U_1650) = c_Groups_Ouminus__class_Ouminus(U_1649,c_Groups_Oone__class_Oone(U_1649))
| ~ c_Orderings_Oord__class_Oless(U_1649,U_1650,c_Groups_Ozero__class_Ozero(U_1649))
| ~ sP178(U_1649,U_1650) ),
inference(clausify,[status(thm)],[f_521_3]) ).
fof(f_522_1,plain,
! [V_x,T_a] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))
| c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) )
& ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a)
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ozero__class_Ozero(T_a),V_x) ) )
| V_x = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a)
| V_x != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Groups_Osgn__if(T_a) ),
inference(fof_nnf,[status(thm)],[fact_sgn__if]) ).
fof(f_522_2,plain,
! [U_1652,U_1651] :
( ( ( ( ( c_Groups_Osgn__class_Osgn(U_1651,U_1652) = c_Groups_Ouminus__class_Ouminus(U_1651,c_Groups_Oone__class_Oone(U_1651))
| c_Orderings_Oord__class_Oless(U_1651,c_Groups_Ozero__class_Ozero(U_1651),U_1652) )
& ( c_Groups_Osgn__class_Osgn(U_1651,U_1652) = c_Groups_Oone__class_Oone(U_1651)
| ~ c_Orderings_Oord__class_Oless(U_1651,c_Groups_Ozero__class_Ozero(U_1651),U_1652) ) )
| U_1652 = c_Groups_Ozero__class_Ozero(U_1651) )
& ( c_Groups_Osgn__class_Osgn(U_1651,U_1652) = c_Groups_Ozero__class_Ozero(U_1651)
| U_1652 != c_Groups_Ozero__class_Ozero(U_1651) ) )
| ~ class_Groups_Osgn__if(U_1651) ),
inference(variable_rename,[status(thm)],[f_522_1]) ).
fof(f_522_3,plain,
( ! [U_1651,U_1652] :
( c_Groups_Osgn__class_Osgn(U_1651,U_1652) = c_Groups_Ouminus__class_Ouminus(U_1651,c_Groups_Oone__class_Oone(U_1651))
| c_Orderings_Oord__class_Oless(U_1651,c_Groups_Ozero__class_Ozero(U_1651),U_1652)
| ~ sP179(U_1651,U_1652) )
& ! [U_1651,U_1652] :
( c_Groups_Osgn__class_Osgn(U_1651,U_1652) = c_Groups_Oone__class_Oone(U_1651)
| ~ c_Orderings_Oord__class_Oless(U_1651,c_Groups_Ozero__class_Ozero(U_1651),U_1652)
| ~ sP179(U_1651,U_1652) )
& ! [U_1651,U_1652] :
( sP179(U_1651,U_1652)
| U_1652 = c_Groups_Ozero__class_Ozero(U_1651)
| ~ sP180(U_1651,U_1652) )
& ! [U_1651,U_1652] :
( c_Groups_Osgn__class_Osgn(U_1651,U_1652) = c_Groups_Ozero__class_Ozero(U_1651)
| U_1652 != c_Groups_Ozero__class_Ozero(U_1651)
| ~ sP180(U_1651,U_1652) )
& ! [U_1651,U_1652] :
( sP180(U_1651,U_1652)
| ~ class_Groups_Osgn__if(U_1651) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179,sP180])],[f_522_2]) ).
cnf(f_522_4,plain,
( sP180(U_1651,U_1652)
| ~ class_Groups_Osgn__if(U_1651) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_5,plain,
( c_Groups_Osgn__class_Osgn(U_1651,U_1652) = c_Groups_Ozero__class_Ozero(U_1651)
| U_1652 != c_Groups_Ozero__class_Ozero(U_1651)
| ~ sP180(U_1651,U_1652) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_6,plain,
( sP179(U_1651,U_1652)
| U_1652 = c_Groups_Ozero__class_Ozero(U_1651)
| ~ sP180(U_1651,U_1652) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_7,plain,
( c_Groups_Osgn__class_Osgn(U_1651,U_1652) = c_Groups_Oone__class_Oone(U_1651)
| ~ c_Orderings_Oord__class_Oless(U_1651,c_Groups_Ozero__class_Ozero(U_1651),U_1652)
| ~ sP179(U_1651,U_1652) ),
inference(clausify,[status(thm)],[f_522_3]) ).
cnf(f_522_8,plain,
( c_Groups_Osgn__class_Osgn(U_1651,U_1652) = c_Groups_Ouminus__class_Ouminus(U_1651,c_Groups_Oone__class_Oone(U_1651))
| c_Orderings_Oord__class_Oless(U_1651,c_Groups_Ozero__class_Ozero(U_1651),U_1652)
| ~ sP179(U_1651,U_1652) ),
inference(clausify,[status(thm)],[f_522_3]) ).
fof(f_523_1,plain,
! [V_x,T_a] :
( ( ( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| V_x = c_Groups_Ozero__class_Ozero(T_a) )
& ( c_RealVector_Onorm__class_Onorm(T_a,c_Groups_Osgn__class_Osgn(T_a,V_x)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_norm__sgn]) ).
fof(f_523_2,plain,
! [U_1654,U_1653] :
( ( ( c_RealVector_Onorm__class_Onorm(U_1653,c_Groups_Osgn__class_Osgn(U_1653,U_1654)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1654 = c_Groups_Ozero__class_Ozero(U_1653) )
& ( c_RealVector_Onorm__class_Onorm(U_1653,c_Groups_Osgn__class_Osgn(U_1653,U_1654)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1654 != c_Groups_Ozero__class_Ozero(U_1653) ) )
| ~ class_RealVector_Oreal__normed__vector(U_1653) ),
inference(variable_rename,[status(thm)],[f_523_1]) ).
fof(f_523_3,plain,
( ! [U_1654,U_1653] :
( c_RealVector_Onorm__class_Onorm(U_1653,c_Groups_Osgn__class_Osgn(U_1653,U_1654)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1654 = c_Groups_Ozero__class_Ozero(U_1653)
| ~ sP181(U_1654,U_1653) )
& ! [U_1654,U_1653] :
( c_RealVector_Onorm__class_Onorm(U_1653,c_Groups_Osgn__class_Osgn(U_1653,U_1654)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1654 != c_Groups_Ozero__class_Ozero(U_1653)
| ~ sP181(U_1654,U_1653) )
& ! [U_1654,U_1653] :
( sP181(U_1654,U_1653)
| ~ class_RealVector_Oreal__normed__vector(U_1653) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181])],[f_523_2]) ).
cnf(f_523_4,plain,
( sP181(U_1654,U_1653)
| ~ class_RealVector_Oreal__normed__vector(U_1653) ),
inference(clausify,[status(thm)],[f_523_3]) ).
cnf(f_523_5,plain,
( c_RealVector_Onorm__class_Onorm(U_1653,c_Groups_Osgn__class_Osgn(U_1653,U_1654)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1654 != c_Groups_Ozero__class_Ozero(U_1653)
| ~ sP181(U_1654,U_1653) ),
inference(clausify,[status(thm)],[f_523_3]) ).
cnf(f_523_6,plain,
( c_RealVector_Onorm__class_Onorm(U_1653,c_Groups_Osgn__class_Osgn(U_1653,U_1654)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| U_1654 = c_Groups_Ozero__class_Ozero(U_1653)
| ~ sP181(U_1654,U_1653) ),
inference(clausify,[status(thm)],[f_523_3]) ).
fof(f_524_1,plain,
! [V_X_2,V_K_2,T_a] :
( c_SEQ_OBseq(T_a,V_X_2)
| ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),V_K_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_K_2)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_BseqI]) ).
fof(f_524_2,plain,
! [U_1658,U_1657,U_1656] :
( c_SEQ_OBseq(U_1656,U_1658)
| ? [U_1655] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1656,hAPP(U_1658,U_1655)),U_1657)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1657)
| ~ class_RealVector_Oreal__normed__vector(U_1656) ),
inference(variable_rename,[status(thm)],[f_524_1]) ).
fof(f_524_3,plain,
! [U_1658,U_1657,U_1656] :
( c_SEQ_OBseq(U_1656,U_1658)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1656,hAPP(U_1658,sK20(U_1658,U_1657,U_1656))),U_1657)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1657)
| ~ class_RealVector_Oreal__normed__vector(U_1656) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_1655,sK20(U_1658,U_1657,U_1656))],[f_524_2]) ).
fof(f_524_4,plain,
! [U_1657,U_1656,U_1658] :
( c_SEQ_OBseq(U_1656,U_1658)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1656,hAPP(U_1658,sK20(U_1658,U_1657,U_1656))),U_1657)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1657)
| ~ class_RealVector_Oreal__normed__vector(U_1656) ),
inference(definitional_conversion,[status(esa)],[f_524_3]) ).
cnf(f_524_5,plain,
( c_SEQ_OBseq(U_1656,U_1658)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1656,hAPP(U_1658,sK20(U_1658,U_1657,U_1656))),U_1657)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1657)
| ~ class_RealVector_Oreal__normed__vector(U_1656) ),
inference(clausify,[status(thm)],[f_524_4]) ).
fof(f_525_1,plain,
! [V_X_2,T_a] :
( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ c_SEQ_OBseq(T_a,V_X_2)
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_BseqD]) ).
fof(f_525_2,plain,
! [U_1662,U_1661] :
( ? [U_1660] :
( ! [U_1659] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1661,hAPP(U_1662,U_1659)),U_1660)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1660) )
| ~ c_SEQ_OBseq(U_1661,U_1662)
| ~ class_RealVector_Oreal__normed__vector(U_1661) ),
inference(variable_rename,[status(thm)],[f_525_1]) ).
fof(f_525_3,plain,
! [U_1662,U_1661] :
( ( ! [U_1659] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1661,hAPP(U_1662,U_1659)),sK21(U_1662,U_1661))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK21(U_1662,U_1661)) )
| ~ c_SEQ_OBseq(U_1661,U_1662)
| ~ class_RealVector_Oreal__normed__vector(U_1661) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_1660,sK21(U_1662,U_1661))],[f_525_2]) ).
fof(f_525_4,plain,
( ! [U_1661,U_1659,U_1662] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1661,hAPP(U_1662,U_1659)),sK21(U_1662,U_1661))
| ~ sP182(U_1661,U_1659,U_1662) )
& ! [U_1661,U_1659,U_1662] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK21(U_1662,U_1661))
| ~ sP182(U_1661,U_1659,U_1662) )
& ! [U_1661,U_1659,U_1662] :
( sP182(U_1661,U_1659,U_1662)
| ~ c_SEQ_OBseq(U_1661,U_1662)
| ~ class_RealVector_Oreal__normed__vector(U_1661) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP182])],[f_525_3]) ).
cnf(f_525_5,plain,
( sP182(U_1661,U_1659,U_1662)
| ~ c_SEQ_OBseq(U_1661,U_1662)
| ~ class_RealVector_Oreal__normed__vector(U_1661) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK21(U_1662,U_1661))
| ~ sP182(U_1661,U_1659,U_1662) ),
inference(clausify,[status(thm)],[f_525_4]) ).
cnf(f_525_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1661,hAPP(U_1662,U_1659)),sK21(U_1662,U_1661))
| ~ sP182(U_1661,U_1659,U_1662) ),
inference(clausify,[status(thm)],[f_525_4]) ).
fof(f_526_1,plain,
! [V_n_2,V_P_2] :
( ? [B_k] :
( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,B_k,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [B_i] :
( ~ hBOOL(hAPP(V_P_2,B_i))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_i,B_k) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_k,V_n_2) )
| ~ hBOOL(hAPP(V_P_2,V_n_2))
| hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).
fof(f_526_2,plain,
! [U_1666,U_1665] :
( ? [U_1664] :
( hBOOL(hAPP(U_1665,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1664,c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_1663] :
( ~ hBOOL(hAPP(U_1665,U_1663))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1663,U_1664) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1664,U_1666) )
| ~ hBOOL(hAPP(U_1665,U_1666))
| hBOOL(hAPP(U_1665,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(variable_rename,[status(thm)],[f_526_1]) ).
fof(f_526_3,plain,
! [U_1666,U_1665] :
( ( hBOOL(hAPP(U_1665,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK22(U_1666,U_1665),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
& ! [U_1663] :
( ~ hBOOL(hAPP(U_1665,U_1663))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1663,sK22(U_1666,U_1665)) )
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK22(U_1666,U_1665),U_1666) )
| ~ hBOOL(hAPP(U_1665,U_1666))
| hBOOL(hAPP(U_1665,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_1664,sK22(U_1666,U_1665))],[f_526_2]) ).
fof(f_526_4,plain,
( ! [U_1663,U_1665,U_1666] :
( hBOOL(hAPP(U_1665,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK22(U_1666,U_1665),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ sP183(U_1663,U_1665,U_1666) )
& ! [U_1663,U_1665,U_1666] :
( ~ hBOOL(hAPP(U_1665,U_1663))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1663,sK22(U_1666,U_1665))
| ~ sP183(U_1663,U_1665,U_1666) )
& ! [U_1663,U_1665,U_1666] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK22(U_1666,U_1665),U_1666)
| ~ sP183(U_1663,U_1665,U_1666) )
& ! [U_1663,U_1665,U_1666] :
( sP183(U_1663,U_1665,U_1666)
| ~ hBOOL(hAPP(U_1665,U_1666))
| hBOOL(hAPP(U_1665,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183])],[f_526_3]) ).
cnf(f_526_5,plain,
( sP183(U_1663,U_1665,U_1666)
| ~ hBOOL(hAPP(U_1665,U_1666))
| hBOOL(hAPP(U_1665,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_526_4]) ).
cnf(f_526_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK22(U_1666,U_1665),U_1666)
| ~ sP183(U_1663,U_1665,U_1666) ),
inference(clausify,[status(thm)],[f_526_4]) ).
cnf(f_526_7,plain,
( ~ hBOOL(hAPP(U_1665,U_1663))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1663,sK22(U_1666,U_1665))
| ~ sP183(U_1663,U_1665,U_1666) ),
inference(clausify,[status(thm)],[f_526_4]) ).
cnf(f_526_8,plain,
( hBOOL(hAPP(U_1665,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,sK22(U_1666,U_1665),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
| ~ sP183(U_1663,U_1665,U_1666) ),
inference(clausify,[status(thm)],[f_526_4]) ).
fof(f_527_1,plain,
! [V_y,T_a] :
( ? [B_K] :
( ! [B_x] : 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),B_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__left_Ononneg__bounded]) ).
fof(f_527_2,plain,
! [U_1670,U_1669] :
( ? [U_1668] :
( ! [U_1667] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1669,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1667),U_1670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1669,U_1667)),U_1668))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1668) )
| ~ class_RealVector_Oreal__normed__algebra(U_1669) ),
inference(variable_rename,[status(thm)],[f_527_1]) ).
fof(f_527_3,plain,
! [U_1670,U_1669] :
( ( ! [U_1667] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1669,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1667),U_1670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1669,U_1667)),sK23(U_1670,U_1669)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK23(U_1670,U_1669)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1669) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1668,sK23(U_1670,U_1669))],[f_527_2]) ).
fof(f_527_4,plain,
( ! [U_1670,U_1669,U_1667] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1669,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1667),U_1670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1669,U_1667)),sK23(U_1670,U_1669)))
| ~ sP184(U_1670,U_1669,U_1667) )
& ! [U_1670,U_1669,U_1667] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK23(U_1670,U_1669))
| ~ sP184(U_1670,U_1669,U_1667) )
& ! [U_1670,U_1669,U_1667] :
( sP184(U_1670,U_1669,U_1667)
| ~ class_RealVector_Oreal__normed__algebra(U_1669) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP184])],[f_527_3]) ).
cnf(f_527_5,plain,
( sP184(U_1670,U_1669,U_1667)
| ~ class_RealVector_Oreal__normed__algebra(U_1669) ),
inference(clausify,[status(thm)],[f_527_4]) ).
cnf(f_527_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK23(U_1670,U_1669))
| ~ sP184(U_1670,U_1669,U_1667) ),
inference(clausify,[status(thm)],[f_527_4]) ).
cnf(f_527_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1669,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1669),U_1667),U_1670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1669,U_1667)),sK23(U_1670,U_1669)))
| ~ sP184(U_1670,U_1669,U_1667) ),
inference(clausify,[status(thm)],[f_527_4]) ).
fof(f_528_1,plain,
! [V_x] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(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__sgn__pos]) ).
fof(f_528_2,plain,
! [U_1671] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1671) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1671) ),
inference(variable_rename,[status(thm)],[f_528_1]) ).
fof(f_528_3,plain,
! [U_1671] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1671) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1671) ),
inference(definitional_conversion,[status(esa)],[f_528_2]) ).
cnf(f_528_4,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1671) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1671) ),
inference(clausify,[status(thm)],[f_528_3]) ).
fof(f_529_1,plain,
! [V_a] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) ) )
| V_a = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_a) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_a != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_sgn__real__def]) ).
fof(f_529_2,plain,
! [U_1672] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1672) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1672) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1672) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1672) ) )
| U_1672 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1672) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1672 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_529_1]) ).
fof(f_529_3,plain,
( ! [U_1674] :
( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1674) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1674) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1674) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1674) ) )
| U_1674 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1673] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1673) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1673 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_529_2]) ).
fof(f_529_4,plain,
( ! [U_1674] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1674) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1674)
| ~ sP185(U_1674) )
& ! [U_1674] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1674) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1674)
| ~ sP185(U_1674) )
& ! [U_1674] :
( sP185(U_1674)
| U_1674 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1673] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1673) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1673 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_529_3]) ).
cnf(f_529_5,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1673) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1673 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_529_4]) ).
cnf(f_529_6,plain,
( sP185(U_1674)
| U_1674 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_529_4]) ).
cnf(f_529_7,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1674) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1674)
| ~ sP185(U_1674) ),
inference(clausify,[status(thm)],[f_529_4]) ).
cnf(f_529_8,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1674) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1674)
| ~ sP185(U_1674) ),
inference(clausify,[status(thm)],[f_529_4]) ).
fof(f_530_1,plain,
! [V_x] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x) ) )
| V_x = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,V_x) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_x != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__sgn__def]) ).
fof(f_530_2,plain,
! [U_1675] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1675) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1675) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1675) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1675) ) )
| U_1675 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1675) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1675 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_530_1]) ).
fof(f_530_3,plain,
( ! [U_1677] :
( ( ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1677) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1677) )
& ( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1677) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1677) ) )
| U_1677 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1676] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1676) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1676 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_530_2]) ).
fof(f_530_4,plain,
( ! [U_1677] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1677) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1677)
| ~ sP186(U_1677) )
& ! [U_1677] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1677) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1677)
| ~ sP186(U_1677) )
& ! [U_1677] :
( sP186(U_1677)
| U_1677 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) )
& ! [U_1676] :
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1676) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1676 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_530_3]) ).
cnf(f_530_5,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1676) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_1676 != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_530_4]) ).
cnf(f_530_6,plain,
( sP186(U_1677)
| U_1677 = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_530_4]) ).
cnf(f_530_7,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1677) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1677)
| ~ sP186(U_1677) ),
inference(clausify,[status(thm)],[f_530_4]) ).
cnf(f_530_8,plain,
( c_Groups_Osgn__class_Osgn(tc_RealDef_Oreal,U_1677) = c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1677)
| ~ sP186(U_1677) ),
inference(clausify,[status(thm)],[f_530_4]) ).
fof(f_531_1,plain,
! [T_a] :
( ? [B_K] :
( ! [B_a,B_b] : 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),B_a),B_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_a)),c_RealVector_Onorm__class_Onorm(T_a,B_b))),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult_Ononneg__bounded]) ).
fof(f_531_2,plain,
! [U_1681] :
( ? [U_1680] :
( ! [U_1679,U_1678] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1681,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1681),U_1679),U_1678)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1681,U_1679)),c_RealVector_Onorm__class_Onorm(U_1681,U_1678))),U_1680))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1680) )
| ~ class_RealVector_Oreal__normed__algebra(U_1681) ),
inference(variable_rename,[status(thm)],[f_531_1]) ).
fof(f_531_3,plain,
! [U_1681] :
( ( ! [U_1679,U_1678] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1681,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1681),U_1679),U_1678)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1681,U_1679)),c_RealVector_Onorm__class_Onorm(U_1681,U_1678))),sK24(U_1681)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(U_1681)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1681) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1680,sK24(U_1681))],[f_531_2]) ).
fof(f_531_4,plain,
( ! [U_1681,U_1678,U_1679] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1681,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1681),U_1679),U_1678)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1681,U_1679)),c_RealVector_Onorm__class_Onorm(U_1681,U_1678))),sK24(U_1681)))
| ~ sP187(U_1681,U_1678,U_1679) )
& ! [U_1681,U_1678,U_1679] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(U_1681))
| ~ sP187(U_1681,U_1678,U_1679) )
& ! [U_1681,U_1678,U_1679] :
( sP187(U_1681,U_1678,U_1679)
| ~ class_RealVector_Oreal__normed__algebra(U_1681) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_531_3]) ).
cnf(f_531_5,plain,
( sP187(U_1681,U_1678,U_1679)
| ~ class_RealVector_Oreal__normed__algebra(U_1681) ),
inference(clausify,[status(thm)],[f_531_4]) ).
cnf(f_531_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK24(U_1681))
| ~ sP187(U_1681,U_1678,U_1679) ),
inference(clausify,[status(thm)],[f_531_4]) ).
cnf(f_531_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1681,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1681),U_1679),U_1678)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1681,U_1679)),c_RealVector_Onorm__class_Onorm(U_1681,U_1678))),sK24(U_1681)))
| ~ sP187(U_1681,U_1678,U_1679) ),
inference(clausify,[status(thm)],[f_531_4]) ).
fof(f_532_1,plain,
! [V_x,T_a] :
( ? [B_K] :
( ! [B_x] : 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),B_x)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_a,B_x)),B_K))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ~ class_RealVector_Oreal__normed__algebra(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__right_Ononneg__bounded]) ).
fof(f_532_2,plain,
! [U_1685,U_1684] :
( ? [U_1683] :
( ! [U_1682] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),U_1685),U_1682)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1684,U_1682)),U_1683))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_1683) )
| ~ class_RealVector_Oreal__normed__algebra(U_1684) ),
inference(variable_rename,[status(thm)],[f_532_1]) ).
fof(f_532_3,plain,
! [U_1685,U_1684] :
( ( ! [U_1682] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),U_1685),U_1682)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1684,U_1682)),sK25(U_1685,U_1684)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(U_1685,U_1684)) )
| ~ class_RealVector_Oreal__normed__algebra(U_1684) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1683,sK25(U_1685,U_1684))],[f_532_2]) ).
fof(f_532_4,plain,
( ! [U_1682,U_1684,U_1685] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),U_1685),U_1682)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1684,U_1682)),sK25(U_1685,U_1684)))
| ~ sP188(U_1682,U_1684,U_1685) )
& ! [U_1682,U_1684,U_1685] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(U_1685,U_1684))
| ~ sP188(U_1682,U_1684,U_1685) )
& ! [U_1682,U_1684,U_1685] :
( sP188(U_1682,U_1684,U_1685)
| ~ class_RealVector_Oreal__normed__algebra(U_1684) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_532_3]) ).
cnf(f_532_5,plain,
( sP188(U_1682,U_1684,U_1685)
| ~ class_RealVector_Oreal__normed__algebra(U_1684) ),
inference(clausify,[status(thm)],[f_532_4]) ).
cnf(f_532_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK25(U_1685,U_1684))
| ~ sP188(U_1682,U_1684,U_1685) ),
inference(clausify,[status(thm)],[f_532_4]) ).
cnf(f_532_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1684,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1684),U_1685),U_1682)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1684,U_1682)),sK25(U_1685,U_1684)))
| ~ sP188(U_1682,U_1684,U_1685) ),
inference(clausify,[status(thm)],[f_532_4]) ).
fof(f_533_1,plain,
! [V_ca_2,V_pa_2,T_a] :
( ( ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2) = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2) )
& ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)
| hAPP(c_Polynomial_Opoly(T_a,V_pa_2),V_ca_2) != c_Groups_Ozero__class_Ozero(T_a) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__eq__0__iff__dvd]) ).
fof(f_533_2,plain,
! [U_1688,U_1687,U_1686] :
( ( ( hAPP(c_Polynomial_Opoly(U_1686,U_1687),U_1688) = c_Groups_Ozero__class_Ozero(U_1686)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1686),c_Polynomial_OpCons(U_1686,c_Groups_Ouminus__class_Ouminus(U_1686,U_1688),c_Polynomial_OpCons(U_1686,c_Groups_Oone__class_Oone(U_1686),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1686)))),U_1687) )
& ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1686),c_Polynomial_OpCons(U_1686,c_Groups_Ouminus__class_Ouminus(U_1686,U_1688),c_Polynomial_OpCons(U_1686,c_Groups_Oone__class_Oone(U_1686),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1686)))),U_1687)
| hAPP(c_Polynomial_Opoly(U_1686,U_1687),U_1688) != c_Groups_Ozero__class_Ozero(U_1686) ) )
| ~ class_Rings_Oidom(U_1686) ),
inference(variable_rename,[status(thm)],[f_533_1]) ).
fof(f_533_3,plain,
( ! [U_1687,U_1686,U_1688] :
( hAPP(c_Polynomial_Opoly(U_1686,U_1687),U_1688) = c_Groups_Ozero__class_Ozero(U_1686)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1686),c_Polynomial_OpCons(U_1686,c_Groups_Ouminus__class_Ouminus(U_1686,U_1688),c_Polynomial_OpCons(U_1686,c_Groups_Oone__class_Oone(U_1686),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1686)))),U_1687)
| ~ sP189(U_1687,U_1686,U_1688) )
& ! [U_1687,U_1686,U_1688] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1686),c_Polynomial_OpCons(U_1686,c_Groups_Ouminus__class_Ouminus(U_1686,U_1688),c_Polynomial_OpCons(U_1686,c_Groups_Oone__class_Oone(U_1686),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1686)))),U_1687)
| hAPP(c_Polynomial_Opoly(U_1686,U_1687),U_1688) != c_Groups_Ozero__class_Ozero(U_1686)
| ~ sP189(U_1687,U_1686,U_1688) )
& ! [U_1687,U_1686,U_1688] :
( sP189(U_1687,U_1686,U_1688)
| ~ class_Rings_Oidom(U_1686) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_533_2]) ).
cnf(f_533_4,plain,
( sP189(U_1687,U_1686,U_1688)
| ~ class_Rings_Oidom(U_1686) ),
inference(clausify,[status(thm)],[f_533_3]) ).
cnf(f_533_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1686),c_Polynomial_OpCons(U_1686,c_Groups_Ouminus__class_Ouminus(U_1686,U_1688),c_Polynomial_OpCons(U_1686,c_Groups_Oone__class_Oone(U_1686),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1686)))),U_1687)
| hAPP(c_Polynomial_Opoly(U_1686,U_1687),U_1688) != c_Groups_Ozero__class_Ozero(U_1686)
| ~ sP189(U_1687,U_1686,U_1688) ),
inference(clausify,[status(thm)],[f_533_3]) ).
cnf(f_533_6,plain,
( hAPP(c_Polynomial_Opoly(U_1686,U_1687),U_1688) = c_Groups_Ozero__class_Ozero(U_1686)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1686),c_Polynomial_OpCons(U_1686,c_Groups_Ouminus__class_Ouminus(U_1686,U_1688),c_Polynomial_OpCons(U_1686,c_Groups_Oone__class_Oone(U_1686),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1686)))),U_1687)
| ~ sP189(U_1687,U_1686,U_1688) ),
inference(clausify,[status(thm)],[f_533_3]) ).
fof(f_534_1,plain,
! [V_pa_2,V_ca_2,T_a] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2)
| hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2)) != c_Groups_Ozero__class_Ozero(T_a) )
& ( hAPP(c_Polynomial_Opoly(T_a,V_pa_2),c_Groups_Ouminus__class_Ouminus(T_a,V_ca_2)) = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_ca_2,c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)))),V_pa_2) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__iff__poly__eq__0]) ).
fof(f_534_2,plain,
! [U_1691,U_1690,U_1689] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1689),c_Polynomial_OpCons(U_1689,U_1690,c_Polynomial_OpCons(U_1689,c_Groups_Oone__class_Oone(U_1689),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1689)))),U_1691)
| hAPP(c_Polynomial_Opoly(U_1689,U_1691),c_Groups_Ouminus__class_Ouminus(U_1689,U_1690)) != c_Groups_Ozero__class_Ozero(U_1689) )
& ( hAPP(c_Polynomial_Opoly(U_1689,U_1691),c_Groups_Ouminus__class_Ouminus(U_1689,U_1690)) = c_Groups_Ozero__class_Ozero(U_1689)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1689),c_Polynomial_OpCons(U_1689,U_1690,c_Polynomial_OpCons(U_1689,c_Groups_Oone__class_Oone(U_1689),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1689)))),U_1691) ) )
| ~ class_Rings_Oidom(U_1689) ),
inference(variable_rename,[status(thm)],[f_534_1]) ).
fof(f_534_3,plain,
( ! [U_1690,U_1689,U_1691] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1689),c_Polynomial_OpCons(U_1689,U_1690,c_Polynomial_OpCons(U_1689,c_Groups_Oone__class_Oone(U_1689),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1689)))),U_1691)
| hAPP(c_Polynomial_Opoly(U_1689,U_1691),c_Groups_Ouminus__class_Ouminus(U_1689,U_1690)) != c_Groups_Ozero__class_Ozero(U_1689)
| ~ sP190(U_1690,U_1689,U_1691) )
& ! [U_1690,U_1689,U_1691] :
( hAPP(c_Polynomial_Opoly(U_1689,U_1691),c_Groups_Ouminus__class_Ouminus(U_1689,U_1690)) = c_Groups_Ozero__class_Ozero(U_1689)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1689),c_Polynomial_OpCons(U_1689,U_1690,c_Polynomial_OpCons(U_1689,c_Groups_Oone__class_Oone(U_1689),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1689)))),U_1691)
| ~ sP190(U_1690,U_1689,U_1691) )
& ! [U_1690,U_1689,U_1691] :
( sP190(U_1690,U_1689,U_1691)
| ~ class_Rings_Oidom(U_1689) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP190])],[f_534_2]) ).
cnf(f_534_4,plain,
( sP190(U_1690,U_1689,U_1691)
| ~ class_Rings_Oidom(U_1689) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_5,plain,
( hAPP(c_Polynomial_Opoly(U_1689,U_1691),c_Groups_Ouminus__class_Ouminus(U_1689,U_1690)) = c_Groups_Ozero__class_Ozero(U_1689)
| ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1689),c_Polynomial_OpCons(U_1689,U_1690,c_Polynomial_OpCons(U_1689,c_Groups_Oone__class_Oone(U_1689),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1689)))),U_1691)
| ~ sP190(U_1690,U_1689,U_1691) ),
inference(clausify,[status(thm)],[f_534_3]) ).
cnf(f_534_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1689),c_Polynomial_OpCons(U_1689,U_1690,c_Polynomial_OpCons(U_1689,c_Groups_Oone__class_Oone(U_1689),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1689)))),U_1691)
| hAPP(c_Polynomial_Opoly(U_1689,U_1691),c_Groups_Ouminus__class_Ouminus(U_1689,U_1690)) != c_Groups_Ozero__class_Ozero(U_1689)
| ~ sP190(U_1690,U_1689,U_1691) ),
inference(clausify,[status(thm)],[f_534_3]) ).
fof(f_535_1,plain,
! [V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__0__right]) ).
fof(f_535_2,plain,
! [U_1693,U_1692] :
( c_Rings_Odvd__class_Odvd(U_1692,U_1693,c_Groups_Ozero__class_Ozero(U_1692))
| ~ class_Rings_Ocomm__semiring__1(U_1692) ),
inference(variable_rename,[status(thm)],[f_535_1]) ).
fof(f_535_3,plain,
! [U_1693,U_1692] :
( c_Rings_Odvd__class_Odvd(U_1692,U_1693,c_Groups_Ozero__class_Ozero(U_1692))
| ~ class_Rings_Ocomm__semiring__1(U_1692) ),
inference(definitional_conversion,[status(esa)],[f_535_2]) ).
cnf(f_535_4,plain,
( c_Rings_Odvd__class_Odvd(U_1692,U_1693,c_Groups_Ozero__class_Ozero(U_1692))
| ~ class_Rings_Ocomm__semiring__1(U_1692) ),
inference(clausify,[status(thm)],[f_535_3]) ).
fof(f_536_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) )
& ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2)
| ~ c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_x_2),V_y_2) ) )
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__dvd__iff]) ).
fof(f_536_2,plain,
! [U_1696,U_1695,U_1694] :
( ( ( c_Rings_Odvd__class_Odvd(U_1694,c_Groups_Ouminus__class_Ouminus(U_1694,U_1695),U_1696)
| ~ c_Rings_Odvd__class_Odvd(U_1694,U_1695,U_1696) )
& ( c_Rings_Odvd__class_Odvd(U_1694,U_1695,U_1696)
| ~ c_Rings_Odvd__class_Odvd(U_1694,c_Groups_Ouminus__class_Ouminus(U_1694,U_1695),U_1696) ) )
| ~ class_Rings_Ocomm__ring__1(U_1694) ),
inference(variable_rename,[status(thm)],[f_536_1]) ).
fof(f_536_3,plain,
( ! [U_1696,U_1694,U_1695] :
( c_Rings_Odvd__class_Odvd(U_1694,c_Groups_Ouminus__class_Ouminus(U_1694,U_1695),U_1696)
| ~ c_Rings_Odvd__class_Odvd(U_1694,U_1695,U_1696)
| ~ sP191(U_1696,U_1694,U_1695) )
& ! [U_1696,U_1694,U_1695] :
( c_Rings_Odvd__class_Odvd(U_1694,U_1695,U_1696)
| ~ c_Rings_Odvd__class_Odvd(U_1694,c_Groups_Ouminus__class_Ouminus(U_1694,U_1695),U_1696)
| ~ sP191(U_1696,U_1694,U_1695) )
& ! [U_1696,U_1694,U_1695] :
( sP191(U_1696,U_1694,U_1695)
| ~ class_Rings_Ocomm__ring__1(U_1694) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP191])],[f_536_2]) ).
cnf(f_536_4,plain,
( sP191(U_1696,U_1694,U_1695)
| ~ class_Rings_Ocomm__ring__1(U_1694) ),
inference(clausify,[status(thm)],[f_536_3]) ).
cnf(f_536_5,plain,
( c_Rings_Odvd__class_Odvd(U_1694,U_1695,U_1696)
| ~ c_Rings_Odvd__class_Odvd(U_1694,c_Groups_Ouminus__class_Ouminus(U_1694,U_1695),U_1696)
| ~ sP191(U_1696,U_1694,U_1695) ),
inference(clausify,[status(thm)],[f_536_3]) ).
cnf(f_536_6,plain,
( c_Rings_Odvd__class_Odvd(U_1694,c_Groups_Ouminus__class_Ouminus(U_1694,U_1695),U_1696)
| ~ c_Rings_Odvd__class_Odvd(U_1694,U_1695,U_1696)
| ~ sP191(U_1696,U_1694,U_1695) ),
inference(clausify,[status(thm)],[f_536_3]) ).
fof(f_537_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2) )
& ( c_Rings_Odvd__class_Odvd(T_a,V_x_2,V_y_2)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_x_2,c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)) ) )
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__minus__iff]) ).
fof(f_537_2,plain,
! [U_1699,U_1698,U_1697] :
( ( ( c_Rings_Odvd__class_Odvd(U_1697,U_1698,c_Groups_Ouminus__class_Ouminus(U_1697,U_1699))
| ~ c_Rings_Odvd__class_Odvd(U_1697,U_1698,U_1699) )
& ( c_Rings_Odvd__class_Odvd(U_1697,U_1698,U_1699)
| ~ c_Rings_Odvd__class_Odvd(U_1697,U_1698,c_Groups_Ouminus__class_Ouminus(U_1697,U_1699)) ) )
| ~ class_Rings_Ocomm__ring__1(U_1697) ),
inference(variable_rename,[status(thm)],[f_537_1]) ).
fof(f_537_3,plain,
( ! [U_1699,U_1698,U_1697] :
( c_Rings_Odvd__class_Odvd(U_1697,U_1698,c_Groups_Ouminus__class_Ouminus(U_1697,U_1699))
| ~ c_Rings_Odvd__class_Odvd(U_1697,U_1698,U_1699)
| ~ sP192(U_1699,U_1698,U_1697) )
& ! [U_1699,U_1698,U_1697] :
( c_Rings_Odvd__class_Odvd(U_1697,U_1698,U_1699)
| ~ c_Rings_Odvd__class_Odvd(U_1697,U_1698,c_Groups_Ouminus__class_Ouminus(U_1697,U_1699))
| ~ sP192(U_1699,U_1698,U_1697) )
& ! [U_1699,U_1698,U_1697] :
( sP192(U_1699,U_1698,U_1697)
| ~ class_Rings_Ocomm__ring__1(U_1697) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192])],[f_537_2]) ).
cnf(f_537_4,plain,
( sP192(U_1699,U_1698,U_1697)
| ~ class_Rings_Ocomm__ring__1(U_1697) ),
inference(clausify,[status(thm)],[f_537_3]) ).
cnf(f_537_5,plain,
( c_Rings_Odvd__class_Odvd(U_1697,U_1698,U_1699)
| ~ c_Rings_Odvd__class_Odvd(U_1697,U_1698,c_Groups_Ouminus__class_Ouminus(U_1697,U_1699))
| ~ sP192(U_1699,U_1698,U_1697) ),
inference(clausify,[status(thm)],[f_537_3]) ).
cnf(f_537_6,plain,
( c_Rings_Odvd__class_Odvd(U_1697,U_1698,c_Groups_Ouminus__class_Ouminus(U_1697,U_1699))
| ~ c_Rings_Odvd__class_Odvd(U_1697,U_1698,U_1699)
| ~ sP192(U_1699,U_1698,U_1697) ),
inference(clausify,[status(thm)],[f_537_3]) ).
fof(f_538_1,plain,
! [V_a,T_a] :
( V_a = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Rings_Odvd__class_Odvd(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__0__left]) ).
fof(f_538_2,plain,
! [U_1701,U_1700] :
( U_1701 = c_Groups_Ozero__class_Ozero(U_1700)
| ~ c_Rings_Odvd__class_Odvd(U_1700,c_Groups_Ozero__class_Ozero(U_1700),U_1701)
| ~ class_Rings_Ocomm__semiring__1(U_1700) ),
inference(variable_rename,[status(thm)],[f_538_1]) ).
fof(f_538_3,plain,
! [U_1701,U_1700] :
( U_1701 = c_Groups_Ozero__class_Ozero(U_1700)
| ~ c_Rings_Odvd__class_Odvd(U_1700,c_Groups_Ozero__class_Ozero(U_1700),U_1701)
| ~ class_Rings_Ocomm__semiring__1(U_1700) ),
inference(definitional_conversion,[status(esa)],[f_538_2]) ).
cnf(f_538_4,plain,
( U_1701 = c_Groups_Ozero__class_Ozero(U_1700)
| ~ c_Rings_Odvd__class_Odvd(U_1700,c_Groups_Ozero__class_Ozero(U_1700),U_1701)
| ~ class_Rings_Ocomm__semiring__1(U_1700) ),
inference(clausify,[status(thm)],[f_538_3]) ).
fof(f_539_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__trans]) ).
fof(f_539_2,plain,
! [U_1705,U_1704,U_1703,U_1702] :
( c_Rings_Odvd__class_Odvd(U_1702,U_1703,U_1705)
| ~ c_Rings_Odvd__class_Odvd(U_1702,U_1704,U_1705)
| ~ c_Rings_Odvd__class_Odvd(U_1702,U_1703,U_1704)
| ~ class_Rings_Ocomm__semiring__1(U_1702) ),
inference(variable_rename,[status(thm)],[f_539_1]) ).
fof(f_539_3,plain,
! [U_1702,U_1705,U_1703,U_1704] :
( c_Rings_Odvd__class_Odvd(U_1702,U_1703,U_1705)
| ~ c_Rings_Odvd__class_Odvd(U_1702,U_1704,U_1705)
| ~ c_Rings_Odvd__class_Odvd(U_1702,U_1703,U_1704)
| ~ class_Rings_Ocomm__semiring__1(U_1702) ),
inference(definitional_conversion,[status(esa)],[f_539_2]) ).
cnf(f_539_4,plain,
( c_Rings_Odvd__class_Odvd(U_1702,U_1703,U_1705)
| ~ c_Rings_Odvd__class_Odvd(U_1702,U_1704,U_1705)
| ~ c_Rings_Odvd__class_Odvd(U_1702,U_1703,U_1704)
| ~ class_Rings_Ocomm__semiring__1(U_1702) ),
inference(clausify,[status(thm)],[f_539_3]) ).
fof(f_540_1,plain,
! [V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_a,V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__refl]) ).
fof(f_540_2,plain,
! [U_1707,U_1706] :
( c_Rings_Odvd__class_Odvd(U_1706,U_1707,U_1707)
| ~ class_Rings_Ocomm__semiring__1(U_1706) ),
inference(variable_rename,[status(thm)],[f_540_1]) ).
fof(f_540_3,plain,
! [U_1707,U_1706] :
( c_Rings_Odvd__class_Odvd(U_1706,U_1707,U_1707)
| ~ class_Rings_Ocomm__semiring__1(U_1706) ),
inference(definitional_conversion,[status(esa)],[f_540_2]) ).
cnf(f_540_4,plain,
( c_Rings_Odvd__class_Odvd(U_1706,U_1707,U_1707)
| ~ class_Rings_Ocomm__semiring__1(U_1706) ),
inference(clausify,[status(thm)],[f_540_3]) ).
fof(f_541_1,plain,
! [V_k,V_l,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_l,V_k)
| c_Groups_Oabs__class_Oabs(T_a,V_l) != c_Groups_Oabs__class_Oabs(T_a,V_k)
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__if__abs__eq]) ).
fof(f_541_2,plain,
! [U_1710,U_1709,U_1708] :
( c_Rings_Odvd__class_Odvd(U_1708,U_1709,U_1710)
| c_Groups_Oabs__class_Oabs(U_1708,U_1709) != c_Groups_Oabs__class_Oabs(U_1708,U_1710)
| ~ class_Rings_Olinordered__idom(U_1708) ),
inference(variable_rename,[status(thm)],[f_541_1]) ).
fof(f_541_3,plain,
! [U_1708,U_1709,U_1710] :
( c_Rings_Odvd__class_Odvd(U_1708,U_1709,U_1710)
| c_Groups_Oabs__class_Oabs(U_1708,U_1709) != c_Groups_Oabs__class_Oabs(U_1708,U_1710)
| ~ class_Rings_Olinordered__idom(U_1708) ),
inference(definitional_conversion,[status(esa)],[f_541_2]) ).
cnf(f_541_4,plain,
( c_Rings_Odvd__class_Odvd(U_1708,U_1709,U_1710)
| c_Groups_Oabs__class_Oabs(U_1708,U_1709) != c_Groups_Oabs__class_Oabs(U_1708,U_1710)
| ~ class_Rings_Olinordered__idom(U_1708) ),
inference(clausify,[status(thm)],[f_541_3]) ).
fof(f_542_1,plain,
! [V_k_2,V_ma_2,T_a] :
( ( ( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oabs__class_Oabs(T_a,V_ma_2),V_k_2)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2) )
& ( c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2)
| ~ c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oabs__class_Oabs(T_a,V_ma_2),V_k_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__dvd__iff]) ).
fof(f_542_2,plain,
! [U_1713,U_1712,U_1711] :
( ( ( c_Rings_Odvd__class_Odvd(U_1711,c_Groups_Oabs__class_Oabs(U_1711,U_1712),U_1713)
| ~ c_Rings_Odvd__class_Odvd(U_1711,U_1712,U_1713) )
& ( c_Rings_Odvd__class_Odvd(U_1711,U_1712,U_1713)
| ~ c_Rings_Odvd__class_Odvd(U_1711,c_Groups_Oabs__class_Oabs(U_1711,U_1712),U_1713) ) )
| ~ class_Rings_Olinordered__idom(U_1711) ),
inference(variable_rename,[status(thm)],[f_542_1]) ).
fof(f_542_3,plain,
( ! [U_1711,U_1712,U_1713] :
( c_Rings_Odvd__class_Odvd(U_1711,c_Groups_Oabs__class_Oabs(U_1711,U_1712),U_1713)
| ~ c_Rings_Odvd__class_Odvd(U_1711,U_1712,U_1713)
| ~ sP193(U_1711,U_1712,U_1713) )
& ! [U_1711,U_1712,U_1713] :
( c_Rings_Odvd__class_Odvd(U_1711,U_1712,U_1713)
| ~ c_Rings_Odvd__class_Odvd(U_1711,c_Groups_Oabs__class_Oabs(U_1711,U_1712),U_1713)
| ~ sP193(U_1711,U_1712,U_1713) )
& ! [U_1711,U_1712,U_1713] :
( sP193(U_1711,U_1712,U_1713)
| ~ class_Rings_Olinordered__idom(U_1711) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193])],[f_542_2]) ).
cnf(f_542_4,plain,
( sP193(U_1711,U_1712,U_1713)
| ~ class_Rings_Olinordered__idom(U_1711) ),
inference(clausify,[status(thm)],[f_542_3]) ).
cnf(f_542_5,plain,
( c_Rings_Odvd__class_Odvd(U_1711,U_1712,U_1713)
| ~ c_Rings_Odvd__class_Odvd(U_1711,c_Groups_Oabs__class_Oabs(U_1711,U_1712),U_1713)
| ~ sP193(U_1711,U_1712,U_1713) ),
inference(clausify,[status(thm)],[f_542_3]) ).
cnf(f_542_6,plain,
( c_Rings_Odvd__class_Odvd(U_1711,c_Groups_Oabs__class_Oabs(U_1711,U_1712),U_1713)
| ~ c_Rings_Odvd__class_Odvd(U_1711,U_1712,U_1713)
| ~ sP193(U_1711,U_1712,U_1713) ),
inference(clausify,[status(thm)],[f_542_3]) ).
fof(f_543_1,plain,
! [V_k_2,V_ma_2,T_a] :
( ( ( c_Rings_Odvd__class_Odvd(T_a,V_ma_2,c_Groups_Oabs__class_Oabs(T_a,V_k_2))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2) )
& ( c_Rings_Odvd__class_Odvd(T_a,V_ma_2,V_k_2)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_ma_2,c_Groups_Oabs__class_Oabs(T_a,V_k_2)) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__abs__iff]) ).
fof(f_543_2,plain,
! [U_1716,U_1715,U_1714] :
( ( ( c_Rings_Odvd__class_Odvd(U_1714,U_1715,c_Groups_Oabs__class_Oabs(U_1714,U_1716))
| ~ c_Rings_Odvd__class_Odvd(U_1714,U_1715,U_1716) )
& ( c_Rings_Odvd__class_Odvd(U_1714,U_1715,U_1716)
| ~ c_Rings_Odvd__class_Odvd(U_1714,U_1715,c_Groups_Oabs__class_Oabs(U_1714,U_1716)) ) )
| ~ class_Rings_Olinordered__idom(U_1714) ),
inference(variable_rename,[status(thm)],[f_543_1]) ).
fof(f_543_3,plain,
( ! [U_1715,U_1716,U_1714] :
( c_Rings_Odvd__class_Odvd(U_1714,U_1715,c_Groups_Oabs__class_Oabs(U_1714,U_1716))
| ~ c_Rings_Odvd__class_Odvd(U_1714,U_1715,U_1716)
| ~ sP194(U_1715,U_1716,U_1714) )
& ! [U_1715,U_1716,U_1714] :
( c_Rings_Odvd__class_Odvd(U_1714,U_1715,U_1716)
| ~ c_Rings_Odvd__class_Odvd(U_1714,U_1715,c_Groups_Oabs__class_Oabs(U_1714,U_1716))
| ~ sP194(U_1715,U_1716,U_1714) )
& ! [U_1715,U_1716,U_1714] :
( sP194(U_1715,U_1716,U_1714)
| ~ class_Rings_Olinordered__idom(U_1714) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP194])],[f_543_2]) ).
cnf(f_543_4,plain,
( sP194(U_1715,U_1716,U_1714)
| ~ class_Rings_Olinordered__idom(U_1714) ),
inference(clausify,[status(thm)],[f_543_3]) ).
cnf(f_543_5,plain,
( c_Rings_Odvd__class_Odvd(U_1714,U_1715,U_1716)
| ~ c_Rings_Odvd__class_Odvd(U_1714,U_1715,c_Groups_Oabs__class_Oabs(U_1714,U_1716))
| ~ sP194(U_1715,U_1716,U_1714) ),
inference(clausify,[status(thm)],[f_543_3]) ).
cnf(f_543_6,plain,
( c_Rings_Odvd__class_Odvd(U_1714,U_1715,c_Groups_Oabs__class_Oabs(U_1714,U_1716))
| ~ c_Rings_Odvd__class_Odvd(U_1714,U_1715,U_1716)
| ~ sP194(U_1715,U_1716,U_1714) ),
inference(clausify,[status(thm)],[f_543_3]) ).
fof(f_544_1,plain,
! [V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,c_Groups_Oone__class_Oone(T_a),V_a)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_one__dvd]) ).
fof(f_544_2,plain,
! [U_1718,U_1717] :
( c_Rings_Odvd__class_Odvd(U_1717,c_Groups_Oone__class_Oone(U_1717),U_1718)
| ~ class_Rings_Ocomm__semiring__1(U_1717) ),
inference(variable_rename,[status(thm)],[f_544_1]) ).
fof(f_544_3,plain,
! [U_1718,U_1717] :
( c_Rings_Odvd__class_Odvd(U_1717,c_Groups_Oone__class_Oone(U_1717),U_1718)
| ~ class_Rings_Ocomm__semiring__1(U_1717) ),
inference(definitional_conversion,[status(esa)],[f_544_2]) ).
cnf(f_544_4,plain,
( c_Rings_Odvd__class_Odvd(U_1717,c_Groups_Oone__class_Oone(U_1717),U_1718)
| ~ class_Rings_Ocomm__semiring__1(U_1717) ),
inference(clausify,[status(thm)],[f_544_3]) ).
fof(f_545_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_a,c_Groups_Oplus__class_Oplus(T_a,V_b,V_c))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__add]) ).
fof(f_545_2,plain,
! [U_1722,U_1721,U_1720,U_1719] :
( c_Rings_Odvd__class_Odvd(U_1719,U_1720,c_Groups_Oplus__class_Oplus(U_1719,U_1721,U_1722))
| ~ c_Rings_Odvd__class_Odvd(U_1719,U_1720,U_1722)
| ~ c_Rings_Odvd__class_Odvd(U_1719,U_1720,U_1721)
| ~ class_Rings_Ocomm__semiring__1(U_1719) ),
inference(variable_rename,[status(thm)],[f_545_1]) ).
fof(f_545_3,plain,
! [U_1722,U_1719,U_1721,U_1720] :
( c_Rings_Odvd__class_Odvd(U_1719,U_1720,c_Groups_Oplus__class_Oplus(U_1719,U_1721,U_1722))
| ~ c_Rings_Odvd__class_Odvd(U_1719,U_1720,U_1722)
| ~ c_Rings_Odvd__class_Odvd(U_1719,U_1720,U_1721)
| ~ class_Rings_Ocomm__semiring__1(U_1719) ),
inference(definitional_conversion,[status(esa)],[f_545_2]) ).
cnf(f_545_4,plain,
( c_Rings_Odvd__class_Odvd(U_1719,U_1720,c_Groups_Oplus__class_Oplus(U_1719,U_1721,U_1722))
| ~ c_Rings_Odvd__class_Odvd(U_1719,U_1720,U_1722)
| ~ c_Rings_Odvd__class_Odvd(U_1719,U_1720,U_1721)
| ~ class_Rings_Ocomm__semiring__1(U_1719) ),
inference(clausify,[status(thm)],[f_545_3]) ).
fof(f_546_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_b,V_c)
| ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__right]) ).
fof(f_546_2,plain,
! [U_1726,U_1725,U_1724,U_1723] :
( c_Rings_Odvd__class_Odvd(U_1723,U_1725,U_1726)
| ~ c_Rings_Odvd__class_Odvd(U_1723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1724),U_1725),U_1726)
| ~ class_Rings_Ocomm__semiring__1(U_1723) ),
inference(variable_rename,[status(thm)],[f_546_1]) ).
fof(f_546_3,plain,
! [U_1724,U_1726,U_1725,U_1723] :
( c_Rings_Odvd__class_Odvd(U_1723,U_1725,U_1726)
| ~ c_Rings_Odvd__class_Odvd(U_1723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1724),U_1725),U_1726)
| ~ class_Rings_Ocomm__semiring__1(U_1723) ),
inference(definitional_conversion,[status(esa)],[f_546_2]) ).
cnf(f_546_4,plain,
( c_Rings_Odvd__class_Odvd(U_1723,U_1725,U_1726)
| ~ c_Rings_Odvd__class_Odvd(U_1723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1723),U_1724),U_1725),U_1726)
| ~ class_Rings_Ocomm__semiring__1(U_1723) ),
inference(clausify,[status(thm)],[f_546_3]) ).
fof(f_547_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
| ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b),V_c)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__left]) ).
fof(f_547_2,plain,
! [U_1730,U_1729,U_1728,U_1727] :
( c_Rings_Odvd__class_Odvd(U_1727,U_1728,U_1730)
| ~ c_Rings_Odvd__class_Odvd(U_1727,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1727),U_1728),U_1729),U_1730)
| ~ class_Rings_Ocomm__semiring__1(U_1727) ),
inference(variable_rename,[status(thm)],[f_547_1]) ).
fof(f_547_3,plain,
! [U_1728,U_1727,U_1729,U_1730] :
( c_Rings_Odvd__class_Odvd(U_1727,U_1728,U_1730)
| ~ c_Rings_Odvd__class_Odvd(U_1727,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1727),U_1728),U_1729),U_1730)
| ~ class_Rings_Ocomm__semiring__1(U_1727) ),
inference(definitional_conversion,[status(esa)],[f_547_2]) ).
cnf(f_547_4,plain,
( c_Rings_Odvd__class_Odvd(U_1727,U_1728,U_1730)
| ~ c_Rings_Odvd__class_Odvd(U_1727,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1727),U_1728),U_1729),U_1730)
| ~ class_Rings_Ocomm__semiring__1(U_1727) ),
inference(clausify,[status(thm)],[f_547_3]) ).
fof(f_548_1,plain,
! [V_k,V_b,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_b,V_a)
| V_a != hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
| ~ class_Rings_Odvd(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvdI]) ).
fof(f_548_2,plain,
! [U_1734,U_1733,U_1732,U_1731] :
( c_Rings_Odvd__class_Odvd(U_1731,U_1733,U_1732)
| U_1732 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1733),U_1734)
| ~ class_Rings_Odvd(U_1731) ),
inference(variable_rename,[status(thm)],[f_548_1]) ).
fof(f_548_3,plain,
! [U_1731,U_1732,U_1733,U_1734] :
( c_Rings_Odvd__class_Odvd(U_1731,U_1733,U_1732)
| U_1732 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1733),U_1734)
| ~ class_Rings_Odvd(U_1731) ),
inference(definitional_conversion,[status(esa)],[f_548_2]) ).
cnf(f_548_4,plain,
( c_Rings_Odvd__class_Odvd(U_1731,U_1733,U_1732)
| U_1732 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1731),U_1733),U_1734)
| ~ class_Rings_Odvd(U_1731) ),
inference(clausify,[status(thm)],[f_548_3]) ).
fof(f_549_1,plain,
! [V_d,V_c,V_b,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(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_Rings_Odvd__class_Odvd(T_a,V_c,V_d)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_mult__dvd__mono]) ).
fof(f_549_2,plain,
! [U_1739,U_1738,U_1737,U_1736,U_1735] :
( c_Rings_Odvd__class_Odvd(U_1735,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1735),U_1736),U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1735),U_1737),U_1739))
| ~ c_Rings_Odvd__class_Odvd(U_1735,U_1738,U_1739)
| ~ c_Rings_Odvd__class_Odvd(U_1735,U_1736,U_1737)
| ~ class_Rings_Ocomm__semiring__1(U_1735) ),
inference(variable_rename,[status(thm)],[f_549_1]) ).
fof(f_549_3,plain,
! [U_1735,U_1736,U_1737,U_1738,U_1739] :
( c_Rings_Odvd__class_Odvd(U_1735,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1735),U_1736),U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1735),U_1737),U_1739))
| ~ c_Rings_Odvd__class_Odvd(U_1735,U_1738,U_1739)
| ~ c_Rings_Odvd__class_Odvd(U_1735,U_1736,U_1737)
| ~ class_Rings_Ocomm__semiring__1(U_1735) ),
inference(definitional_conversion,[status(esa)],[f_549_2]) ).
cnf(f_549_4,plain,
( c_Rings_Odvd__class_Odvd(U_1735,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1735),U_1736),U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1735),U_1737),U_1739))
| ~ c_Rings_Odvd__class_Odvd(U_1735,U_1738,U_1739)
| ~ c_Rings_Odvd__class_Odvd(U_1735,U_1736,U_1737)
| ~ class_Rings_Ocomm__semiring__1(U_1735) ),
inference(clausify,[status(thm)],[f_549_3]) ).
fof(f_550_1,plain,
! [V_b,V_c,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_c)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult]) ).
fof(f_550_2,plain,
! [U_1743,U_1742,U_1741,U_1740] :
( c_Rings_Odvd__class_Odvd(U_1740,U_1741,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1740),U_1743),U_1742))
| ~ c_Rings_Odvd__class_Odvd(U_1740,U_1741,U_1742)
| ~ class_Rings_Ocomm__semiring__1(U_1740) ),
inference(variable_rename,[status(thm)],[f_550_1]) ).
fof(f_550_3,plain,
! [U_1742,U_1741,U_1743,U_1740] :
( c_Rings_Odvd__class_Odvd(U_1740,U_1741,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1740),U_1743),U_1742))
| ~ c_Rings_Odvd__class_Odvd(U_1740,U_1741,U_1742)
| ~ class_Rings_Ocomm__semiring__1(U_1740) ),
inference(definitional_conversion,[status(esa)],[f_550_2]) ).
cnf(f_550_4,plain,
( c_Rings_Odvd__class_Odvd(U_1740,U_1741,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1740),U_1743),U_1742))
| ~ c_Rings_Odvd__class_Odvd(U_1740,U_1741,U_1742)
| ~ class_Rings_Ocomm__semiring__1(U_1740) ),
inference(clausify,[status(thm)],[f_550_3]) ).
fof(f_551_1,plain,
! [V_c,V_b,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_a,V_b)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult2]) ).
fof(f_551_2,plain,
! [U_1747,U_1746,U_1745,U_1744] :
( c_Rings_Odvd__class_Odvd(U_1744,U_1745,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1744),U_1746),U_1747))
| ~ c_Rings_Odvd__class_Odvd(U_1744,U_1745,U_1746)
| ~ class_Rings_Ocomm__semiring__1(U_1744) ),
inference(variable_rename,[status(thm)],[f_551_1]) ).
fof(f_551_3,plain,
! [U_1745,U_1744,U_1746,U_1747] :
( c_Rings_Odvd__class_Odvd(U_1744,U_1745,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1744),U_1746),U_1747))
| ~ c_Rings_Odvd__class_Odvd(U_1744,U_1745,U_1746)
| ~ class_Rings_Ocomm__semiring__1(U_1744) ),
inference(definitional_conversion,[status(esa)],[f_551_2]) ).
cnf(f_551_4,plain,
( c_Rings_Odvd__class_Odvd(U_1744,U_1745,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1744),U_1746),U_1747))
| ~ c_Rings_Odvd__class_Odvd(U_1744,U_1745,U_1746)
| ~ class_Rings_Ocomm__semiring__1(U_1744) ),
inference(clausify,[status(thm)],[f_551_3]) ).
fof(f_552_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_a,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_dvd__triv__right]) ).
fof(f_552_2,plain,
! [U_1750,U_1749,U_1748] :
( c_Rings_Odvd__class_Odvd(U_1748,U_1749,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1750),U_1749))
| ~ class_Rings_Ocomm__semiring__1(U_1748) ),
inference(variable_rename,[status(thm)],[f_552_1]) ).
fof(f_552_3,plain,
! [U_1749,U_1750,U_1748] :
( c_Rings_Odvd__class_Odvd(U_1748,U_1749,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1750),U_1749))
| ~ class_Rings_Ocomm__semiring__1(U_1748) ),
inference(definitional_conversion,[status(esa)],[f_552_2]) ).
cnf(f_552_4,plain,
( c_Rings_Odvd__class_Odvd(U_1748,U_1749,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1750),U_1749))
| ~ class_Rings_Ocomm__semiring__1(U_1748) ),
inference(clausify,[status(thm)],[f_552_3]) ).
fof(f_553_1,plain,
! [V_b,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__triv__left]) ).
fof(f_553_2,plain,
! [U_1753,U_1752,U_1751] :
( c_Rings_Odvd__class_Odvd(U_1751,U_1752,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1751),U_1752),U_1753))
| ~ class_Rings_Ocomm__semiring__1(U_1751) ),
inference(variable_rename,[status(thm)],[f_553_1]) ).
fof(f_553_3,plain,
! [U_1751,U_1752,U_1753] :
( c_Rings_Odvd__class_Odvd(U_1751,U_1752,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1751),U_1752),U_1753))
| ~ class_Rings_Ocomm__semiring__1(U_1751) ),
inference(definitional_conversion,[status(esa)],[f_553_2]) ).
cnf(f_553_4,plain,
( c_Rings_Odvd__class_Odvd(U_1751,U_1752,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1751),U_1752),U_1753))
| ~ class_Rings_Ocomm__semiring__1(U_1751) ),
inference(clausify,[status(thm)],[f_553_3]) ).
fof(f_554_1,plain,
! [V_b_2,V_a_2,V_ca_2,T_a] :
( ( ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))
| ( ~ c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2)
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2)
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2)) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__left]) ).
fof(f_554_2,plain,
! [U_1757,U_1756,U_1755,U_1754] :
( ( ( c_Rings_Odvd__class_Odvd(U_1754,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1757))
| ( ~ c_Rings_Odvd__class_Odvd(U_1754,U_1756,U_1757)
& U_1755 != c_Groups_Ozero__class_Ozero(U_1754) ) )
& ( c_Rings_Odvd__class_Odvd(U_1754,U_1756,U_1757)
| U_1755 = c_Groups_Ozero__class_Ozero(U_1754)
| ~ c_Rings_Odvd__class_Odvd(U_1754,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1757)) ) )
| ~ class_Rings_Oidom(U_1754) ),
inference(variable_rename,[status(thm)],[f_554_1]) ).
fof(f_554_3,plain,
( ! [U_1754,U_1755,U_1756,U_1757] :
( ~ c_Rings_Odvd__class_Odvd(U_1754,U_1756,U_1757)
| ~ sP195(U_1754,U_1755,U_1756,U_1757) )
& ! [U_1754,U_1755,U_1756,U_1757] :
( U_1755 != c_Groups_Ozero__class_Ozero(U_1754)
| ~ sP195(U_1754,U_1755,U_1756,U_1757) )
& ! [U_1754,U_1755,U_1756,U_1757] :
( c_Rings_Odvd__class_Odvd(U_1754,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1757))
| sP195(U_1754,U_1755,U_1756,U_1757)
| ~ sP196(U_1754,U_1755,U_1756,U_1757) )
& ! [U_1754,U_1755,U_1756,U_1757] :
( c_Rings_Odvd__class_Odvd(U_1754,U_1756,U_1757)
| U_1755 = c_Groups_Ozero__class_Ozero(U_1754)
| ~ c_Rings_Odvd__class_Odvd(U_1754,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1757))
| ~ sP196(U_1754,U_1755,U_1756,U_1757) )
& ! [U_1754,U_1755,U_1756,U_1757] :
( sP196(U_1754,U_1755,U_1756,U_1757)
| ~ class_Rings_Oidom(U_1754) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195,sP196])],[f_554_2]) ).
cnf(f_554_4,plain,
( sP196(U_1754,U_1755,U_1756,U_1757)
| ~ class_Rings_Oidom(U_1754) ),
inference(clausify,[status(thm)],[f_554_3]) ).
cnf(f_554_5,plain,
( c_Rings_Odvd__class_Odvd(U_1754,U_1756,U_1757)
| U_1755 = c_Groups_Ozero__class_Ozero(U_1754)
| ~ c_Rings_Odvd__class_Odvd(U_1754,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1757))
| ~ sP196(U_1754,U_1755,U_1756,U_1757) ),
inference(clausify,[status(thm)],[f_554_3]) ).
cnf(f_554_6,plain,
( c_Rings_Odvd__class_Odvd(U_1754,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1756),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),U_1755),U_1757))
| sP195(U_1754,U_1755,U_1756,U_1757)
| ~ sP196(U_1754,U_1755,U_1756,U_1757) ),
inference(clausify,[status(thm)],[f_554_3]) ).
cnf(f_554_7,plain,
( U_1755 != c_Groups_Ozero__class_Ozero(U_1754)
| ~ sP195(U_1754,U_1755,U_1756,U_1757) ),
inference(clausify,[status(thm)],[f_554_3]) ).
cnf(f_554_8,plain,
( ~ c_Rings_Odvd__class_Odvd(U_1754,U_1756,U_1757)
| ~ sP195(U_1754,U_1755,U_1756,U_1757) ),
inference(clausify,[status(thm)],[f_554_3]) ).
fof(f_555_1,plain,
! [V_b_2,V_ca_2,V_a_2,T_a] :
( ( ( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))
| ( ~ c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2)
& V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) ) )
& ( c_Rings_Odvd__class_Odvd(T_a,V_a_2,V_b_2)
| V_ca_2 = c_Groups_Ozero__class_Ozero(T_a)
| ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel__right]) ).
fof(f_555_2,plain,
! [U_1761,U_1760,U_1759,U_1758] :
( ( ( c_Rings_Odvd__class_Odvd(U_1758,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1759),U_1760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1761),U_1760))
| ( ~ c_Rings_Odvd__class_Odvd(U_1758,U_1759,U_1761)
& U_1760 != c_Groups_Ozero__class_Ozero(U_1758) ) )
& ( c_Rings_Odvd__class_Odvd(U_1758,U_1759,U_1761)
| U_1760 = c_Groups_Ozero__class_Ozero(U_1758)
| ~ c_Rings_Odvd__class_Odvd(U_1758,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1759),U_1760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1761),U_1760)) ) )
| ~ class_Rings_Oidom(U_1758) ),
inference(variable_rename,[status(thm)],[f_555_1]) ).
fof(f_555_3,plain,
( ! [U_1759,U_1760,U_1761,U_1758] :
( ~ c_Rings_Odvd__class_Odvd(U_1758,U_1759,U_1761)
| ~ sP197(U_1759,U_1760,U_1761,U_1758) )
& ! [U_1759,U_1760,U_1761,U_1758] :
( U_1760 != c_Groups_Ozero__class_Ozero(U_1758)
| ~ sP197(U_1759,U_1760,U_1761,U_1758) )
& ! [U_1759,U_1760,U_1761,U_1758] :
( c_Rings_Odvd__class_Odvd(U_1758,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1759),U_1760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1761),U_1760))
| sP197(U_1759,U_1760,U_1761,U_1758)
| ~ sP198(U_1759,U_1760,U_1761,U_1758) )
& ! [U_1759,U_1760,U_1761,U_1758] :
( c_Rings_Odvd__class_Odvd(U_1758,U_1759,U_1761)
| U_1760 = c_Groups_Ozero__class_Ozero(U_1758)
| ~ c_Rings_Odvd__class_Odvd(U_1758,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1759),U_1760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1761),U_1760))
| ~ sP198(U_1759,U_1760,U_1761,U_1758) )
& ! [U_1759,U_1760,U_1761,U_1758] :
( sP198(U_1759,U_1760,U_1761,U_1758)
| ~ class_Rings_Oidom(U_1758) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197,sP198])],[f_555_2]) ).
cnf(f_555_4,plain,
( sP198(U_1759,U_1760,U_1761,U_1758)
| ~ class_Rings_Oidom(U_1758) ),
inference(clausify,[status(thm)],[f_555_3]) ).
cnf(f_555_5,plain,
( c_Rings_Odvd__class_Odvd(U_1758,U_1759,U_1761)
| U_1760 = c_Groups_Ozero__class_Ozero(U_1758)
| ~ c_Rings_Odvd__class_Odvd(U_1758,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1759),U_1760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1761),U_1760))
| ~ sP198(U_1759,U_1760,U_1761,U_1758) ),
inference(clausify,[status(thm)],[f_555_3]) ).
cnf(f_555_6,plain,
( c_Rings_Odvd__class_Odvd(U_1758,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1759),U_1760),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1758),U_1761),U_1760))
| sP197(U_1759,U_1760,U_1761,U_1758)
| ~ sP198(U_1759,U_1760,U_1761,U_1758) ),
inference(clausify,[status(thm)],[f_555_3]) ).
cnf(f_555_7,plain,
( U_1760 != c_Groups_Ozero__class_Ozero(U_1758)
| ~ sP197(U_1759,U_1760,U_1761,U_1758) ),
inference(clausify,[status(thm)],[f_555_3]) ).
cnf(f_555_8,plain,
( ~ c_Rings_Odvd__class_Odvd(U_1758,U_1759,U_1761)
| ~ sP197(U_1759,U_1760,U_1761,U_1758) ),
inference(clausify,[status(thm)],[f_555_3]) ).
fof(f_556_1,plain,
! [V_l_2,V_P_2,T_a] :
( ( ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x)))
| ! [B_x] :
( ~ hBOOL(hAPP(V_P_2,B_x))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a))) ) )
& ( ? [B_x] :
( hBOOL(hAPP(V_P_2,B_x))
& c_Rings_Odvd__class_Odvd(T_a,V_l_2,c_Groups_Oplus__class_Oplus(T_a,B_x,c_Groups_Ozero__class_Ozero(T_a))) )
| ! [B_x] : ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_l_2),B_x))) ) )
| ~ class_Rings_Osemiring__0(T_a)
| ~ class_Rings_Odvd(T_a) ),
inference(fof_nnf,[status(thm)],[fact_unity__coeff__ex]) ).
fof(f_556_2,plain,
! [U_1768,U_1767,U_1766] :
( ( ( ? [U_1765] : hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),U_1765)))
| ! [U_1764] :
( ~ hBOOL(hAPP(U_1767,U_1764))
| ~ c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,U_1764,c_Groups_Ozero__class_Ozero(U_1766))) ) )
& ( ? [U_1763] :
( hBOOL(hAPP(U_1767,U_1763))
& c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,U_1763,c_Groups_Ozero__class_Ozero(U_1766))) )
| ! [U_1762] : ~ hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),U_1762))) ) )
| ~ class_Rings_Osemiring__0(U_1766)
| ~ class_Rings_Odvd(U_1766) ),
inference(variable_rename,[status(thm)],[f_556_1]) ).
fof(f_556_3,plain,
! [U_1768,U_1767,U_1766] :
( ( ( ? [U_1765] : hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),U_1765)))
| ! [U_1764] :
( ~ hBOOL(hAPP(U_1767,U_1764))
| ~ c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,U_1764,c_Groups_Ozero__class_Ozero(U_1766))) ) )
& ( ( hBOOL(hAPP(U_1767,sK26(U_1768,U_1767,U_1766)))
& c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,sK26(U_1768,U_1767,U_1766),c_Groups_Ozero__class_Ozero(U_1766))) )
| ! [U_1762] : ~ hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),U_1762))) ) )
| ~ class_Rings_Osemiring__0(U_1766)
| ~ class_Rings_Odvd(U_1766) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1763,sK26(U_1768,U_1767,U_1766))],[f_556_2]) ).
fof(f_556_4,plain,
! [U_1768,U_1767,U_1766] :
( ( ( hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),sK27(U_1768,U_1767,U_1766))))
| ! [U_1764] :
( ~ hBOOL(hAPP(U_1767,U_1764))
| ~ c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,U_1764,c_Groups_Ozero__class_Ozero(U_1766))) ) )
& ( ( hBOOL(hAPP(U_1767,sK26(U_1768,U_1767,U_1766)))
& c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,sK26(U_1768,U_1767,U_1766),c_Groups_Ozero__class_Ozero(U_1766))) )
| ! [U_1762] : ~ hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),U_1762))) ) )
| ~ class_Rings_Osemiring__0(U_1766)
| ~ class_Rings_Odvd(U_1766) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1765,sK27(U_1768,U_1767,U_1766))],[f_556_3]) ).
fof(f_556_5,plain,
( ! [U_1766,U_1767,U_1768] :
( hBOOL(hAPP(U_1767,sK26(U_1768,U_1767,U_1766)))
| ~ sP199(U_1766,U_1767,U_1768) )
& ! [U_1766,U_1767,U_1768] :
( c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,sK26(U_1768,U_1767,U_1766),c_Groups_Ozero__class_Ozero(U_1766)))
| ~ sP199(U_1766,U_1767,U_1768) )
& ! [U_1766,U_1764,U_1767,U_1762,U_1768] :
( hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),sK27(U_1768,U_1767,U_1766))))
| ~ hBOOL(hAPP(U_1767,U_1764))
| ~ c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,U_1764,c_Groups_Ozero__class_Ozero(U_1766)))
| ~ sP200(U_1766,U_1764,U_1767,U_1762,U_1768) )
& ! [U_1766,U_1764,U_1767,U_1762,U_1768] :
( sP199(U_1766,U_1767,U_1768)
| ~ hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),U_1762)))
| ~ sP200(U_1766,U_1764,U_1767,U_1762,U_1768) )
& ! [U_1766,U_1764,U_1767,U_1762,U_1768] :
( sP200(U_1766,U_1764,U_1767,U_1762,U_1768)
| ~ class_Rings_Osemiring__0(U_1766)
| ~ class_Rings_Odvd(U_1766) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199,sP200])],[f_556_4]) ).
cnf(f_556_6,plain,
( sP200(U_1766,U_1764,U_1767,U_1762,U_1768)
| ~ class_Rings_Osemiring__0(U_1766)
| ~ class_Rings_Odvd(U_1766) ),
inference(clausify,[status(thm)],[f_556_5]) ).
cnf(f_556_7,plain,
( sP199(U_1766,U_1767,U_1768)
| ~ hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),U_1762)))
| ~ sP200(U_1766,U_1764,U_1767,U_1762,U_1768) ),
inference(clausify,[status(thm)],[f_556_5]) ).
cnf(f_556_8,plain,
( hBOOL(hAPP(U_1767,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1766),U_1768),sK27(U_1768,U_1767,U_1766))))
| ~ hBOOL(hAPP(U_1767,U_1764))
| ~ c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,U_1764,c_Groups_Ozero__class_Ozero(U_1766)))
| ~ sP200(U_1766,U_1764,U_1767,U_1762,U_1768) ),
inference(clausify,[status(thm)],[f_556_5]) ).
cnf(f_556_9,plain,
( c_Rings_Odvd__class_Odvd(U_1766,U_1768,c_Groups_Oplus__class_Oplus(U_1766,sK26(U_1768,U_1767,U_1766),c_Groups_Ozero__class_Ozero(U_1766)))
| ~ sP199(U_1766,U_1767,U_1768) ),
inference(clausify,[status(thm)],[f_556_5]) ).
cnf(f_556_10,plain,
( hBOOL(hAPP(U_1767,sK26(U_1768,U_1767,U_1766)))
| ~ sP199(U_1766,U_1767,U_1768) ),
inference(clausify,[status(thm)],[f_556_5]) ).
fof(f_557_1,plain,
! [V_p,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p)
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__1]) ).
fof(f_557_2,plain,
! [U_1771,U_1770,U_1769] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1769),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1769)),c_Polynomial_OpCons(U_1769,c_Groups_Ouminus__class_Ouminus(U_1769,U_1770),c_Polynomial_OpCons(U_1769,c_Groups_Oone__class_Oone(U_1769),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1769))))),c_Polynomial_Oorder(U_1769,U_1770,U_1771)),U_1771)
| ~ class_Rings_Oidom(U_1769) ),
inference(variable_rename,[status(thm)],[f_557_1]) ).
fof(f_557_3,plain,
! [U_1770,U_1771,U_1769] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1769),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1769)),c_Polynomial_OpCons(U_1769,c_Groups_Ouminus__class_Ouminus(U_1769,U_1770),c_Polynomial_OpCons(U_1769,c_Groups_Oone__class_Oone(U_1769),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1769))))),c_Polynomial_Oorder(U_1769,U_1770,U_1771)),U_1771)
| ~ class_Rings_Oidom(U_1769) ),
inference(definitional_conversion,[status(esa)],[f_557_2]) ).
cnf(f_557_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_1769),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1769)),c_Polynomial_OpCons(U_1769,c_Groups_Ouminus__class_Ouminus(U_1769,U_1770),c_Polynomial_OpCons(U_1769,c_Groups_Oone__class_Oone(U_1769),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_1769))))),c_Polynomial_Oorder(U_1769,U_1770,U_1771)),U_1771)
| ~ class_Rings_Oidom(U_1769) ),
inference(clausify,[status(thm)],[f_557_3]) ).
fof(f_558_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_Oincseq(T_a,V_X_2)
| ? [B_m,B_n] :
( ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) ) )
& ( ! [B_m,B_n] :
( c_Orderings_Oord__class_Oless__eq(T_a,hAPP(V_X_2,B_m),hAPP(V_X_2,B_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B_m,B_n) )
| ~ c_SEQ_Oincseq(T_a,V_X_2) ) )
| ~ class_Orderings_Oorder(T_a) ),
inference(fof_nnf,[status(thm)],[fact_incseq__def]) ).
fof(f_558_2,plain,
! [U_1777,U_1776] :
( ( ( c_SEQ_Oincseq(U_1776,U_1777)
| ? [U_1775,U_1774] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,U_1775),hAPP(U_1777,U_1774))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1775,U_1774) ) )
& ( ! [U_1773,U_1772] :
( c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,U_1773),hAPP(U_1777,U_1772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1773,U_1772) )
| ~ c_SEQ_Oincseq(U_1776,U_1777) ) )
| ~ class_Orderings_Oorder(U_1776) ),
inference(variable_rename,[status(thm)],[f_558_1]) ).
fof(f_558_3,plain,
! [U_1777,U_1776] :
( ( ( c_SEQ_Oincseq(U_1776,U_1777)
| ? [U_1774] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,sK28(U_1777,U_1776)),hAPP(U_1777,U_1774))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK28(U_1777,U_1776),U_1774) ) )
& ( ! [U_1773,U_1772] :
( c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,U_1773),hAPP(U_1777,U_1772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1773,U_1772) )
| ~ c_SEQ_Oincseq(U_1776,U_1777) ) )
| ~ class_Orderings_Oorder(U_1776) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1775,sK28(U_1777,U_1776))],[f_558_2]) ).
fof(f_558_4,plain,
! [U_1777,U_1776] :
( ( ( c_SEQ_Oincseq(U_1776,U_1777)
| ( ~ c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,sK28(U_1777,U_1776)),hAPP(U_1777,sK29(U_1777,U_1776)))
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK28(U_1777,U_1776),sK29(U_1777,U_1776)) ) )
& ( ! [U_1773,U_1772] :
( c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,U_1773),hAPP(U_1777,U_1772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1773,U_1772) )
| ~ c_SEQ_Oincseq(U_1776,U_1777) ) )
| ~ class_Orderings_Oorder(U_1776) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1774,sK29(U_1777,U_1776))],[f_558_3]) ).
fof(f_558_5,plain,
( ! [U_1777,U_1776] :
( ~ c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,sK28(U_1777,U_1776)),hAPP(U_1777,sK29(U_1777,U_1776)))
| ~ sP201(U_1777,U_1776) )
& ! [U_1777,U_1776] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK28(U_1777,U_1776),sK29(U_1777,U_1776))
| ~ sP201(U_1777,U_1776) )
& ! [U_1772,U_1777,U_1773,U_1776] :
( c_SEQ_Oincseq(U_1776,U_1777)
| sP201(U_1777,U_1776)
| ~ sP202(U_1772,U_1777,U_1773,U_1776) )
& ! [U_1772,U_1777,U_1773,U_1776] :
( c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,U_1773),hAPP(U_1777,U_1772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1773,U_1772)
| ~ c_SEQ_Oincseq(U_1776,U_1777)
| ~ sP202(U_1772,U_1777,U_1773,U_1776) )
& ! [U_1772,U_1777,U_1773,U_1776] :
( sP202(U_1772,U_1777,U_1773,U_1776)
| ~ class_Orderings_Oorder(U_1776) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201,sP202])],[f_558_4]) ).
cnf(f_558_6,plain,
( sP202(U_1772,U_1777,U_1773,U_1776)
| ~ class_Orderings_Oorder(U_1776) ),
inference(clausify,[status(thm)],[f_558_5]) ).
cnf(f_558_7,plain,
( c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,U_1773),hAPP(U_1777,U_1772))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1773,U_1772)
| ~ c_SEQ_Oincseq(U_1776,U_1777)
| ~ sP202(U_1772,U_1777,U_1773,U_1776) ),
inference(clausify,[status(thm)],[f_558_5]) ).
cnf(f_558_8,plain,
( c_SEQ_Oincseq(U_1776,U_1777)
| sP201(U_1777,U_1776)
| ~ sP202(U_1772,U_1777,U_1773,U_1776) ),
inference(clausify,[status(thm)],[f_558_5]) ).
cnf(f_558_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,sK28(U_1777,U_1776),sK29(U_1777,U_1776))
| ~ sP201(U_1777,U_1776) ),
inference(clausify,[status(thm)],[f_558_5]) ).
cnf(f_558_10,plain,
( ~ c_Orderings_Oord__class_Oless__eq(U_1776,hAPP(U_1777,sK28(U_1777,U_1776)),hAPP(U_1777,sK29(U_1777,U_1776)))
| ~ sP201(U_1777,U_1776) ),
inference(clausify,[status(thm)],[f_558_5]) ).
fof(f_559_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_559_2,plain,
! [U_1778] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1778,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1778),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_1778) ),
inference(variable_rename,[status(thm)],[f_559_1]) ).
fof(f_559_3,plain,
! [U_1778] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1778,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1778),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_1778) ),
inference(definitional_conversion,[status(esa)],[f_559_2]) ).
cnf(f_559_4,plain,
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_1778,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_1778),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_1778) ),
inference(clausify,[status(thm)],[f_559_3]) ).
fof(f_560_1,plain,
! [V_ma_2] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| V_ma_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( V_ma_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__dvd__1__iff__1]) ).
fof(f_560_2,plain,
! [U_1779] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1779,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| U_1779 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( U_1779 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1779,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_560_1]) ).
fof(f_560_3,plain,
( ! [U_1781] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1781,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| U_1781 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1780] :
( U_1780 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1780,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_560_2]) ).
fof(f_560_4,plain,
( ! [U_1781] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1781,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| U_1781 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ! [U_1780] :
( U_1780 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1780,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa)],[f_560_3]) ).
cnf(f_560_5,plain,
( U_1780 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1780,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_560_4]) ).
cnf(f_560_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1781,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| U_1781 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_560_4]) ).
fof(f_561_1,plain,
! [V_n_2,V_k_2] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,V_n_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k_2,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n_2,V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd__reduce]) ).
fof(f_561_2,plain,
! [U_1783,U_1782] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1782,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1783,U_1782))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1782,U_1783) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1782,U_1783)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1782,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1783,U_1782)) ) ),
inference(variable_rename,[status(thm)],[f_561_1]) ).
fof(f_561_3,plain,
( ! [U_1787,U_1785] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1785,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1787,U_1785))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1785,U_1787) )
& ! [U_1786,U_1784] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1784,U_1786)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1784,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1786,U_1784)) ) ),
inference(miniscope,[status(thm)],[f_561_2]) ).
fof(f_561_4,plain,
( ! [U_1787,U_1785] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1785,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1787,U_1785))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1785,U_1787) )
& ! [U_1784,U_1786] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1784,U_1786)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1784,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1786,U_1784)) ) ),
inference(definitional_conversion,[status(esa)],[f_561_3]) ).
cnf(f_561_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1784,U_1786)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1784,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1786,U_1784)) ),
inference(clausify,[status(thm)],[f_561_4]) ).
cnf(f_561_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1785,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1787,U_1785))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1785,U_1787) ),
inference(clausify,[status(thm)],[f_561_4]) ).
fof(f_562_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_562_2,plain,
! [U_1789,U_1788] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1788),U_1789),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1789
| ~ class_Rings_Ocomm__semiring__1(U_1788) ),
inference(variable_rename,[status(thm)],[f_562_1]) ).
fof(f_562_3,plain,
! [U_1788,U_1789] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1788),U_1789),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1789
| ~ class_Rings_Ocomm__semiring__1(U_1788) ),
inference(definitional_conversion,[status(esa)],[f_562_2]) ).
cnf(f_562_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1788),U_1789),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1789
| ~ class_Rings_Ocomm__semiring__1(U_1788) ),
inference(clausify,[status(thm)],[f_562_3]) ).
fof(f_563_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_563_2,plain,
! [U_1793,U_1792,U_1791,U_1790] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1790),hAPP(hAPP(c_Power_Opower__class_Opower(U_1790),U_1791),U_1792)),U_1793) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1790),U_1791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1792),U_1793))
| ~ class_Rings_Ocomm__semiring__1(U_1790) ),
inference(variable_rename,[status(thm)],[f_563_1]) ).
fof(f_563_3,plain,
! [U_1790,U_1791,U_1792,U_1793] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1790),hAPP(hAPP(c_Power_Opower__class_Opower(U_1790),U_1791),U_1792)),U_1793) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1790),U_1791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1792),U_1793))
| ~ class_Rings_Ocomm__semiring__1(U_1790) ),
inference(definitional_conversion,[status(esa)],[f_563_2]) ).
cnf(f_563_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1790),hAPP(hAPP(c_Power_Opower__class_Opower(U_1790),U_1791),U_1792)),U_1793) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1790),U_1791),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1792),U_1793))
| ~ class_Rings_Ocomm__semiring__1(U_1790) ),
inference(clausify,[status(thm)],[f_563_3]) ).
fof(f_564_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_564_2,plain,
! [U_1797,U_1796,U_1795,U_1794] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),U_1796)),U_1797) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),hAPP(hAPP(c_Power_Opower__class_Opower(U_1794),U_1795),U_1797)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1794),U_1796),U_1797))
| ~ class_Rings_Ocomm__semiring__1(U_1794) ),
inference(variable_rename,[status(thm)],[f_564_1]) ).
fof(f_564_3,plain,
! [U_1794,U_1795,U_1796,U_1797] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),U_1796)),U_1797) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),hAPP(hAPP(c_Power_Opower__class_Opower(U_1794),U_1795),U_1797)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1794),U_1796),U_1797))
| ~ class_Rings_Ocomm__semiring__1(U_1794) ),
inference(definitional_conversion,[status(esa)],[f_564_2]) ).
cnf(f_564_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1794),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),U_1795),U_1796)),U_1797) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1794),hAPP(hAPP(c_Power_Opower__class_Opower(U_1794),U_1795),U_1797)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1794),U_1796),U_1797))
| ~ class_Rings_Ocomm__semiring__1(U_1794) ),
inference(clausify,[status(thm)],[f_564_3]) ).
fof(f_565_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_565_2,plain,
! [U_1800,U_1799,U_1798] :
( c_RealVector_Onorm__class_Onorm(U_1798,hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1800)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1798,U_1799)),U_1800)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1798) ),
inference(variable_rename,[status(thm)],[f_565_1]) ).
fof(f_565_3,plain,
! [U_1798,U_1799,U_1800] :
( c_RealVector_Onorm__class_Onorm(U_1798,hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1800)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1798,U_1799)),U_1800)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1798) ),
inference(definitional_conversion,[status(esa)],[f_565_2]) ).
cnf(f_565_4,plain,
( c_RealVector_Onorm__class_Onorm(U_1798,hAPP(hAPP(c_Power_Opower__class_Opower(U_1798),U_1799),U_1800)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1798,U_1799)),U_1800)
| ~ class_RealVector_Oreal__normed__div__algebra(U_1798) ),
inference(clausify,[status(thm)],[f_565_3]) ).
fof(f_566_1,plain,
! [V_x,V_n,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),V_p),V_n)),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Polynomial_Opoly(T_a,V_p),V_x)),V_n)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__power]) ).
fof(f_566_2,plain,
! [U_1804,U_1803,U_1802,U_1801] :
( hAPP(c_Polynomial_Opoly(U_1801,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1801)),U_1802),U_1803)),U_1804) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1801),hAPP(c_Polynomial_Opoly(U_1801,U_1802),U_1804)),U_1803)
| ~ class_Rings_Ocomm__semiring__1(U_1801) ),
inference(variable_rename,[status(thm)],[f_566_1]) ).
fof(f_566_3,plain,
! [U_1802,U_1801,U_1803,U_1804] :
( hAPP(c_Polynomial_Opoly(U_1801,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1801)),U_1802),U_1803)),U_1804) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1801),hAPP(c_Polynomial_Opoly(U_1801,U_1802),U_1804)),U_1803)
| ~ class_Rings_Ocomm__semiring__1(U_1801) ),
inference(definitional_conversion,[status(esa)],[f_566_2]) ).
cnf(f_566_4,plain,
( hAPP(c_Polynomial_Opoly(U_1801,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_1801)),U_1802),U_1803)),U_1804) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1801),hAPP(c_Polynomial_Opoly(U_1801,U_1802),U_1804)),U_1803)
| ~ class_Rings_Ocomm__semiring__1(U_1801) ),
inference(clausify,[status(thm)],[f_566_3]) ).
fof(f_567_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_567_2,plain,
! [U_1807,U_1806,U_1805] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1805,hAPP(hAPP(c_Power_Opower__class_Opower(U_1805),U_1806),U_1807)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1805,U_1806)),U_1807))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1805) ),
inference(variable_rename,[status(thm)],[f_567_1]) ).
fof(f_567_3,plain,
! [U_1805,U_1806,U_1807] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1805,hAPP(hAPP(c_Power_Opower__class_Opower(U_1805),U_1806),U_1807)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1805,U_1806)),U_1807))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1805) ),
inference(definitional_conversion,[status(esa)],[f_567_2]) ).
cnf(f_567_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_1805,hAPP(hAPP(c_Power_Opower__class_Opower(U_1805),U_1806),U_1807)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_1805,U_1806)),U_1807))
| ~ class_RealVector_Oreal__normed__algebra__1(U_1805) ),
inference(clausify,[status(thm)],[f_567_3]) ).
fof(f_568_1,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_natceiling__zero]) ).
fof(f_568_2,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_568_1]) ).
cnf(f_568_3,plain,
c_RComplete_Onatceiling(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_568_2]) ).
fof(f_569_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(V_x)),
inference(fof_nnf,[status(thm)],[fact_zero__le__natceiling]) ).
fof(f_569_2,plain,
! [U_1808] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_1808)),
inference(variable_rename,[status(thm)],[f_569_1]) ).
fof(f_569_3,plain,
! [U_1808] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_1808)),
inference(definitional_conversion,[status(esa)],[f_569_2]) ).
cnf(f_569_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatceiling(U_1808)),
inference(clausify,[status(thm)],[f_569_3]) ).
fof(f_570_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),c_RComplete_Onatceiling(V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__mono]) ).
fof(f_570_2,plain,
! [U_1810,U_1809] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1809),c_RComplete_Onatceiling(U_1810))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1809,U_1810) ),
inference(variable_rename,[status(thm)],[f_570_1]) ).
fof(f_570_3,plain,
! [U_1809,U_1810] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1809),c_RComplete_Onatceiling(U_1810))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1809,U_1810) ),
inference(definitional_conversion,[status(esa)],[f_570_2]) ).
cnf(f_570_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1809),c_RComplete_Onatceiling(U_1810))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1809,U_1810) ),
inference(clausify,[status(thm)],[f_570_3]) ).
fof(f_571_1,plain,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_natceiling__one]) ).
fof(f_571_2,plain,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_571_1]) ).
cnf(f_571_3,plain,
c_RComplete_Onatceiling(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_571_2]) ).
fof(f_572_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_572_2,plain,
! [U_1812,U_1811] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1811),U_1812),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1811)
| ~ class_Rings_Ocomm__semiring__1(U_1811) ),
inference(variable_rename,[status(thm)],[f_572_1]) ).
fof(f_572_3,plain,
! [U_1811,U_1812] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1811),U_1812),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1811)
| ~ class_Rings_Ocomm__semiring__1(U_1811) ),
inference(definitional_conversion,[status(esa)],[f_572_2]) ).
cnf(f_572_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1811),U_1812),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1811)
| ~ class_Rings_Ocomm__semiring__1(U_1811) ),
inference(clausify,[status(thm)],[f_572_3]) ).
fof(f_573_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_573_2,plain,
! [U_1816,U_1815,U_1814,U_1813] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1813),hAPP(hAPP(c_Power_Opower__class_Opower(U_1813),U_1814),U_1815)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1813),U_1814),U_1816)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1813),U_1814),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1815,U_1816))
| ~ class_Rings_Ocomm__semiring__1(U_1813) ),
inference(variable_rename,[status(thm)],[f_573_1]) ).
fof(f_573_3,plain,
! [U_1813,U_1814,U_1815,U_1816] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1813),hAPP(hAPP(c_Power_Opower__class_Opower(U_1813),U_1814),U_1815)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1813),U_1814),U_1816)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1813),U_1814),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1815,U_1816))
| ~ class_Rings_Ocomm__semiring__1(U_1813) ),
inference(definitional_conversion,[status(esa)],[f_573_2]) ).
cnf(f_573_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1813),hAPP(hAPP(c_Power_Opower__class_Opower(U_1813),U_1814),U_1815)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1813),U_1814),U_1816)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1813),U_1814),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1815,U_1816))
| ~ class_Rings_Ocomm__semiring__1(U_1813) ),
inference(clausify,[status(thm)],[f_573_3]) ).
fof(f_574_1,plain,
! [V_n,V_m] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,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_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m) ),
inference(fof_nnf,[status(thm)],[fact_nat__dvd__not__less]) ).
fof(f_574_2,plain,
! [U_1818,U_1817] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1818,U_1817)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1817,U_1818)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1817) ),
inference(variable_rename,[status(thm)],[f_574_1]) ).
fof(f_574_3,plain,
! [U_1818,U_1817] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1818,U_1817)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1817,U_1818)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1817) ),
inference(definitional_conversion,[status(esa)],[f_574_2]) ).
cnf(f_574_4,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1818,U_1817)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1817,U_1818)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1817) ),
inference(clausify,[status(thm)],[f_574_3]) ).
fof(f_575_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2)
& V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2)
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_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__dvd__cancel__disj]) ).
fof(f_575_2,plain,
! [U_1821,U_1820,U_1819] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1819),U_1820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1819),U_1821))
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1820,U_1821)
& U_1819 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1820,U_1821)
| U_1819 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1819),U_1820),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1819),U_1821)) ) ),
inference(variable_rename,[status(thm)],[f_575_1]) ).
fof(f_575_3,plain,
( ! [U_1827,U_1825,U_1823] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1827))
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1825,U_1827)
& U_1823 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_1826,U_1824,U_1822] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1824,U_1826)
| U_1822 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1826)) ) ),
inference(miniscope,[status(thm)],[f_575_2]) ).
fof(f_575_4,plain,
( ! [U_1827,U_1825,U_1823] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1825,U_1827)
| ~ sP203(U_1827,U_1825,U_1823) )
& ! [U_1827,U_1825,U_1823] :
( U_1823 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP203(U_1827,U_1825,U_1823) )
& ! [U_1827,U_1825,U_1823] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1827))
| sP203(U_1827,U_1825,U_1823) )
& ! [U_1824,U_1822,U_1826] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1824,U_1826)
| U_1822 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1826)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_575_3]) ).
cnf(f_575_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1824,U_1826)
| U_1822 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1824),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1822),U_1826)) ),
inference(clausify,[status(thm)],[f_575_4]) ).
cnf(f_575_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1825),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1823),U_1827))
| sP203(U_1827,U_1825,U_1823) ),
inference(clausify,[status(thm)],[f_575_4]) ).
cnf(f_575_7,plain,
( U_1823 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP203(U_1827,U_1825,U_1823) ),
inference(clausify,[status(thm)],[f_575_4]) ).
cnf(f_575_8,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1825,U_1827)
| ~ sP203(U_1827,U_1825,U_1823) ),
inference(clausify,[status(thm)],[f_575_4]) ).
fof(f_576_1,plain,
! [V_x] :
( c_RComplete_Onatceiling(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__neg]) ).
fof(f_576_2,plain,
! [U_1828] :
( c_RComplete_Onatceiling(U_1828) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1828,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_576_1]) ).
fof(f_576_3,plain,
! [U_1828] :
( c_RComplete_Onatceiling(U_1828) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1828,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(definitional_conversion,[status(esa)],[f_576_2]) ).
cnf(f_576_4,plain,
( c_RComplete_Onatceiling(U_1828) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1828,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_576_3]) ).
fof(f_577_1,plain,
! [V_n,V_k] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n) ),
inference(fof_nnf,[status(thm)],[fact_dvd__imp__le]) ).
fof(f_577_2,plain,
! [U_1830,U_1829] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1829,U_1830)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1830)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1829,U_1830) ),
inference(variable_rename,[status(thm)],[f_577_1]) ).
fof(f_577_3,plain,
! [U_1829,U_1830] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1829,U_1830)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1830)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1829,U_1830) ),
inference(definitional_conversion,[status(esa)],[f_577_2]) ).
cnf(f_577_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1829,U_1830)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1830)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1829,U_1830) ),
inference(clausify,[status(thm)],[f_577_3]) ).
fof(f_578_1,plain,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k)
| ~ c_Rings_Odvd__class_Odvd(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_dvd__mult__cancel]) ).
fof(f_578_2,plain,
! [U_1833,U_1832,U_1831] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1832,U_1833)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1831)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1833)) ),
inference(variable_rename,[status(thm)],[f_578_1]) ).
fof(f_578_3,plain,
! [U_1833,U_1832,U_1831] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1832,U_1833)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1831)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1833)) ),
inference(definitional_conversion,[status(esa)],[f_578_2]) ).
cnf(f_578_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1832,U_1833)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1831)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1832),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1831),U_1833)) ),
inference(clausify,[status(thm)],[f_578_3]) ).
fof(f_579_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_ma_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,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_k_2) ),
inference(fof_nnf,[status(thm)],[fact_nat__mult__dvd__cancel1]) ).
fof(f_579_2,plain,
! [U_1836,U_1835,U_1834] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1836))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1835,U_1836) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1835,U_1836)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1836)) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1834) ),
inference(variable_rename,[status(thm)],[f_579_1]) ).
fof(f_579_3,plain,
( ! [U_1834,U_1835,U_1836] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1836))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1835,U_1836)
| ~ sP204(U_1834,U_1835,U_1836) )
& ! [U_1834,U_1835,U_1836] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1835,U_1836)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1836))
| ~ sP204(U_1834,U_1835,U_1836) )
& ! [U_1834,U_1835,U_1836] :
( sP204(U_1834,U_1835,U_1836)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1834) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_579_2]) ).
cnf(f_579_4,plain,
( sP204(U_1834,U_1835,U_1836)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1834) ),
inference(clausify,[status(thm)],[f_579_3]) ).
cnf(f_579_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1835,U_1836)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1836))
| ~ sP204(U_1834,U_1835,U_1836) ),
inference(clausify,[status(thm)],[f_579_3]) ).
cnf(f_579_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1835),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1834),U_1836))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1835,U_1836)
| ~ sP204(U_1834,U_1835,U_1836) ),
inference(clausify,[status(thm)],[f_579_3]) ).
fof(f_580_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq__one]) ).
fof(f_580_2,plain,
! [U_1837] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1837),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1837,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1837,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1837),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_580_1]) ).
fof(f_580_3,plain,
( ! [U_1839] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1839),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1839,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_1838] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1838,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1838),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_580_2]) ).
fof(f_580_4,plain,
( ! [U_1839] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1839),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1839,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) )
& ! [U_1838] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1838,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1838),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa)],[f_580_3]) ).
cnf(f_580_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1838,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1838),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_580_4]) ).
cnf(f_580_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_1839),c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_1839,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_580_4]) ).
fof(f_581_1,plain,
! [V_n_2,V_ma_2] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2),V_ma_2)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_2),V_n_2),V_ma_2) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel1]) ).
fof(f_581_2,plain,
! [U_1841,U_1840] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1840),U_1841),U_1840)
| U_1841 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( U_1841 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1840),U_1841),U_1840) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1840) ),
inference(variable_rename,[status(thm)],[f_581_1]) ).
fof(f_581_3,plain,
( ! [U_1841,U_1840] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1840),U_1841),U_1840)
| U_1841 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP205(U_1841,U_1840) )
& ! [U_1841,U_1840] :
( U_1841 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1840),U_1841),U_1840)
| ~ sP205(U_1841,U_1840) )
& ! [U_1841,U_1840] :
( sP205(U_1841,U_1840)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1840) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_581_2]) ).
cnf(f_581_4,plain,
( sP205(U_1841,U_1840)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1840) ),
inference(clausify,[status(thm)],[f_581_3]) ).
cnf(f_581_5,plain,
( U_1841 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1840),U_1841),U_1840)
| ~ sP205(U_1841,U_1840) ),
inference(clausify,[status(thm)],[f_581_3]) ).
cnf(f_581_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1840),U_1841),U_1840)
| U_1841 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP205(U_1841,U_1840) ),
inference(clausify,[status(thm)],[f_581_3]) ).
fof(f_582_1,plain,
! [V_n_2,V_ma_2] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ma_2),V_ma_2)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_ma_2),V_ma_2) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_dvd__mult__cancel2]) ).
fof(f_582_2,plain,
! [U_1843,U_1842] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1843),U_1842),U_1842)
| U_1843 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
& ( U_1843 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1843),U_1842),U_1842) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1842) ),
inference(variable_rename,[status(thm)],[f_582_1]) ).
fof(f_582_3,plain,
( ! [U_1843,U_1842] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1843),U_1842),U_1842)
| U_1843 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP206(U_1843,U_1842) )
& ! [U_1843,U_1842] :
( U_1843 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1843),U_1842),U_1842)
| ~ sP206(U_1843,U_1842) )
& ! [U_1843,U_1842] :
( sP206(U_1843,U_1842)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1842) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_582_2]) ).
cnf(f_582_4,plain,
( sP206(U_1843,U_1842)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1842) ),
inference(clausify,[status(thm)],[f_582_3]) ).
cnf(f_582_5,plain,
( U_1843 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1843),U_1842),U_1842)
| ~ sP206(U_1843,U_1842) ),
inference(clausify,[status(thm)],[f_582_3]) ).
cnf(f_582_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1843),U_1842),U_1842)
| U_1843 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
| ~ sP206(U_1843,U_1842) ),
inference(clausify,[status(thm)],[f_582_3]) ).
fof(f_583_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_583_2,plain,
! [U_1847,U_1846,U_1845,U_1844] :
( c_Orderings_Oord__class_Oless(U_1844,hAPP(hAPP(c_Power_Opower__class_Opower(U_1844),U_1845),U_1847),hAPP(hAPP(c_Power_Opower__class_Opower(U_1844),U_1846),U_1847))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1847)
| ~ c_Orderings_Oord__class_Oless__eq(U_1844,c_Groups_Ozero__class_Ozero(U_1844),U_1845)
| ~ c_Orderings_Oord__class_Oless(U_1844,U_1845,U_1846)
| ~ class_Rings_Olinordered__semidom(U_1844) ),
inference(variable_rename,[status(thm)],[f_583_1]) ).
fof(f_583_3,plain,
! [U_1847,U_1846,U_1844,U_1845] :
( c_Orderings_Oord__class_Oless(U_1844,hAPP(hAPP(c_Power_Opower__class_Opower(U_1844),U_1845),U_1847),hAPP(hAPP(c_Power_Opower__class_Opower(U_1844),U_1846),U_1847))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1847)
| ~ c_Orderings_Oord__class_Oless__eq(U_1844,c_Groups_Ozero__class_Ozero(U_1844),U_1845)
| ~ c_Orderings_Oord__class_Oless(U_1844,U_1845,U_1846)
| ~ class_Rings_Olinordered__semidom(U_1844) ),
inference(definitional_conversion,[status(esa)],[f_583_2]) ).
cnf(f_583_4,plain,
( c_Orderings_Oord__class_Oless(U_1844,hAPP(hAPP(c_Power_Opower__class_Opower(U_1844),U_1845),U_1847),hAPP(hAPP(c_Power_Opower__class_Opower(U_1844),U_1846),U_1847))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1847)
| ~ c_Orderings_Oord__class_Oless__eq(U_1844,c_Groups_Ozero__class_Ozero(U_1844),U_1845)
| ~ c_Orderings_Oord__class_Oless(U_1844,U_1845,U_1846)
| ~ class_Rings_Olinordered__semidom(U_1844) ),
inference(clausify,[status(thm)],[f_583_3]) ).
fof(f_584_1,plain,
! [V_x,V_n,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_x,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))
| ( V_x != c_Groups_Oone__class_Oone(T_a)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) )
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__power]) ).
fof(f_584_2,plain,
! [U_1850,U_1849,U_1848] :
( c_Rings_Odvd__class_Odvd(U_1848,U_1850,hAPP(hAPP(c_Power_Opower__class_Opower(U_1848),U_1850),U_1849))
| ( U_1850 != c_Groups_Oone__class_Oone(U_1848)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1849) )
| ~ class_Rings_Ocomm__semiring__1(U_1848) ),
inference(variable_rename,[status(thm)],[f_584_1]) ).
fof(f_584_3,plain,
( ! [U_1849,U_1848,U_1850] :
( U_1850 != c_Groups_Oone__class_Oone(U_1848)
| ~ sP207(U_1849,U_1848,U_1850) )
& ! [U_1849,U_1848,U_1850] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1849)
| ~ sP207(U_1849,U_1848,U_1850) )
& ! [U_1849,U_1848,U_1850] :
( c_Rings_Odvd__class_Odvd(U_1848,U_1850,hAPP(hAPP(c_Power_Opower__class_Opower(U_1848),U_1850),U_1849))
| sP207(U_1849,U_1848,U_1850)
| ~ class_Rings_Ocomm__semiring__1(U_1848) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_584_2]) ).
cnf(f_584_4,plain,
( c_Rings_Odvd__class_Odvd(U_1848,U_1850,hAPP(hAPP(c_Power_Opower__class_Opower(U_1848),U_1850),U_1849))
| sP207(U_1849,U_1848,U_1850)
| ~ class_Rings_Ocomm__semiring__1(U_1848) ),
inference(clausify,[status(thm)],[f_584_3]) ).
cnf(f_584_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1849)
| ~ sP207(U_1849,U_1848,U_1850) ),
inference(clausify,[status(thm)],[f_584_3]) ).
cnf(f_584_6,plain,
( U_1850 != c_Groups_Oone__class_Oone(U_1848)
| ~ sP207(U_1849,U_1848,U_1850) ),
inference(clausify,[status(thm)],[f_584_3]) ).
fof(f_585_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_585_2,plain,
! [U_1853,U_1852,U_1851] :
( c_Orderings_Oord__class_Oless(U_1851,c_Groups_Oone__class_Oone(U_1851),hAPP(hAPP(c_Power_Opower__class_Opower(U_1851),U_1852),U_1853))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1853)
| ~ c_Orderings_Oord__class_Oless(U_1851,c_Groups_Oone__class_Oone(U_1851),U_1852)
| ~ class_Rings_Olinordered__semidom(U_1851) ),
inference(variable_rename,[status(thm)],[f_585_1]) ).
fof(f_585_3,plain,
! [U_1851,U_1852,U_1853] :
( c_Orderings_Oord__class_Oless(U_1851,c_Groups_Oone__class_Oone(U_1851),hAPP(hAPP(c_Power_Opower__class_Opower(U_1851),U_1852),U_1853))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1853)
| ~ c_Orderings_Oord__class_Oless(U_1851,c_Groups_Oone__class_Oone(U_1851),U_1852)
| ~ class_Rings_Olinordered__semidom(U_1851) ),
inference(definitional_conversion,[status(esa)],[f_585_2]) ).
cnf(f_585_4,plain,
( c_Orderings_Oord__class_Oless(U_1851,c_Groups_Oone__class_Oone(U_1851),hAPP(hAPP(c_Power_Opower__class_Opower(U_1851),U_1852),U_1853))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1853)
| ~ c_Orderings_Oord__class_Oless(U_1851,c_Groups_Oone__class_Oone(U_1851),U_1852)
| ~ class_Rings_Olinordered__semidom(U_1851) ),
inference(clausify,[status(thm)],[f_585_3]) ).
fof(f_586_1,plain,
! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_x),
inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__refl]) ).
fof(f_586_2,plain,
! [U_1854] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1854,U_1854),
inference(variable_rename,[status(thm)],[f_586_1]) ).
fof(f_586_3,plain,
! [U_1854] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1854,U_1854),
inference(definitional_conversion,[status(esa)],[f_586_2]) ).
cnf(f_586_4,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1854,U_1854),
inference(clausify,[status(thm)],[f_586_3]) ).
fof(f_587_1,plain,
! [V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym]) ).
fof(f_587_2,plain,
! [U_1856,U_1855] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1855,U_1856)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1856,U_1855)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1856,U_1855)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1855,U_1856) ),
inference(variable_rename,[status(thm)],[f_587_1]) ).
fof(f_587_3,plain,
! [U_1855,U_1856] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1855,U_1856)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1856,U_1855)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1856,U_1855)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1855,U_1856) ),
inference(definitional_conversion,[status(esa)],[f_587_2]) ).
cnf(f_587_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1855,U_1856)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1856,U_1855)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1856,U_1855)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1855,U_1856) ),
inference(clausify,[status(thm)],[f_587_3]) ).
fof(f_588_1,plain,
! [V_z,V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) )
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__trans]) ).
fof(f_588_2,plain,
! [U_1859,U_1858,U_1857] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1859,U_1857)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1857,U_1859) )
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1859,U_1858)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1858,U_1859)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1858,U_1857)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1857,U_1858) ),
inference(variable_rename,[status(thm)],[f_588_1]) ).
fof(f_588_3,plain,
( ! [U_1857,U_1859] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1859,U_1857)
| ~ sP208(U_1857,U_1859) )
& ! [U_1857,U_1859] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1857,U_1859)
| ~ sP208(U_1857,U_1859) )
& ! [U_1857,U_1858,U_1859] :
( sP208(U_1857,U_1859)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1859,U_1858)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1858,U_1859)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1858,U_1857)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1857,U_1858) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208])],[f_588_2]) ).
cnf(f_588_4,plain,
( sP208(U_1857,U_1859)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1859,U_1858)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1858,U_1859)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1858,U_1857)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1857,U_1858) ),
inference(clausify,[status(thm)],[f_588_3]) ).
cnf(f_588_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1857,U_1859)
| ~ sP208(U_1857,U_1859) ),
inference(clausify,[status(thm)],[f_588_3]) ).
cnf(f_588_6,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1859,U_1857)
| ~ sP208(U_1857,U_1859) ),
inference(clausify,[status(thm)],[f_588_3]) ).
fof(f_589_1,plain,
! [V_b,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__asym_H]) ).
fof(f_589_2,plain,
! [U_1861,U_1860] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1860,U_1861)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1861,U_1860)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1861,U_1860)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1860,U_1861) ),
inference(variable_rename,[status(thm)],[f_589_1]) ).
fof(f_589_3,plain,
! [U_1861,U_1860] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1860,U_1861)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1861,U_1860)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1861,U_1860)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1860,U_1861) ),
inference(definitional_conversion,[status(esa)],[f_589_2]) ).
cnf(f_589_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1860,U_1861)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1861,U_1860)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1861,U_1860)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1860,U_1861) ),
inference(clausify,[status(thm)],[f_589_3]) ).
fof(f_590_1,plain,
! [V_z,V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le__trans]) ).
fof(f_590_2,plain,
! [U_1864,U_1863,U_1862] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1864,U_1862)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1862,U_1864) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1863,U_1864)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1863,U_1862)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1862,U_1863) ),
inference(variable_rename,[status(thm)],[f_590_1]) ).
fof(f_590_3,plain,
( ! [U_1862,U_1864] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1864,U_1862)
| ~ sP209(U_1862,U_1864) )
& ! [U_1862,U_1864] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1862,U_1864)
| ~ sP209(U_1862,U_1864) )
& ! [U_1862,U_1863,U_1864] :
( sP209(U_1862,U_1864)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1863,U_1864)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1863,U_1862)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1862,U_1863) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP209])],[f_590_2]) ).
cnf(f_590_4,plain,
( sP209(U_1862,U_1864)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1863,U_1864)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1863,U_1862)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1862,U_1863) ),
inference(clausify,[status(thm)],[f_590_3]) ).
cnf(f_590_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1862,U_1864)
| ~ sP209(U_1862,U_1864) ),
inference(clausify,[status(thm)],[f_590_3]) ).
cnf(f_590_6,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1864,U_1862)
| ~ sP209(U_1862,U_1864) ),
inference(clausify,[status(thm)],[f_590_3]) ).
fof(f_591_1,plain,
! [V_c,V_b,V_a] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) )
| V_b != V_c
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__less__eq__trans]) ).
fof(f_591_2,plain,
! [U_1867,U_1866,U_1865] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1867,U_1865)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1865,U_1867) )
| U_1866 != U_1867
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1866,U_1865)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1865,U_1866) ),
inference(variable_rename,[status(thm)],[f_591_1]) ).
fof(f_591_3,plain,
( ! [U_1865,U_1867] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1867,U_1865)
| ~ sP210(U_1865,U_1867) )
& ! [U_1865,U_1867] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1865,U_1867)
| ~ sP210(U_1865,U_1867) )
& ! [U_1866,U_1865,U_1867] :
( sP210(U_1865,U_1867)
| U_1866 != U_1867
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1866,U_1865)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1865,U_1866) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_591_2]) ).
cnf(f_591_4,plain,
( sP210(U_1865,U_1867)
| U_1866 != U_1867
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1866,U_1865)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1865,U_1866) ),
inference(clausify,[status(thm)],[f_591_3]) ).
cnf(f_591_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1865,U_1867)
| ~ sP210(U_1865,U_1867) ),
inference(clausify,[status(thm)],[f_591_3]) ).
cnf(f_591_6,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1867,U_1865)
| ~ sP210(U_1865,U_1867) ),
inference(clausify,[status(thm)],[f_591_3]) ).
fof(f_592_1,plain,
! [V_y,V_x] :
( V_y != V_x
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq2]) ).
fof(f_592_2,plain,
! [U_1869,U_1868] :
( U_1869 != U_1868
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1869,U_1868)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1868,U_1869) ),
inference(variable_rename,[status(thm)],[f_592_1]) ).
fof(f_592_3,plain,
! [U_1868,U_1869] :
( U_1869 != U_1868
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1869,U_1868)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1868,U_1869) ),
inference(definitional_conversion,[status(esa)],[f_592_2]) ).
cnf(f_592_4,plain,
( U_1869 != U_1868
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1869,U_1868)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1868,U_1869) ),
inference(clausify,[status(thm)],[f_592_3]) ).
fof(f_593_1,plain,
! [V_y,V_x] :
( V_x != V_y
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__eq]) ).
fof(f_593_2,plain,
! [U_1871,U_1870] :
( U_1870 != U_1871
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1871,U_1870)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1870,U_1871) ),
inference(variable_rename,[status(thm)],[f_593_1]) ).
fof(f_593_3,plain,
! [U_1870,U_1871] :
( U_1870 != U_1871
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1871,U_1870)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1870,U_1871) ),
inference(definitional_conversion,[status(esa)],[f_593_2]) ).
cnf(f_593_4,plain,
( U_1870 != U_1871
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1871,U_1870)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1870,U_1871) ),
inference(clausify,[status(thm)],[f_593_3]) ).
fof(f_594_1,plain,
! [V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__not__less]) ).
fof(f_594_2,plain,
! [U_1873,U_1872] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1872,U_1873)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1873,U_1872)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1873,U_1872)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1872,U_1873) ),
inference(variable_rename,[status(thm)],[f_594_1]) ).
fof(f_594_3,plain,
! [U_1873,U_1872] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1872,U_1873)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1873,U_1872)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1873,U_1872)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1872,U_1873) ),
inference(definitional_conversion,[status(esa)],[f_594_2]) ).
cnf(f_594_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1872,U_1873)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1873,U_1872)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1873,U_1872)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1872,U_1873) ),
inference(clausify,[status(thm)],[f_594_3]) ).
fof(f_595_1,plain,
! [V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__le]) ).
fof(f_595_2,plain,
! [U_1875,U_1874] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1874,U_1875)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1875,U_1874)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1874,U_1875) ),
inference(variable_rename,[status(thm)],[f_595_1]) ).
fof(f_595_3,plain,
! [U_1874,U_1875] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1874,U_1875)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1875,U_1874)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1874,U_1875) ),
inference(definitional_conversion,[status(esa)],[f_595_2]) ).
cnf(f_595_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1874,U_1875)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1875,U_1874)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1874,U_1875) ),
inference(clausify,[status(thm)],[f_595_3]) ).
fof(f_596_1,plain,
! [V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__not__sym]) ).
fof(f_596_2,plain,
! [U_1877,U_1876] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1876,U_1877)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1877,U_1876)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1877,U_1876)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1876,U_1877) ),
inference(variable_rename,[status(thm)],[f_596_1]) ).
fof(f_596_3,plain,
! [U_1877,U_1876] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1876,U_1877)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1877,U_1876)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1877,U_1876)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1876,U_1877) ),
inference(definitional_conversion,[status(esa)],[f_596_2]) ).
cnf(f_596_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1876,U_1877)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1877,U_1876)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1877,U_1876)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1876,U_1877) ),
inference(clausify,[status(thm)],[f_596_3]) ).
fof(f_597_1,plain,
! [V_y,V_x] :
( V_x != V_y
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__imp__neq]) ).
fof(f_597_2,plain,
! [U_1879,U_1878] :
( U_1878 != U_1879
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1879,U_1878)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1878,U_1879) ),
inference(variable_rename,[status(thm)],[f_597_1]) ).
fof(f_597_3,plain,
! [U_1879,U_1878] :
( U_1878 != U_1879
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1879,U_1878)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1878,U_1879) ),
inference(definitional_conversion,[status(esa)],[f_597_2]) ).
cnf(f_597_4,plain,
( U_1878 != U_1879
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1879,U_1878)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1878,U_1879) ),
inference(clausify,[status(thm)],[f_597_3]) ).
fof(f_598_1,plain,
! [V_z,V_y,V_x] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z) )
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_z,V_y)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less__trans]) ).
fof(f_598_2,plain,
! [U_1882,U_1881,U_1880] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1882,U_1880)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1880,U_1882) )
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1882,U_1881)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1881,U_1882)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1880,U_1881) ),
inference(variable_rename,[status(thm)],[f_598_1]) ).
fof(f_598_3,plain,
( ! [U_1882,U_1880] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1882,U_1880)
| ~ sP211(U_1882,U_1880) )
& ! [U_1882,U_1880] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1880,U_1882)
| ~ sP211(U_1882,U_1880) )
& ! [U_1882,U_1881,U_1880] :
( sP211(U_1882,U_1880)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1882,U_1881)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1881,U_1882)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1880,U_1881) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211])],[f_598_2]) ).
cnf(f_598_4,plain,
( sP211(U_1882,U_1880)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1882,U_1881)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1881,U_1882)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1880,U_1881) ),
inference(clausify,[status(thm)],[f_598_3]) ).
cnf(f_598_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1880,U_1882)
| ~ sP211(U_1882,U_1880) ),
inference(clausify,[status(thm)],[f_598_3]) ).
cnf(f_598_6,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1882,U_1880)
| ~ sP211(U_1882,U_1880) ),
inference(clausify,[status(thm)],[f_598_3]) ).
fof(f_599_1,plain,
! [V_c,V_b,V_a] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c) )
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_c,V_b)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
| V_a != V_b ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__less__trans]) ).
fof(f_599_2,plain,
! [U_1885,U_1884,U_1883] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1885,U_1883)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1883,U_1885) )
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1885,U_1884)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1884,U_1885)
| U_1883 != U_1884 ),
inference(variable_rename,[status(thm)],[f_599_1]) ).
fof(f_599_3,plain,
( ! [U_1883,U_1885] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1885,U_1883)
| ~ sP212(U_1883,U_1885) )
& ! [U_1883,U_1885] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1883,U_1885)
| ~ sP212(U_1883,U_1885) )
& ! [U_1883,U_1884,U_1885] :
( sP212(U_1883,U_1885)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1885,U_1884)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1884,U_1885)
| U_1883 != U_1884 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP212])],[f_599_2]) ).
cnf(f_599_4,plain,
( sP212(U_1883,U_1885)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1885,U_1884)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1884,U_1885)
| U_1883 != U_1884 ),
inference(clausify,[status(thm)],[f_599_3]) ).
cnf(f_599_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1883,U_1885)
| ~ sP212(U_1883,U_1885) ),
inference(clausify,[status(thm)],[f_599_3]) ).
cnf(f_599_6,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1885,U_1883)
| ~ sP212(U_1883,U_1885) ),
inference(clausify,[status(thm)],[f_599_3]) ).
fof(f_600_1,plain,
! [V_z,V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_z)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_z)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oorder__trans]) ).
fof(f_600_2,plain,
! [U_1888,U_1887,U_1886] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1886,U_1888)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1887,U_1888)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1886,U_1887) ),
inference(variable_rename,[status(thm)],[f_600_1]) ).
fof(f_600_3,plain,
! [U_1888,U_1886,U_1887] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1886,U_1888)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1887,U_1888)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1886,U_1887) ),
inference(definitional_conversion,[status(esa)],[f_600_2]) ).
cnf(f_600_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1886,U_1888)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1887,U_1888)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1886,U_1887) ),
inference(clausify,[status(thm)],[f_600_3]) ).
fof(f_601_1,plain,
! [V_y,V_x] :
( V_x = V_y
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym]) ).
fof(f_601_2,plain,
! [U_1890,U_1889] :
( U_1889 = U_1890
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1890,U_1889)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1889,U_1890) ),
inference(variable_rename,[status(thm)],[f_601_1]) ).
fof(f_601_3,plain,
! [U_1890,U_1889] :
( U_1889 = U_1890
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1890,U_1889)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1889,U_1890) ),
inference(definitional_conversion,[status(esa)],[f_601_2]) ).
cnf(f_601_4,plain,
( U_1889 = U_1890
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1890,U_1889)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1889,U_1890) ),
inference(clausify,[status(thm)],[f_601_3]) ).
fof(f_602_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_n,V_m)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_dvd__antisym]) ).
fof(f_602_2,plain,
! [U_1892,U_1891] :
( U_1891 = U_1892
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1892,U_1891)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1891,U_1892) ),
inference(variable_rename,[status(thm)],[f_602_1]) ).
fof(f_602_3,plain,
! [U_1892,U_1891] :
( U_1891 = U_1892
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1892,U_1891)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1891,U_1892) ),
inference(definitional_conversion,[status(esa)],[f_602_2]) ).
cnf(f_602_4,plain,
( U_1891 = U_1892
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1892,U_1891)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1891,U_1892) ),
inference(clausify,[status(thm)],[f_602_3]) ).
fof(f_603_1,plain,
! [V_c,V_b,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
| V_b != V_c
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__le__eq__trans]) ).
fof(f_603_2,plain,
! [U_1895,U_1894,U_1893] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1893,U_1895)
| U_1894 != U_1895
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1893,U_1894) ),
inference(variable_rename,[status(thm)],[f_603_1]) ).
fof(f_603_3,plain,
! [U_1894,U_1895,U_1893] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1893,U_1895)
| U_1894 != U_1895
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1893,U_1894) ),
inference(definitional_conversion,[status(esa)],[f_603_2]) ).
cnf(f_603_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1893,U_1895)
| U_1894 != U_1895
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1893,U_1894) ),
inference(clausify,[status(thm)],[f_603_3]) ).
fof(f_604_1,plain,
! [V_c,V_b,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_c)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_c)
| V_a != V_b ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oord__eq__le__trans]) ).
fof(f_604_2,plain,
! [U_1898,U_1897,U_1896] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1896,U_1898)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1897,U_1898)
| U_1896 != U_1897 ),
inference(variable_rename,[status(thm)],[f_604_1]) ).
fof(f_604_3,plain,
! [U_1898,U_1896,U_1897] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1896,U_1898)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1897,U_1898)
| U_1896 != U_1897 ),
inference(definitional_conversion,[status(esa)],[f_604_2]) ).
cnf(f_604_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1896,U_1898)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1897,U_1898)
| U_1896 != U_1897 ),
inference(clausify,[status(thm)],[f_604_3]) ).
fof(f_605_1,plain,
! [V_b,V_a] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) )
| V_a = V_b
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__neq__trans]) ).
fof(f_605_2,plain,
! [U_1900,U_1899] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1900,U_1899)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1899,U_1900) )
| U_1899 = U_1900
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1899,U_1900) ),
inference(variable_rename,[status(thm)],[f_605_1]) ).
fof(f_605_3,plain,
( ! [U_1899,U_1900] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1900,U_1899)
| ~ sP213(U_1899,U_1900) )
& ! [U_1899,U_1900] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1899,U_1900)
| ~ sP213(U_1899,U_1900) )
& ! [U_1899,U_1900] :
( sP213(U_1899,U_1900)
| U_1899 = U_1900
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1899,U_1900) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213])],[f_605_2]) ).
cnf(f_605_4,plain,
( sP213(U_1899,U_1900)
| U_1899 = U_1900
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1899,U_1900) ),
inference(clausify,[status(thm)],[f_605_3]) ).
cnf(f_605_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1899,U_1900)
| ~ sP213(U_1899,U_1900) ),
inference(clausify,[status(thm)],[f_605_3]) ).
cnf(f_605_6,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1900,U_1899)
| ~ sP213(U_1899,U_1900) ),
inference(clausify,[status(thm)],[f_605_3]) ).
fof(f_606_1,plain,
! [V_y,V_x] :
( V_x = V_y
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y,V_x)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__imp__less__or__eq]) ).
fof(f_606_2,plain,
! [U_1902,U_1901] :
( U_1901 = U_1902
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1902,U_1901)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1901,U_1902) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1901,U_1902) ),
inference(variable_rename,[status(thm)],[f_606_1]) ).
fof(f_606_3,plain,
( ! [U_1901,U_1902] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1902,U_1901)
| ~ sP214(U_1901,U_1902) )
& ! [U_1901,U_1902] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1901,U_1902)
| ~ sP214(U_1901,U_1902) )
& ! [U_1901,U_1902] :
( U_1901 = U_1902
| sP214(U_1901,U_1902)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1901,U_1902) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP214])],[f_606_2]) ).
cnf(f_606_4,plain,
( U_1901 = U_1902
| sP214(U_1901,U_1902)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1901,U_1902) ),
inference(clausify,[status(thm)],[f_606_3]) ).
cnf(f_606_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1901,U_1902)
| ~ sP214(U_1901,U_1902) ),
inference(clausify,[status(thm)],[f_606_3]) ).
cnf(f_606_6,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1902,U_1901)
| ~ sP214(U_1901,U_1902) ),
inference(clausify,[status(thm)],[f_606_3]) ).
fof(f_607_1,plain,
! [V_x_2,V_y_2] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
| V_x_2 != V_y_2 )
& ( V_x_2 = V_y_2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oantisym__conv]) ).
fof(f_607_2,plain,
! [U_1904,U_1903] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1904,U_1903)
| U_1904 != U_1903 )
& ( U_1904 = U_1903
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1904,U_1903) ) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1903,U_1904) ),
inference(variable_rename,[status(thm)],[f_607_1]) ).
fof(f_607_3,plain,
( ! [U_1903,U_1904] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1904,U_1903)
| U_1904 != U_1903
| ~ sP215(U_1903,U_1904) )
& ! [U_1903,U_1904] :
( U_1904 = U_1903
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1904,U_1903)
| ~ sP215(U_1903,U_1904) )
& ! [U_1903,U_1904] :
( sP215(U_1903,U_1904)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1903,U_1904) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215])],[f_607_2]) ).
cnf(f_607_4,plain,
( sP215(U_1903,U_1904)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_607_3]) ).
cnf(f_607_5,plain,
( U_1904 = U_1903
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1904,U_1903)
| ~ sP215(U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_607_3]) ).
cnf(f_607_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1904,U_1903)
| U_1904 != U_1903
| ~ sP215(U_1903,U_1904) ),
inference(clausify,[status(thm)],[f_607_3]) ).
fof(f_608_1,plain,
! [V_y,V_x] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,V_y)
| V_x != V_y ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__refl]) ).
fof(f_608_2,plain,
! [U_1906,U_1905] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1905,U_1906)
| U_1905 != U_1906 ),
inference(variable_rename,[status(thm)],[f_608_1]) ).
fof(f_608_3,plain,
! [U_1905,U_1906] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1905,U_1906)
| U_1905 != U_1906 ),
inference(definitional_conversion,[status(esa)],[f_608_2]) ).
cnf(f_608_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1905,U_1906)
| U_1905 != U_1906 ),
inference(clausify,[status(thm)],[f_608_3]) ).
fof(f_609_1,plain,
! [V_b,V_a] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_b,V_a)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
| V_a = V_b ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oneq__le__trans]) ).
fof(f_609_2,plain,
! [U_1908,U_1907] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1908,U_1907)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1907,U_1908) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1907,U_1908)
| U_1907 = U_1908 ),
inference(variable_rename,[status(thm)],[f_609_1]) ).
fof(f_609_3,plain,
( ! [U_1907,U_1908] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1908,U_1907)
| ~ sP216(U_1907,U_1908) )
& ! [U_1907,U_1908] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1907,U_1908)
| ~ sP216(U_1907,U_1908) )
& ! [U_1907,U_1908] :
( sP216(U_1907,U_1908)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1907,U_1908)
| U_1907 = U_1908 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP216])],[f_609_2]) ).
cnf(f_609_4,plain,
( sP216(U_1907,U_1908)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1907,U_1908)
| U_1907 = U_1908 ),
inference(clausify,[status(thm)],[f_609_3]) ).
cnf(f_609_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1907,U_1908)
| ~ sP216(U_1907,U_1908) ),
inference(clausify,[status(thm)],[f_609_3]) ).
cnf(f_609_6,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1908,U_1907)
| ~ sP216(U_1907,U_1908) ),
inference(clausify,[status(thm)],[f_609_3]) ).
fof(f_610_1,plain,
! [V_y_2,V_x_2] :
( ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
| V_x_2 = V_y_2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
& ( ( V_x_2 != V_y_2
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oless__le]) ).
fof(f_610_2,plain,
! [U_1910,U_1909] :
( ( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1910,U_1909)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1909,U_1910) )
| U_1909 = U_1910
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1909,U_1910) )
& ( ( U_1909 != U_1910
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1909,U_1910) )
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1910,U_1909)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1909,U_1910) ) ),
inference(variable_rename,[status(thm)],[f_610_1]) ).
fof(f_610_3,plain,
( ! [U_1914,U_1912] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1914,U_1912)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1912,U_1914) )
| U_1912 = U_1914
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1912,U_1914) )
& ! [U_1913,U_1911] :
( ( U_1911 != U_1913
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1911,U_1913) )
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1913,U_1911)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1911,U_1913) ) ),
inference(miniscope,[status(thm)],[f_610_2]) ).
fof(f_610_4,plain,
( ! [U_1914,U_1912] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1914,U_1912)
| ~ sP218(U_1914,U_1912) )
& ! [U_1914,U_1912] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1912,U_1914)
| ~ sP218(U_1914,U_1912) )
& ! [U_1911,U_1913] :
( U_1911 != U_1913
| ~ sP217(U_1911,U_1913) )
& ! [U_1911,U_1913] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1911,U_1913)
| ~ sP217(U_1911,U_1913) )
& ! [U_1914,U_1912] :
( sP218(U_1914,U_1912)
| U_1912 = U_1914
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1912,U_1914) )
& ! [U_1911,U_1913] :
( sP217(U_1911,U_1913)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1913,U_1911)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1911,U_1913) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217,sP218])],[f_610_3]) ).
cnf(f_610_5,plain,
( sP217(U_1911,U_1913)
| c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1913,U_1911)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1911,U_1913) ),
inference(clausify,[status(thm)],[f_610_4]) ).
cnf(f_610_6,plain,
( sP218(U_1914,U_1912)
| U_1912 = U_1914
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1912,U_1914) ),
inference(clausify,[status(thm)],[f_610_4]) ).
cnf(f_610_7,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1911,U_1913)
| ~ sP217(U_1911,U_1913) ),
inference(clausify,[status(thm)],[f_610_4]) ).
cnf(f_610_8,plain,
( U_1911 != U_1913
| ~ sP217(U_1911,U_1913) ),
inference(clausify,[status(thm)],[f_610_4]) ).
cnf(f_610_9,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1912,U_1914)
| ~ sP218(U_1914,U_1912) ),
inference(clausify,[status(thm)],[f_610_4]) ).
cnf(f_610_10,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1914,U_1912)
| ~ sP218(U_1914,U_1912) ),
inference(clausify,[status(thm)],[f_610_4]) ).
fof(f_611_1,plain,
! [V_y_2,V_x_2] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2)
| ( V_x_2 != V_y_2
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ) )
& ( V_x_2 = V_y_2
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Ole__less]) ).
fof(f_611_2,plain,
! [U_1916,U_1915] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1915,U_1916)
| ( U_1915 != U_1916
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1916,U_1915)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1915,U_1916) ) ) )
& ( U_1915 = U_1916
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1916,U_1915)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1915,U_1916) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1915,U_1916) ) ),
inference(variable_rename,[status(thm)],[f_611_1]) ).
fof(f_611_3,plain,
( ! [U_1920,U_1918] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1918,U_1920)
| ( U_1918 != U_1920
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1920,U_1918)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1918,U_1920) ) ) )
& ! [U_1919,U_1917] :
( U_1917 = U_1919
| ( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1919,U_1917)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1917,U_1919) )
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1917,U_1919) ) ),
inference(miniscope,[status(thm)],[f_611_2]) ).
fof(f_611_4,plain,
( ! [U_1918,U_1920] :
( U_1918 != U_1920
| ~ sP220(U_1918,U_1920) )
& ! [U_1918,U_1920] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1920,U_1918)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1918,U_1920)
| ~ sP220(U_1918,U_1920) )
& ! [U_1919,U_1917] :
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1919,U_1917)
| ~ sP219(U_1919,U_1917) )
& ! [U_1919,U_1917] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1917,U_1919)
| ~ sP219(U_1919,U_1917) )
& ! [U_1918,U_1920] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1918,U_1920)
| sP220(U_1918,U_1920) )
& ! [U_1919,U_1917] :
( U_1917 = U_1919
| sP219(U_1919,U_1917)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1917,U_1919) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219,sP220])],[f_611_3]) ).
cnf(f_611_5,plain,
( U_1917 = U_1919
| sP219(U_1919,U_1917)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1917,U_1919) ),
inference(clausify,[status(thm)],[f_611_4]) ).
cnf(f_611_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1918,U_1920)
| sP220(U_1918,U_1920) ),
inference(clausify,[status(thm)],[f_611_4]) ).
cnf(f_611_7,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1917,U_1919)
| ~ sP219(U_1919,U_1917) ),
inference(clausify,[status(thm)],[f_611_4]) ).
cnf(f_611_8,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1919,U_1917)
| ~ sP219(U_1919,U_1917) ),
inference(clausify,[status(thm)],[f_611_4]) ).
cnf(f_611_9,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1920,U_1918)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1918,U_1920)
| ~ sP220(U_1918,U_1920) ),
inference(clausify,[status(thm)],[f_611_4]) ).
cnf(f_611_10,plain,
( U_1918 != U_1920
| ~ sP220(U_1918,U_1920) ),
inference(clausify,[status(thm)],[f_611_4]) ).
fof(f_612_1,plain,
! [V_y_2,V_x_2] :
( ( V_x_2 = V_y_2
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
& ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_y_2,V_x_2)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x_2,V_y_2) )
| V_x_2 != V_y_2 ) ),
inference(fof_nnf,[status(thm)],[fact_dvd_Oeq__iff]) ).
fof(f_612_2,plain,
! [U_1922,U_1921] :
( ( U_1921 = U_1922
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1922,U_1921)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1921,U_1922) )
& ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1922,U_1921)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1921,U_1922) )
| U_1921 != U_1922 ) ),
inference(variable_rename,[status(thm)],[f_612_1]) ).
fof(f_612_3,plain,
( ! [U_1926,U_1924] :
( U_1924 = U_1926
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1926,U_1924)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1924,U_1926) )
& ! [U_1925,U_1923] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1925,U_1923)
& c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1923,U_1925) )
| U_1923 != U_1925 ) ),
inference(miniscope,[status(thm)],[f_612_2]) ).
fof(f_612_4,plain,
( ! [U_1923,U_1925] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1925,U_1923)
| ~ sP221(U_1923,U_1925) )
& ! [U_1923,U_1925] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1923,U_1925)
| ~ sP221(U_1923,U_1925) )
& ! [U_1924,U_1926] :
( U_1924 = U_1926
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1926,U_1924)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1924,U_1926) )
& ! [U_1923,U_1925] :
( sP221(U_1923,U_1925)
| U_1923 != U_1925 ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_612_3]) ).
cnf(f_612_5,plain,
( sP221(U_1923,U_1925)
| U_1923 != U_1925 ),
inference(clausify,[status(thm)],[f_612_4]) ).
cnf(f_612_6,plain,
( U_1924 = U_1926
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1926,U_1924)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1924,U_1926) ),
inference(clausify,[status(thm)],[f_612_4]) ).
cnf(f_612_7,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1923,U_1925)
| ~ sP221(U_1923,U_1925) ),
inference(clausify,[status(thm)],[f_612_4]) ).
cnf(f_612_8,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_1925,U_1923)
| ~ sP221(U_1923,U_1925) ),
inference(clausify,[status(thm)],[f_612_4]) ).
fof(f_613_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_613_2,plain,
! [U_1929,U_1928,U_1927] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1927),U_1928)),U_1929) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1928),U_1929)),
inference(variable_rename,[status(thm)],[f_613_1]) ).
fof(f_613_3,plain,
! [U_1928,U_1927,U_1929] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1927),U_1928)),U_1929) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1928),U_1929)),
inference(definitional_conversion,[status(esa)],[f_613_2]) ).
cnf(f_613_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1927),U_1928)),U_1929) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1928),U_1929)),
inference(clausify,[status(thm)],[f_613_3]) ).
fof(f_614_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_614_2,plain,
! [U_1932,U_1931,U_1930] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1930),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1931,U_1932)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1930),U_1931)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1930),U_1932)),
inference(variable_rename,[status(thm)],[f_614_1]) ).
fof(f_614_3,plain,
! [U_1930,U_1931,U_1932] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1930),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1931,U_1932)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1930),U_1931)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1930),U_1932)),
inference(definitional_conversion,[status(esa)],[f_614_2]) ).
cnf(f_614_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1930),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_1931,U_1932)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1930),U_1931)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_1930),U_1932)),
inference(clausify,[status(thm)],[f_614_3]) ).
fof(f_615_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(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_2)),V_n_2))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_x_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2)),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__zpower__abs__iff]) ).
fof(f_615_2,plain,
! [U_1934,U_1933] :
( ( c_Orderings_Oord__class_Oless(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_1933)),U_1934))
| ( U_1934 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1933 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ( U_1934 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1933 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(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_1933)),U_1934)) ) ),
inference(variable_rename,[status(thm)],[f_615_1]) ).
fof(f_615_3,plain,
( ! [U_1938,U_1936] :
( c_Orderings_Oord__class_Oless(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_1936)),U_1938))
| ( U_1938 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1936 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
& ! [U_1937,U_1935] :
( U_1937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1935 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(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_1935)),U_1937)) ) ),
inference(miniscope,[status(thm)],[f_615_2]) ).
fof(f_615_4,plain,
( ! [U_1938,U_1936] :
( U_1938 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP222(U_1938,U_1936) )
& ! [U_1938,U_1936] :
( U_1936 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP222(U_1938,U_1936) )
& ! [U_1938,U_1936] :
( c_Orderings_Oord__class_Oless(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_1936)),U_1938))
| sP222(U_1938,U_1936) )
& ! [U_1937,U_1935] :
( U_1937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1935 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(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_1935)),U_1937)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222])],[f_615_3]) ).
cnf(f_615_5,plain,
( U_1937 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1935 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(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_1935)),U_1937)) ),
inference(clausify,[status(thm)],[f_615_4]) ).
cnf(f_615_6,plain,
( c_Orderings_Oord__class_Oless(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_1936)),U_1938))
| sP222(U_1938,U_1936) ),
inference(clausify,[status(thm)],[f_615_4]) ).
cnf(f_615_7,plain,
( U_1936 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ sP222(U_1938,U_1936) ),
inference(clausify,[status(thm)],[f_615_4]) ).
cnf(f_615_8,plain,
( U_1938 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP222(U_1938,U_1936) ),
inference(clausify,[status(thm)],[f_615_4]) ).
fof(f_616_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
| ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2) ) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__zero__less__power__iff]) ).
fof(f_616_2,plain,
! [U_1940,U_1939] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1939),U_1940))
| ( U_1940 != 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_1939) ) )
& ( U_1940 = 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_1939)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1939),U_1940)) ) ),
inference(variable_rename,[status(thm)],[f_616_1]) ).
fof(f_616_3,plain,
( ! [U_1944,U_1942] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1942),U_1944))
| ( U_1944 != 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_1942) ) )
& ! [U_1943,U_1941] :
( U_1943 = 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_1941)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1941),U_1943)) ) ),
inference(miniscope,[status(thm)],[f_616_2]) ).
fof(f_616_4,plain,
( ! [U_1944,U_1942] :
( U_1944 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP223(U_1944,U_1942) )
& ! [U_1944,U_1942] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1942)
| ~ sP223(U_1944,U_1942) )
& ! [U_1944,U_1942] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1942),U_1944))
| sP223(U_1944,U_1942) )
& ! [U_1943,U_1941] :
( U_1943 = 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_1941)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1941),U_1943)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP223])],[f_616_3]) ).
cnf(f_616_5,plain,
( U_1943 = 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_1941)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1941),U_1943)) ),
inference(clausify,[status(thm)],[f_616_4]) ).
cnf(f_616_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1942),U_1944))
| sP223(U_1944,U_1942) ),
inference(clausify,[status(thm)],[f_616_4]) ).
cnf(f_616_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1942)
| ~ sP223(U_1944,U_1942) ),
inference(clausify,[status(thm)],[f_616_4]) ).
cnf(f_616_8,plain,
( U_1944 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP223(U_1944,U_1942) ),
inference(clausify,[status(thm)],[f_616_4]) ).
fof(f_617_1,plain,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i) ),
inference(fof_nnf,[status(thm)],[fact_nat__power__less__imp__less]) ).
fof(f_617_2,plain,
! [U_1947,U_1946,U_1945] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1946,U_1947)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1945),U_1946),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1945),U_1947))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1945) ),
inference(variable_rename,[status(thm)],[f_617_1]) ).
fof(f_617_3,plain,
! [U_1945,U_1946,U_1947] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1946,U_1947)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1945),U_1946),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1945),U_1947))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1945) ),
inference(definitional_conversion,[status(esa)],[f_617_2]) ).
cnf(f_617_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_1946,U_1947)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1945),U_1946),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1945),U_1947))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_1945) ),
inference(clausify,[status(thm)],[f_617_3]) ).
fof(f_618_1,plain,
! [V_n,V_m,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_i)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_power__dvd__imp__le]) ).
fof(f_618_2,plain,
! [U_1950,U_1949,U_1948] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1949,U_1950)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1948)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1948),U_1949),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1948),U_1950)) ),
inference(variable_rename,[status(thm)],[f_618_1]) ).
fof(f_618_3,plain,
! [U_1948,U_1949,U_1950] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1949,U_1950)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1948)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1948),U_1949),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1948),U_1950)) ),
inference(definitional_conversion,[status(esa)],[f_618_2]) ).
cnf(f_618_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_1949,U_1950)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_1948)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1948),U_1949),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_1948),U_1950)) ),
inference(clausify,[status(thm)],[f_618_3]) ).
fof(f_619_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_619_2,plain,
! [U_1953,U_1952,U_1951] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1951),U_1952),U_1953) != c_Groups_Ozero__class_Ozero(U_1951)
| U_1952 = c_Groups_Ozero__class_Ozero(U_1951)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1951) ),
inference(variable_rename,[status(thm)],[f_619_1]) ).
fof(f_619_3,plain,
! [U_1951,U_1952,U_1953] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1951),U_1952),U_1953) != c_Groups_Ozero__class_Ozero(U_1951)
| U_1952 = c_Groups_Ozero__class_Ozero(U_1951)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1951) ),
inference(definitional_conversion,[status(esa)],[f_619_2]) ).
cnf(f_619_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1951),U_1952),U_1953) != c_Groups_Ozero__class_Ozero(U_1951)
| U_1952 = c_Groups_Ozero__class_Ozero(U_1951)
| ~ class_Rings_Oring__1__no__zero__divisors(U_1951) ),
inference(clausify,[status(thm)],[f_619_3]) ).
fof(f_620_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_620_2,plain,
! [U_1956,U_1955,U_1954] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),hAPP(hAPP(c_Power_Opower__class_Opower(U_1954),U_1955),U_1956)),U_1955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),U_1955),hAPP(hAPP(c_Power_Opower__class_Opower(U_1954),U_1955),U_1956))
| ~ class_Groups_Omonoid__mult(U_1954) ),
inference(variable_rename,[status(thm)],[f_620_1]) ).
fof(f_620_3,plain,
! [U_1954,U_1955,U_1956] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),hAPP(hAPP(c_Power_Opower__class_Opower(U_1954),U_1955),U_1956)),U_1955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),U_1955),hAPP(hAPP(c_Power_Opower__class_Opower(U_1954),U_1955),U_1956))
| ~ class_Groups_Omonoid__mult(U_1954) ),
inference(definitional_conversion,[status(esa)],[f_620_2]) ).
cnf(f_620_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),hAPP(hAPP(c_Power_Opower__class_Opower(U_1954),U_1955),U_1956)),U_1955) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1954),U_1955),hAPP(hAPP(c_Power_Opower__class_Opower(U_1954),U_1955),U_1956))
| ~ class_Groups_Omonoid__mult(U_1954) ),
inference(clausify,[status(thm)],[f_620_3]) ).
fof(f_621_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_621_2,plain,
! [U_1960,U_1959,U_1958,U_1957] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1958),U_1959)),U_1960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),hAPP(hAPP(c_Power_Opower__class_Opower(U_1957),U_1958),U_1960)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1957),U_1959),U_1960))
| ~ class_Groups_Ocomm__monoid__mult(U_1957) ),
inference(variable_rename,[status(thm)],[f_621_1]) ).
fof(f_621_3,plain,
! [U_1957,U_1958,U_1959,U_1960] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1958),U_1959)),U_1960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),hAPP(hAPP(c_Power_Opower__class_Opower(U_1957),U_1958),U_1960)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1957),U_1959),U_1960))
| ~ class_Groups_Ocomm__monoid__mult(U_1957) ),
inference(definitional_conversion,[status(esa)],[f_621_2]) ).
cnf(f_621_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),U_1958),U_1959)),U_1960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1957),hAPP(hAPP(c_Power_Opower__class_Opower(U_1957),U_1958),U_1960)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1957),U_1959),U_1960))
| ~ class_Groups_Ocomm__monoid__mult(U_1957) ),
inference(clausify,[status(thm)],[f_621_3]) ).
fof(f_622_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_622_2,plain,
! [U_1962,U_1961] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1961),c_Groups_Oone__class_Oone(U_1961)),U_1962) = c_Groups_Oone__class_Oone(U_1961)
| ~ class_Groups_Omonoid__mult(U_1961) ),
inference(variable_rename,[status(thm)],[f_622_1]) ).
fof(f_622_3,plain,
! [U_1962,U_1961] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1961),c_Groups_Oone__class_Oone(U_1961)),U_1962) = c_Groups_Oone__class_Oone(U_1961)
| ~ class_Groups_Omonoid__mult(U_1961) ),
inference(definitional_conversion,[status(esa)],[f_622_2]) ).
cnf(f_622_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1961),c_Groups_Oone__class_Oone(U_1961)),U_1962) = c_Groups_Oone__class_Oone(U_1961)
| ~ class_Groups_Omonoid__mult(U_1961) ),
inference(clausify,[status(thm)],[f_622_3]) ).
fof(f_623_1,plain,
! [V_n,V_y,V_x,T_a] :
( c_Rings_Odvd__class_Odvd(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_y),V_n))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__power__same]) ).
fof(f_623_2,plain,
! [U_1966,U_1965,U_1964,U_1963] :
( c_Rings_Odvd__class_Odvd(U_1963,hAPP(hAPP(c_Power_Opower__class_Opower(U_1963),U_1964),U_1966),hAPP(hAPP(c_Power_Opower__class_Opower(U_1963),U_1965),U_1966))
| ~ c_Rings_Odvd__class_Odvd(U_1963,U_1964,U_1965)
| ~ class_Rings_Ocomm__semiring__1(U_1963) ),
inference(variable_rename,[status(thm)],[f_623_1]) ).
fof(f_623_3,plain,
! [U_1963,U_1964,U_1965,U_1966] :
( c_Rings_Odvd__class_Odvd(U_1963,hAPP(hAPP(c_Power_Opower__class_Opower(U_1963),U_1964),U_1966),hAPP(hAPP(c_Power_Opower__class_Opower(U_1963),U_1965),U_1966))
| ~ c_Rings_Odvd__class_Odvd(U_1963,U_1964,U_1965)
| ~ class_Rings_Ocomm__semiring__1(U_1963) ),
inference(definitional_conversion,[status(esa)],[f_623_2]) ).
cnf(f_623_4,plain,
( c_Rings_Odvd__class_Odvd(U_1963,hAPP(hAPP(c_Power_Opower__class_Opower(U_1963),U_1964),U_1966),hAPP(hAPP(c_Power_Opower__class_Opower(U_1963),U_1965),U_1966))
| ~ c_Rings_Odvd__class_Odvd(U_1963,U_1964,U_1965)
| ~ class_Rings_Ocomm__semiring__1(U_1963) ),
inference(clausify,[status(thm)],[f_623_3]) ).
fof(f_624_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_624_2,plain,
! [U_1970,U_1969,U_1968,U_1967] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1967),U_1968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1969),U_1970)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1967),hAPP(hAPP(c_Power_Opower__class_Opower(U_1967),U_1968),U_1969)),U_1970)
| ~ class_Groups_Omonoid__mult(U_1967) ),
inference(variable_rename,[status(thm)],[f_624_1]) ).
fof(f_624_3,plain,
! [U_1968,U_1969,U_1970,U_1967] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1967),U_1968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1969),U_1970)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1967),hAPP(hAPP(c_Power_Opower__class_Opower(U_1967),U_1968),U_1969)),U_1970)
| ~ class_Groups_Omonoid__mult(U_1967) ),
inference(definitional_conversion,[status(esa)],[f_624_2]) ).
cnf(f_624_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1967),U_1968),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1969),U_1970)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1967),hAPP(hAPP(c_Power_Opower__class_Opower(U_1967),U_1968),U_1969)),U_1970)
| ~ class_Groups_Omonoid__mult(U_1967) ),
inference(clausify,[status(thm)],[f_624_3]) ).
fof(f_625_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_625_2,plain,
! [U_1973,U_1972,U_1971] :
( c_Groups_Oabs__class_Oabs(U_1971,hAPP(hAPP(c_Power_Opower__class_Opower(U_1971),U_1972),U_1973)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1971),c_Groups_Oabs__class_Oabs(U_1971,U_1972)),U_1973)
| ~ class_Rings_Olinordered__idom(U_1971) ),
inference(variable_rename,[status(thm)],[f_625_1]) ).
fof(f_625_3,plain,
! [U_1971,U_1972,U_1973] :
( c_Groups_Oabs__class_Oabs(U_1971,hAPP(hAPP(c_Power_Opower__class_Opower(U_1971),U_1972),U_1973)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1971),c_Groups_Oabs__class_Oabs(U_1971,U_1972)),U_1973)
| ~ class_Rings_Olinordered__idom(U_1971) ),
inference(definitional_conversion,[status(esa)],[f_625_2]) ).
cnf(f_625_4,plain,
( c_Groups_Oabs__class_Oabs(U_1971,hAPP(hAPP(c_Power_Opower__class_Opower(U_1971),U_1972),U_1973)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1971),c_Groups_Oabs__class_Oabs(U_1971,U_1972)),U_1973)
| ~ class_Rings_Olinordered__idom(U_1971) ),
inference(clausify,[status(thm)],[f_625_3]) ).
fof(f_626_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_626_2,plain,
! [U_1975,U_1974] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1974),U_1975),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1975
| ~ class_Groups_Omonoid__mult(U_1974) ),
inference(variable_rename,[status(thm)],[f_626_1]) ).
fof(f_626_3,plain,
! [U_1974,U_1975] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1974),U_1975),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1975
| ~ class_Groups_Omonoid__mult(U_1974) ),
inference(definitional_conversion,[status(esa)],[f_626_2]) ).
cnf(f_626_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1974),U_1975),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_1975
| ~ class_Groups_Omonoid__mult(U_1974) ),
inference(clausify,[status(thm)],[f_626_3]) ).
fof(f_627_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_627_2,plain,
! [U_1978,U_1977,U_1976] :
( c_Orderings_Oord__class_Oless__eq(U_1976,c_Groups_Ozero__class_Ozero(U_1976),hAPP(hAPP(c_Power_Opower__class_Opower(U_1976),U_1977),U_1978))
| ~ c_Orderings_Oord__class_Oless__eq(U_1976,c_Groups_Ozero__class_Ozero(U_1976),U_1977)
| ~ class_Rings_Olinordered__semidom(U_1976) ),
inference(variable_rename,[status(thm)],[f_627_1]) ).
fof(f_627_3,plain,
! [U_1976,U_1977,U_1978] :
( c_Orderings_Oord__class_Oless__eq(U_1976,c_Groups_Ozero__class_Ozero(U_1976),hAPP(hAPP(c_Power_Opower__class_Opower(U_1976),U_1977),U_1978))
| ~ c_Orderings_Oord__class_Oless__eq(U_1976,c_Groups_Ozero__class_Ozero(U_1976),U_1977)
| ~ class_Rings_Olinordered__semidom(U_1976) ),
inference(definitional_conversion,[status(esa)],[f_627_2]) ).
cnf(f_627_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1976,c_Groups_Ozero__class_Ozero(U_1976),hAPP(hAPP(c_Power_Opower__class_Opower(U_1976),U_1977),U_1978))
| ~ c_Orderings_Oord__class_Oless__eq(U_1976,c_Groups_Ozero__class_Ozero(U_1976),U_1977)
| ~ class_Rings_Olinordered__semidom(U_1976) ),
inference(clausify,[status(thm)],[f_627_3]) ).
fof(f_628_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_628_2,plain,
! [U_1982,U_1981,U_1980,U_1979] :
( c_Orderings_Oord__class_Oless__eq(U_1979,hAPP(hAPP(c_Power_Opower__class_Opower(U_1979),U_1980),U_1982),hAPP(hAPP(c_Power_Opower__class_Opower(U_1979),U_1981),U_1982))
| ~ c_Orderings_Oord__class_Oless__eq(U_1979,c_Groups_Ozero__class_Ozero(U_1979),U_1980)
| ~ c_Orderings_Oord__class_Oless__eq(U_1979,U_1980,U_1981)
| ~ class_Rings_Olinordered__semidom(U_1979) ),
inference(variable_rename,[status(thm)],[f_628_1]) ).
fof(f_628_3,plain,
! [U_1979,U_1980,U_1981,U_1982] :
( c_Orderings_Oord__class_Oless__eq(U_1979,hAPP(hAPP(c_Power_Opower__class_Opower(U_1979),U_1980),U_1982),hAPP(hAPP(c_Power_Opower__class_Opower(U_1979),U_1981),U_1982))
| ~ c_Orderings_Oord__class_Oless__eq(U_1979,c_Groups_Ozero__class_Ozero(U_1979),U_1980)
| ~ c_Orderings_Oord__class_Oless__eq(U_1979,U_1980,U_1981)
| ~ class_Rings_Olinordered__semidom(U_1979) ),
inference(definitional_conversion,[status(esa)],[f_628_2]) ).
cnf(f_628_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1979,hAPP(hAPP(c_Power_Opower__class_Opower(U_1979),U_1980),U_1982),hAPP(hAPP(c_Power_Opower__class_Opower(U_1979),U_1981),U_1982))
| ~ c_Orderings_Oord__class_Oless__eq(U_1979,c_Groups_Ozero__class_Ozero(U_1979),U_1980)
| ~ c_Orderings_Oord__class_Oless__eq(U_1979,U_1980,U_1981)
| ~ class_Rings_Olinordered__semidom(U_1979) ),
inference(clausify,[status(thm)],[f_628_3]) ).
fof(f_629_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_629_2,plain,
! [U_1985,U_1984,U_1983] :
( c_Orderings_Oord__class_Oless(U_1983,c_Groups_Ozero__class_Ozero(U_1983),hAPP(hAPP(c_Power_Opower__class_Opower(U_1983),U_1984),U_1985))
| ~ c_Orderings_Oord__class_Oless(U_1983,c_Groups_Ozero__class_Ozero(U_1983),U_1984)
| ~ class_Rings_Olinordered__semidom(U_1983) ),
inference(variable_rename,[status(thm)],[f_629_1]) ).
fof(f_629_3,plain,
! [U_1984,U_1983,U_1985] :
( c_Orderings_Oord__class_Oless(U_1983,c_Groups_Ozero__class_Ozero(U_1983),hAPP(hAPP(c_Power_Opower__class_Opower(U_1983),U_1984),U_1985))
| ~ c_Orderings_Oord__class_Oless(U_1983,c_Groups_Ozero__class_Ozero(U_1983),U_1984)
| ~ class_Rings_Olinordered__semidom(U_1983) ),
inference(definitional_conversion,[status(esa)],[f_629_2]) ).
cnf(f_629_4,plain,
( c_Orderings_Oord__class_Oless(U_1983,c_Groups_Ozero__class_Ozero(U_1983),hAPP(hAPP(c_Power_Opower__class_Opower(U_1983),U_1984),U_1985))
| ~ c_Orderings_Oord__class_Oless(U_1983,c_Groups_Ozero__class_Ozero(U_1983),U_1984)
| ~ class_Rings_Olinordered__semidom(U_1983) ),
inference(clausify,[status(thm)],[f_629_3]) ).
fof(f_630_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_630_2,plain,
! [U_1988,U_1987,U_1986] :
( c_Orderings_Oord__class_Oless__eq(U_1986,c_Groups_Oone__class_Oone(U_1986),hAPP(hAPP(c_Power_Opower__class_Opower(U_1986),U_1987),U_1988))
| ~ c_Orderings_Oord__class_Oless__eq(U_1986,c_Groups_Oone__class_Oone(U_1986),U_1987)
| ~ class_Rings_Olinordered__semidom(U_1986) ),
inference(variable_rename,[status(thm)],[f_630_1]) ).
fof(f_630_3,plain,
! [U_1986,U_1987,U_1988] :
( c_Orderings_Oord__class_Oless__eq(U_1986,c_Groups_Oone__class_Oone(U_1986),hAPP(hAPP(c_Power_Opower__class_Opower(U_1986),U_1987),U_1988))
| ~ c_Orderings_Oord__class_Oless__eq(U_1986,c_Groups_Oone__class_Oone(U_1986),U_1987)
| ~ class_Rings_Olinordered__semidom(U_1986) ),
inference(definitional_conversion,[status(esa)],[f_630_2]) ).
cnf(f_630_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_1986,c_Groups_Oone__class_Oone(U_1986),hAPP(hAPP(c_Power_Opower__class_Opower(U_1986),U_1987),U_1988))
| ~ c_Orderings_Oord__class_Oless__eq(U_1986,c_Groups_Oone__class_Oone(U_1986),U_1987)
| ~ class_Rings_Olinordered__semidom(U_1986) ),
inference(clausify,[status(thm)],[f_630_3]) ).
fof(f_631_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_631_2,plain,
! [U_1991,U_1990,U_1989] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1989),U_1990),U_1991) = c_Groups_Ozero__class_Ozero(U_1989)
| U_1991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1990 != c_Groups_Ozero__class_Ozero(U_1989) )
& ( ( U_1991 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_1990 = c_Groups_Ozero__class_Ozero(U_1989) )
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1989),U_1990),U_1991) != c_Groups_Ozero__class_Ozero(U_1989) ) )
| ~ class_Rings_Ozero__neq__one(U_1989)
| ~ class_Rings_Ono__zero__divisors(U_1989)
| ~ class_Rings_Omult__zero(U_1989)
| ~ class_Power_Opower(U_1989) ),
inference(variable_rename,[status(thm)],[f_631_1]) ).
fof(f_631_3,plain,
( ! [U_1989,U_1990,U_1991] :
( U_1991 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP224(U_1989,U_1990,U_1991) )
& ! [U_1989,U_1990,U_1991] :
( U_1990 = c_Groups_Ozero__class_Ozero(U_1989)
| ~ sP224(U_1989,U_1990,U_1991) )
& ! [U_1989,U_1990,U_1991] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1989),U_1990),U_1991) = c_Groups_Ozero__class_Ozero(U_1989)
| U_1991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1990 != c_Groups_Ozero__class_Ozero(U_1989)
| ~ sP225(U_1989,U_1990,U_1991) )
& ! [U_1989,U_1990,U_1991] :
( sP224(U_1989,U_1990,U_1991)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1989),U_1990),U_1991) != c_Groups_Ozero__class_Ozero(U_1989)
| ~ sP225(U_1989,U_1990,U_1991) )
& ! [U_1989,U_1990,U_1991] :
( sP225(U_1989,U_1990,U_1991)
| ~ class_Rings_Ozero__neq__one(U_1989)
| ~ class_Rings_Ono__zero__divisors(U_1989)
| ~ class_Rings_Omult__zero(U_1989)
| ~ class_Power_Opower(U_1989) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP224,sP225])],[f_631_2]) ).
cnf(f_631_4,plain,
( sP225(U_1989,U_1990,U_1991)
| ~ class_Rings_Ozero__neq__one(U_1989)
| ~ class_Rings_Ono__zero__divisors(U_1989)
| ~ class_Rings_Omult__zero(U_1989)
| ~ class_Power_Opower(U_1989) ),
inference(clausify,[status(thm)],[f_631_3]) ).
cnf(f_631_5,plain,
( sP224(U_1989,U_1990,U_1991)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1989),U_1990),U_1991) != c_Groups_Ozero__class_Ozero(U_1989)
| ~ sP225(U_1989,U_1990,U_1991) ),
inference(clausify,[status(thm)],[f_631_3]) ).
cnf(f_631_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1989),U_1990),U_1991) = c_Groups_Ozero__class_Ozero(U_1989)
| U_1991 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_1990 != c_Groups_Ozero__class_Ozero(U_1989)
| ~ sP225(U_1989,U_1990,U_1991) ),
inference(clausify,[status(thm)],[f_631_3]) ).
cnf(f_631_7,plain,
( U_1990 = c_Groups_Ozero__class_Ozero(U_1989)
| ~ sP224(U_1989,U_1990,U_1991) ),
inference(clausify,[status(thm)],[f_631_3]) ).
cnf(f_631_8,plain,
( U_1991 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP224(U_1989,U_1990,U_1991) ),
inference(clausify,[status(thm)],[f_631_3]) ).
fof(f_632_1,plain,
! [V_n_2,V_ma_2,V_a_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_ma_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_ma_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_632_2,plain,
! [U_1995,U_1994,U_1993,U_1992] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1994) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1995)
| U_1994 != U_1995 )
& ( U_1994 = U_1995
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1994) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1995) ) )
| ~ c_Orderings_Oord__class_Oless(U_1992,c_Groups_Oone__class_Oone(U_1992),U_1993)
| ~ class_Rings_Olinordered__semidom(U_1992) ),
inference(variable_rename,[status(thm)],[f_632_1]) ).
fof(f_632_3,plain,
( ! [U_1992,U_1993,U_1994,U_1995] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1994) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1995)
| U_1994 != U_1995
| ~ sP226(U_1992,U_1993,U_1994,U_1995) )
& ! [U_1992,U_1993,U_1994,U_1995] :
( U_1994 = U_1995
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1994) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1995)
| ~ sP226(U_1992,U_1993,U_1994,U_1995) )
& ! [U_1992,U_1993,U_1994,U_1995] :
( sP226(U_1992,U_1993,U_1994,U_1995)
| ~ c_Orderings_Oord__class_Oless(U_1992,c_Groups_Oone__class_Oone(U_1992),U_1993)
| ~ class_Rings_Olinordered__semidom(U_1992) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP226])],[f_632_2]) ).
cnf(f_632_4,plain,
( sP226(U_1992,U_1993,U_1994,U_1995)
| ~ c_Orderings_Oord__class_Oless(U_1992,c_Groups_Oone__class_Oone(U_1992),U_1993)
| ~ class_Rings_Olinordered__semidom(U_1992) ),
inference(clausify,[status(thm)],[f_632_3]) ).
cnf(f_632_5,plain,
( U_1994 = U_1995
| hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1994) != hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1995)
| ~ sP226(U_1992,U_1993,U_1994,U_1995) ),
inference(clausify,[status(thm)],[f_632_3]) ).
cnf(f_632_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1994) = hAPP(hAPP(c_Power_Opower__class_Opower(U_1992),U_1993),U_1995)
| U_1994 != U_1995
| ~ sP226(U_1992,U_1993,U_1994,U_1995) ),
inference(clausify,[status(thm)],[f_632_3]) ).
fof(f_633_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_633_2,plain,
! [U_1997,U_1996] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1996),U_1997),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1996)
| ~ class_Power_Opower(U_1996) ),
inference(variable_rename,[status(thm)],[f_633_1]) ).
fof(f_633_3,plain,
! [U_1997,U_1996] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1996),U_1997),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1996)
| ~ class_Power_Opower(U_1996) ),
inference(definitional_conversion,[status(esa)],[f_633_2]) ).
cnf(f_633_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1996),U_1997),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1996)
| ~ class_Power_Opower(U_1996) ),
inference(clausify,[status(thm)],[f_633_3]) ).
fof(f_634_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_634_2,plain,
! [U_2001,U_2000,U_1999,U_1998] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1998),U_1999),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2000,U_2001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1998),hAPP(hAPP(c_Power_Opower__class_Opower(U_1998),U_1999),U_2000)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1998),U_1999),U_2001))
| ~ class_Groups_Omonoid__mult(U_1998) ),
inference(variable_rename,[status(thm)],[f_634_1]) ).
fof(f_634_3,plain,
! [U_1998,U_1999,U_2000,U_2001] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1998),U_1999),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2000,U_2001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1998),hAPP(hAPP(c_Power_Opower__class_Opower(U_1998),U_1999),U_2000)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1998),U_1999),U_2001))
| ~ class_Groups_Omonoid__mult(U_1998) ),
inference(definitional_conversion,[status(esa)],[f_634_2]) ).
cnf(f_634_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_1998),U_1999),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2000,U_2001)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1998),hAPP(hAPP(c_Power_Opower__class_Opower(U_1998),U_1999),U_2000)),hAPP(hAPP(c_Power_Opower__class_Opower(U_1998),U_1999),U_2001))
| ~ class_Groups_Omonoid__mult(U_1998) ),
inference(clausify,[status(thm)],[f_634_3]) ).
fof(f_635_1,plain,
! [V_a,V_n,V_m,T_a] :
( c_Rings_Odvd__class_Odvd(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)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__power__dvd]) ).
fof(f_635_2,plain,
! [U_2005,U_2004,U_2003,U_2002] :
( c_Rings_Odvd__class_Odvd(U_2002,hAPP(hAPP(c_Power_Opower__class_Opower(U_2002),U_2005),U_2003),hAPP(hAPP(c_Power_Opower__class_Opower(U_2002),U_2005),U_2004))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2003,U_2004)
| ~ class_Rings_Ocomm__semiring__1(U_2002) ),
inference(variable_rename,[status(thm)],[f_635_1]) ).
fof(f_635_3,plain,
! [U_2002,U_2003,U_2004,U_2005] :
( c_Rings_Odvd__class_Odvd(U_2002,hAPP(hAPP(c_Power_Opower__class_Opower(U_2002),U_2005),U_2003),hAPP(hAPP(c_Power_Opower__class_Opower(U_2002),U_2005),U_2004))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2003,U_2004)
| ~ class_Rings_Ocomm__semiring__1(U_2002) ),
inference(definitional_conversion,[status(esa)],[f_635_2]) ).
cnf(f_635_4,plain,
( c_Rings_Odvd__class_Odvd(U_2002,hAPP(hAPP(c_Power_Opower__class_Opower(U_2002),U_2005),U_2003),hAPP(hAPP(c_Power_Opower__class_Opower(U_2002),U_2005),U_2004))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2003,U_2004)
| ~ class_Rings_Ocomm__semiring__1(U_2002) ),
inference(clausify,[status(thm)],[f_635_3]) ).
fof(f_636_1,plain,
! [V_m,V_n,V_y,V_x,T_a] :
( c_Rings_Odvd__class_Odvd(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_y),V_m))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__power__le]) ).
fof(f_636_2,plain,
! [U_2010,U_2009,U_2008,U_2007,U_2006] :
( c_Rings_Odvd__class_Odvd(U_2006,hAPP(hAPP(c_Power_Opower__class_Opower(U_2006),U_2007),U_2009),hAPP(hAPP(c_Power_Opower__class_Opower(U_2006),U_2008),U_2010))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2009,U_2010)
| ~ c_Rings_Odvd__class_Odvd(U_2006,U_2007,U_2008)
| ~ class_Rings_Ocomm__semiring__1(U_2006) ),
inference(variable_rename,[status(thm)],[f_636_1]) ).
fof(f_636_3,plain,
! [U_2007,U_2008,U_2006,U_2009,U_2010] :
( c_Rings_Odvd__class_Odvd(U_2006,hAPP(hAPP(c_Power_Opower__class_Opower(U_2006),U_2007),U_2009),hAPP(hAPP(c_Power_Opower__class_Opower(U_2006),U_2008),U_2010))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2009,U_2010)
| ~ c_Rings_Odvd__class_Odvd(U_2006,U_2007,U_2008)
| ~ class_Rings_Ocomm__semiring__1(U_2006) ),
inference(definitional_conversion,[status(esa)],[f_636_2]) ).
cnf(f_636_4,plain,
( c_Rings_Odvd__class_Odvd(U_2006,hAPP(hAPP(c_Power_Opower__class_Opower(U_2006),U_2007),U_2009),hAPP(hAPP(c_Power_Opower__class_Opower(U_2006),U_2008),U_2010))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2009,U_2010)
| ~ c_Rings_Odvd__class_Odvd(U_2006,U_2007,U_2008)
| ~ class_Rings_Ocomm__semiring__1(U_2006) ),
inference(clausify,[status(thm)],[f_636_3]) ).
fof(f_637_1,plain,
! [V_m,V_b,V_n,V_a,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m,V_n)
| ~ c_Rings_Odvd__class_Odvd(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n),V_b)
| ~ class_Rings_Ocomm__semiring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__le__dvd]) ).
fof(f_637_2,plain,
! [U_2015,U_2014,U_2013,U_2012,U_2011] :
( c_Rings_Odvd__class_Odvd(U_2011,hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2012),U_2015),U_2014)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2015,U_2013)
| ~ c_Rings_Odvd__class_Odvd(U_2011,hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2012),U_2013),U_2014)
| ~ class_Rings_Ocomm__semiring__1(U_2011) ),
inference(variable_rename,[status(thm)],[f_637_1]) ).
fof(f_637_3,plain,
! [U_2011,U_2012,U_2013,U_2014,U_2015] :
( c_Rings_Odvd__class_Odvd(U_2011,hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2012),U_2015),U_2014)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2015,U_2013)
| ~ c_Rings_Odvd__class_Odvd(U_2011,hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2012),U_2013),U_2014)
| ~ class_Rings_Ocomm__semiring__1(U_2011) ),
inference(definitional_conversion,[status(esa)],[f_637_2]) ).
cnf(f_637_4,plain,
( c_Rings_Odvd__class_Odvd(U_2011,hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2012),U_2015),U_2014)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2015,U_2013)
| ~ c_Rings_Odvd__class_Odvd(U_2011,hAPP(hAPP(c_Power_Opower__class_Opower(U_2011),U_2012),U_2013),U_2014)
| ~ class_Rings_Ocomm__semiring__1(U_2011) ),
inference(clausify,[status(thm)],[f_637_3]) ).
fof(f_638_1,plain,
! [V_n,V_a,T_a] :
( c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n)) = c_Groups_Oabs__class_Oabs(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__power__minus]) ).
fof(f_638_2,plain,
! [U_2018,U_2017,U_2016] :
( c_Groups_Oabs__class_Oabs(U_2016,hAPP(hAPP(c_Power_Opower__class_Opower(U_2016),c_Groups_Ouminus__class_Ouminus(U_2016,U_2017)),U_2018)) = c_Groups_Oabs__class_Oabs(U_2016,hAPP(hAPP(c_Power_Opower__class_Opower(U_2016),U_2017),U_2018))
| ~ class_Rings_Olinordered__idom(U_2016) ),
inference(variable_rename,[status(thm)],[f_638_1]) ).
fof(f_638_3,plain,
! [U_2016,U_2017,U_2018] :
( c_Groups_Oabs__class_Oabs(U_2016,hAPP(hAPP(c_Power_Opower__class_Opower(U_2016),c_Groups_Ouminus__class_Ouminus(U_2016,U_2017)),U_2018)) = c_Groups_Oabs__class_Oabs(U_2016,hAPP(hAPP(c_Power_Opower__class_Opower(U_2016),U_2017),U_2018))
| ~ class_Rings_Olinordered__idom(U_2016) ),
inference(definitional_conversion,[status(esa)],[f_638_2]) ).
cnf(f_638_4,plain,
( c_Groups_Oabs__class_Oabs(U_2016,hAPP(hAPP(c_Power_Opower__class_Opower(U_2016),c_Groups_Ouminus__class_Ouminus(U_2016,U_2017)),U_2018)) = c_Groups_Oabs__class_Oabs(U_2016,hAPP(hAPP(c_Power_Opower__class_Opower(U_2016),U_2017),U_2018))
| ~ class_Rings_Olinordered__idom(U_2016) ),
inference(clausify,[status(thm)],[f_638_3]) ).
fof(f_639_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_639_2,plain,
! [U_2022,U_2021,U_2020,U_2019] :
( c_Orderings_Oord__class_Oless(U_2019,U_2020,U_2022)
| ~ c_Orderings_Oord__class_Oless__eq(U_2019,c_Groups_Ozero__class_Ozero(U_2019),U_2022)
| ~ c_Orderings_Oord__class_Oless(U_2019,hAPP(hAPP(c_Power_Opower__class_Opower(U_2019),U_2020),U_2021),hAPP(hAPP(c_Power_Opower__class_Opower(U_2019),U_2022),U_2021))
| ~ class_Rings_Olinordered__semidom(U_2019) ),
inference(variable_rename,[status(thm)],[f_639_1]) ).
fof(f_639_3,plain,
! [U_2019,U_2020,U_2021,U_2022] :
( c_Orderings_Oord__class_Oless(U_2019,U_2020,U_2022)
| ~ c_Orderings_Oord__class_Oless__eq(U_2019,c_Groups_Ozero__class_Ozero(U_2019),U_2022)
| ~ c_Orderings_Oord__class_Oless(U_2019,hAPP(hAPP(c_Power_Opower__class_Opower(U_2019),U_2020),U_2021),hAPP(hAPP(c_Power_Opower__class_Opower(U_2019),U_2022),U_2021))
| ~ class_Rings_Olinordered__semidom(U_2019) ),
inference(definitional_conversion,[status(esa)],[f_639_2]) ).
cnf(f_639_4,plain,
( c_Orderings_Oord__class_Oless(U_2019,U_2020,U_2022)
| ~ c_Orderings_Oord__class_Oless__eq(U_2019,c_Groups_Ozero__class_Ozero(U_2019),U_2022)
| ~ c_Orderings_Oord__class_Oless(U_2019,hAPP(hAPP(c_Power_Opower__class_Opower(U_2019),U_2020),U_2021),hAPP(hAPP(c_Power_Opower__class_Opower(U_2019),U_2022),U_2021))
| ~ class_Rings_Olinordered__semidom(U_2019) ),
inference(clausify,[status(thm)],[f_639_3]) ).
fof(f_640_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_640_2,plain,
! [U_2025,U_2024,U_2023] :
( c_Orderings_Oord__class_Oless(U_2023,c_Groups_Oone__class_Oone(U_2023),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),U_2024),hAPP(hAPP(c_Power_Opower__class_Opower(U_2023),U_2024),U_2025)))
| ~ c_Orderings_Oord__class_Oless(U_2023,c_Groups_Oone__class_Oone(U_2023),U_2024)
| ~ class_Rings_Olinordered__semidom(U_2023) ),
inference(variable_rename,[status(thm)],[f_640_1]) ).
fof(f_640_3,plain,
! [U_2024,U_2023,U_2025] :
( c_Orderings_Oord__class_Oless(U_2023,c_Groups_Oone__class_Oone(U_2023),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),U_2024),hAPP(hAPP(c_Power_Opower__class_Opower(U_2023),U_2024),U_2025)))
| ~ c_Orderings_Oord__class_Oless(U_2023,c_Groups_Oone__class_Oone(U_2023),U_2024)
| ~ class_Rings_Olinordered__semidom(U_2023) ),
inference(definitional_conversion,[status(esa)],[f_640_2]) ).
cnf(f_640_4,plain,
( c_Orderings_Oord__class_Oless(U_2023,c_Groups_Oone__class_Oone(U_2023),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2023),U_2024),hAPP(hAPP(c_Power_Opower__class_Opower(U_2023),U_2024),U_2025)))
| ~ c_Orderings_Oord__class_Oless(U_2023,c_Groups_Oone__class_Oone(U_2023),U_2024)
| ~ class_Rings_Olinordered__semidom(U_2023) ),
inference(clausify,[status(thm)],[f_640_3]) ).
fof(f_641_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_641_2,plain,
! [U_2028,U_2027,U_2026] :
( c_Orderings_Oord__class_Oless(U_2026,hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2027),U_2028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2026),U_2027),hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2027),U_2028)))
| ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Oone__class_Oone(U_2026),U_2027)
| ~ class_Rings_Olinordered__semidom(U_2026) ),
inference(variable_rename,[status(thm)],[f_641_1]) ).
fof(f_641_3,plain,
! [U_2026,U_2027,U_2028] :
( c_Orderings_Oord__class_Oless(U_2026,hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2027),U_2028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2026),U_2027),hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2027),U_2028)))
| ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Oone__class_Oone(U_2026),U_2027)
| ~ class_Rings_Olinordered__semidom(U_2026) ),
inference(definitional_conversion,[status(esa)],[f_641_2]) ).
cnf(f_641_4,plain,
( c_Orderings_Oord__class_Oless(U_2026,hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2027),U_2028),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2026),U_2027),hAPP(hAPP(c_Power_Opower__class_Opower(U_2026),U_2027),U_2028)))
| ~ c_Orderings_Oord__class_Oless(U_2026,c_Groups_Oone__class_Oone(U_2026),U_2027)
| ~ class_Rings_Olinordered__semidom(U_2026) ),
inference(clausify,[status(thm)],[f_641_3]) ).
fof(f_642_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_642_2,plain,
! [U_2030,U_2029] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2029),c_Groups_Ozero__class_Ozero(U_2029)),U_2030) = c_Groups_Ozero__class_Ozero(U_2029)
| U_2030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2029),c_Groups_Ozero__class_Ozero(U_2029)),U_2030) = c_Groups_Oone__class_Oone(U_2029)
| U_2030 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
| ~ class_Rings_Osemiring__0(U_2029)
| ~ class_Power_Opower(U_2029) ),
inference(variable_rename,[status(thm)],[f_642_1]) ).
fof(f_642_3,plain,
( ! [U_2029,U_2030] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2029),c_Groups_Ozero__class_Ozero(U_2029)),U_2030) = c_Groups_Ozero__class_Ozero(U_2029)
| U_2030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP227(U_2029,U_2030) )
& ! [U_2029,U_2030] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2029),c_Groups_Ozero__class_Ozero(U_2029)),U_2030) = c_Groups_Oone__class_Oone(U_2029)
| U_2030 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP227(U_2029,U_2030) )
& ! [U_2029,U_2030] :
( sP227(U_2029,U_2030)
| ~ class_Rings_Osemiring__0(U_2029)
| ~ class_Power_Opower(U_2029) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP227])],[f_642_2]) ).
cnf(f_642_4,plain,
( sP227(U_2029,U_2030)
| ~ class_Rings_Osemiring__0(U_2029)
| ~ class_Power_Opower(U_2029) ),
inference(clausify,[status(thm)],[f_642_3]) ).
cnf(f_642_5,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2029),c_Groups_Ozero__class_Ozero(U_2029)),U_2030) = c_Groups_Oone__class_Oone(U_2029)
| U_2030 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP227(U_2029,U_2030) ),
inference(clausify,[status(thm)],[f_642_3]) ).
cnf(f_642_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2029),c_Groups_Ozero__class_Ozero(U_2029)),U_2030) = c_Groups_Ozero__class_Ozero(U_2029)
| U_2030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP227(U_2029,U_2030) ),
inference(clausify,[status(thm)],[f_642_3]) ).
fof(f_643_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_643_2,plain,
! [U_2033,U_2032,U_2031] :
( c_Orderings_Oord__class_Oless__eq(U_2031,c_Groups_Ozero__class_Ozero(U_2031),hAPP(hAPP(c_Power_Opower__class_Opower(U_2031),c_Groups_Oabs__class_Oabs(U_2031,U_2032)),U_2033))
| ~ class_Rings_Olinordered__idom(U_2031) ),
inference(variable_rename,[status(thm)],[f_643_1]) ).
fof(f_643_3,plain,
! [U_2032,U_2033,U_2031] :
( c_Orderings_Oord__class_Oless__eq(U_2031,c_Groups_Ozero__class_Ozero(U_2031),hAPP(hAPP(c_Power_Opower__class_Opower(U_2031),c_Groups_Oabs__class_Oabs(U_2031,U_2032)),U_2033))
| ~ class_Rings_Olinordered__idom(U_2031) ),
inference(definitional_conversion,[status(esa)],[f_643_2]) ).
cnf(f_643_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2031,c_Groups_Ozero__class_Ozero(U_2031),hAPP(hAPP(c_Power_Opower__class_Opower(U_2031),c_Groups_Oabs__class_Oabs(U_2031,U_2032)),U_2033))
| ~ class_Rings_Olinordered__idom(U_2031) ),
inference(clausify,[status(thm)],[f_643_3]) ).
fof(f_644_1,plain,
! [V_n,V_a,T_a] :
( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))
| ~ class_Rings_Oring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__minus]) ).
fof(f_644_2,plain,
! [U_2036,U_2035,U_2034] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2034),c_Groups_Ouminus__class_Ouminus(U_2034,U_2035)),U_2036) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2034),hAPP(hAPP(c_Power_Opower__class_Opower(U_2034),c_Groups_Ouminus__class_Ouminus(U_2034,c_Groups_Oone__class_Oone(U_2034))),U_2036)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2034),U_2035),U_2036))
| ~ class_Rings_Oring__1(U_2034) ),
inference(variable_rename,[status(thm)],[f_644_1]) ).
fof(f_644_3,plain,
! [U_2034,U_2035,U_2036] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2034),c_Groups_Ouminus__class_Ouminus(U_2034,U_2035)),U_2036) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2034),hAPP(hAPP(c_Power_Opower__class_Opower(U_2034),c_Groups_Ouminus__class_Ouminus(U_2034,c_Groups_Oone__class_Oone(U_2034))),U_2036)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2034),U_2035),U_2036))
| ~ class_Rings_Oring__1(U_2034) ),
inference(definitional_conversion,[status(esa)],[f_644_2]) ).
cnf(f_644_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2034),c_Groups_Ouminus__class_Ouminus(U_2034,U_2035)),U_2036) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2034),hAPP(hAPP(c_Power_Opower__class_Opower(U_2034),c_Groups_Ouminus__class_Ouminus(U_2034,c_Groups_Oone__class_Oone(U_2034))),U_2036)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2034),U_2035),U_2036))
| ~ class_Rings_Oring__1(U_2034) ),
inference(clausify,[status(thm)],[f_644_3]) ).
fof(f_645_1,plain,
! [V_y_2,V_x_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_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__strict__increasing__iff]) ).
fof(f_645_2,plain,
! [U_2040,U_2039,U_2038,U_2037] :
( ( ( c_Orderings_Oord__class_Oless(U_2037,hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2039),hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2040))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2039,U_2040) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2039,U_2040)
| ~ c_Orderings_Oord__class_Oless(U_2037,hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2039),hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2040)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2037,c_Groups_Oone__class_Oone(U_2037),U_2038)
| ~ class_Rings_Olinordered__semidom(U_2037) ),
inference(variable_rename,[status(thm)],[f_645_1]) ).
fof(f_645_3,plain,
( ! [U_2037,U_2038,U_2039,U_2040] :
( c_Orderings_Oord__class_Oless(U_2037,hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2039),hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2040))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2039,U_2040)
| ~ sP228(U_2037,U_2038,U_2039,U_2040) )
& ! [U_2037,U_2038,U_2039,U_2040] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2039,U_2040)
| ~ c_Orderings_Oord__class_Oless(U_2037,hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2039),hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2040))
| ~ sP228(U_2037,U_2038,U_2039,U_2040) )
& ! [U_2037,U_2038,U_2039,U_2040] :
( sP228(U_2037,U_2038,U_2039,U_2040)
| ~ c_Orderings_Oord__class_Oless(U_2037,c_Groups_Oone__class_Oone(U_2037),U_2038)
| ~ class_Rings_Olinordered__semidom(U_2037) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228])],[f_645_2]) ).
cnf(f_645_4,plain,
( sP228(U_2037,U_2038,U_2039,U_2040)
| ~ c_Orderings_Oord__class_Oless(U_2037,c_Groups_Oone__class_Oone(U_2037),U_2038)
| ~ class_Rings_Olinordered__semidom(U_2037) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2039,U_2040)
| ~ c_Orderings_Oord__class_Oless(U_2037,hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2039),hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2040))
| ~ sP228(U_2037,U_2038,U_2039,U_2040) ),
inference(clausify,[status(thm)],[f_645_3]) ).
cnf(f_645_6,plain,
( c_Orderings_Oord__class_Oless(U_2037,hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2039),hAPP(hAPP(c_Power_Opower__class_Opower(U_2037),U_2038),U_2040))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2039,U_2040)
| ~ sP228(U_2037,U_2038,U_2039,U_2040) ),
inference(clausify,[status(thm)],[f_645_3]) ).
fof(f_646_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_646_2,plain,
! [U_2044,U_2043,U_2042,U_2041] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2043,U_2044)
| ~ c_Orderings_Oord__class_Oless(U_2041,hAPP(hAPP(c_Power_Opower__class_Opower(U_2041),U_2042),U_2043),hAPP(hAPP(c_Power_Opower__class_Opower(U_2041),U_2042),U_2044))
| ~ c_Orderings_Oord__class_Oless(U_2041,c_Groups_Oone__class_Oone(U_2041),U_2042)
| ~ class_Rings_Olinordered__semidom(U_2041) ),
inference(variable_rename,[status(thm)],[f_646_1]) ).
fof(f_646_3,plain,
! [U_2041,U_2043,U_2044,U_2042] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2043,U_2044)
| ~ c_Orderings_Oord__class_Oless(U_2041,hAPP(hAPP(c_Power_Opower__class_Opower(U_2041),U_2042),U_2043),hAPP(hAPP(c_Power_Opower__class_Opower(U_2041),U_2042),U_2044))
| ~ c_Orderings_Oord__class_Oless(U_2041,c_Groups_Oone__class_Oone(U_2041),U_2042)
| ~ class_Rings_Olinordered__semidom(U_2041) ),
inference(definitional_conversion,[status(esa)],[f_646_2]) ).
cnf(f_646_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2043,U_2044)
| ~ c_Orderings_Oord__class_Oless(U_2041,hAPP(hAPP(c_Power_Opower__class_Opower(U_2041),U_2042),U_2043),hAPP(hAPP(c_Power_Opower__class_Opower(U_2041),U_2042),U_2044))
| ~ c_Orderings_Oord__class_Oless(U_2041,c_Groups_Oone__class_Oone(U_2041),U_2042)
| ~ class_Rings_Olinordered__semidom(U_2041) ),
inference(clausify,[status(thm)],[f_646_3]) ).
fof(f_647_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_647_2,plain,
! [U_2048,U_2047,U_2046,U_2045] :
( c_Orderings_Oord__class_Oless(U_2045,hAPP(hAPP(c_Power_Opower__class_Opower(U_2045),U_2048),U_2046),hAPP(hAPP(c_Power_Opower__class_Opower(U_2045),U_2048),U_2047))
| ~ c_Orderings_Oord__class_Oless(U_2045,c_Groups_Oone__class_Oone(U_2045),U_2048)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2046,U_2047)
| ~ class_Rings_Olinordered__semidom(U_2045) ),
inference(variable_rename,[status(thm)],[f_647_1]) ).
fof(f_647_3,plain,
! [U_2048,U_2045,U_2047,U_2046] :
( c_Orderings_Oord__class_Oless(U_2045,hAPP(hAPP(c_Power_Opower__class_Opower(U_2045),U_2048),U_2046),hAPP(hAPP(c_Power_Opower__class_Opower(U_2045),U_2048),U_2047))
| ~ c_Orderings_Oord__class_Oless(U_2045,c_Groups_Oone__class_Oone(U_2045),U_2048)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2046,U_2047)
| ~ class_Rings_Olinordered__semidom(U_2045) ),
inference(definitional_conversion,[status(esa)],[f_647_2]) ).
cnf(f_647_4,plain,
( c_Orderings_Oord__class_Oless(U_2045,hAPP(hAPP(c_Power_Opower__class_Opower(U_2045),U_2048),U_2046),hAPP(hAPP(c_Power_Opower__class_Opower(U_2045),U_2048),U_2047))
| ~ c_Orderings_Oord__class_Oless(U_2045,c_Groups_Oone__class_Oone(U_2045),U_2048)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2046,U_2047)
| ~ class_Rings_Olinordered__semidom(U_2045) ),
inference(clausify,[status(thm)],[f_647_3]) ).
fof(f_648_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_648_2,plain,
! [U_2052,U_2051,U_2050,U_2049] :
( c_Orderings_Oord__class_Oless__eq(U_2049,hAPP(hAPP(c_Power_Opower__class_Opower(U_2049),U_2052),U_2050),hAPP(hAPP(c_Power_Opower__class_Opower(U_2049),U_2052),U_2051))
| ~ c_Orderings_Oord__class_Oless__eq(U_2049,c_Groups_Oone__class_Oone(U_2049),U_2052)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2050,U_2051)
| ~ class_Rings_Olinordered__semidom(U_2049) ),
inference(variable_rename,[status(thm)],[f_648_1]) ).
fof(f_648_3,plain,
! [U_2049,U_2050,U_2051,U_2052] :
( c_Orderings_Oord__class_Oless__eq(U_2049,hAPP(hAPP(c_Power_Opower__class_Opower(U_2049),U_2052),U_2050),hAPP(hAPP(c_Power_Opower__class_Opower(U_2049),U_2052),U_2051))
| ~ c_Orderings_Oord__class_Oless__eq(U_2049,c_Groups_Oone__class_Oone(U_2049),U_2052)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2050,U_2051)
| ~ class_Rings_Olinordered__semidom(U_2049) ),
inference(definitional_conversion,[status(esa)],[f_648_2]) ).
cnf(f_648_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2049,hAPP(hAPP(c_Power_Opower__class_Opower(U_2049),U_2052),U_2050),hAPP(hAPP(c_Power_Opower__class_Opower(U_2049),U_2052),U_2051))
| ~ c_Orderings_Oord__class_Oless__eq(U_2049,c_Groups_Oone__class_Oone(U_2049),U_2052)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2050,U_2051)
| ~ class_Rings_Olinordered__semidom(U_2049) ),
inference(clausify,[status(thm)],[f_648_3]) ).
fof(f_649_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_649_2,plain,
! [U_2055,U_2054,U_2053] :
( c_Orderings_Oord__class_Oless(U_2053,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),hAPP(hAPP(c_Power_Opower__class_Opower(U_2053),U_2054),U_2055)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2053),U_2054),U_2055))
| ~ c_Orderings_Oord__class_Oless(U_2053,U_2054,c_Groups_Oone__class_Oone(U_2053))
| ~ c_Orderings_Oord__class_Oless(U_2053,c_Groups_Ozero__class_Ozero(U_2053),U_2054)
| ~ class_Rings_Olinordered__semidom(U_2053) ),
inference(variable_rename,[status(thm)],[f_649_1]) ).
fof(f_649_3,plain,
! [U_2053,U_2054,U_2055] :
( c_Orderings_Oord__class_Oless(U_2053,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),hAPP(hAPP(c_Power_Opower__class_Opower(U_2053),U_2054),U_2055)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2053),U_2054),U_2055))
| ~ c_Orderings_Oord__class_Oless(U_2053,U_2054,c_Groups_Oone__class_Oone(U_2053))
| ~ c_Orderings_Oord__class_Oless(U_2053,c_Groups_Ozero__class_Ozero(U_2053),U_2054)
| ~ class_Rings_Olinordered__semidom(U_2053) ),
inference(definitional_conversion,[status(esa)],[f_649_2]) ).
cnf(f_649_4,plain,
( c_Orderings_Oord__class_Oless(U_2053,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2053),U_2054),hAPP(hAPP(c_Power_Opower__class_Opower(U_2053),U_2054),U_2055)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2053),U_2054),U_2055))
| ~ c_Orderings_Oord__class_Oless(U_2053,U_2054,c_Groups_Oone__class_Oone(U_2053))
| ~ c_Orderings_Oord__class_Oless(U_2053,c_Groups_Ozero__class_Ozero(U_2053),U_2054)
| ~ class_Rings_Olinordered__semidom(U_2053) ),
inference(clausify,[status(thm)],[f_649_3]) ).
fof(f_650_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_650_2,plain,
! [U_2059,U_2058,U_2057,U_2056] :
( c_Orderings_Oord__class_Oless(U_2056,hAPP(hAPP(c_Power_Opower__class_Opower(U_2056),U_2059),U_2058),hAPP(hAPP(c_Power_Opower__class_Opower(U_2056),U_2059),U_2057))
| ~ c_Orderings_Oord__class_Oless(U_2056,U_2059,c_Groups_Oone__class_Oone(U_2056))
| ~ c_Orderings_Oord__class_Oless(U_2056,c_Groups_Ozero__class_Ozero(U_2056),U_2059)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2057,U_2058)
| ~ class_Rings_Olinordered__semidom(U_2056) ),
inference(variable_rename,[status(thm)],[f_650_1]) ).
fof(f_650_3,plain,
! [U_2056,U_2057,U_2058,U_2059] :
( c_Orderings_Oord__class_Oless(U_2056,hAPP(hAPP(c_Power_Opower__class_Opower(U_2056),U_2059),U_2058),hAPP(hAPP(c_Power_Opower__class_Opower(U_2056),U_2059),U_2057))
| ~ c_Orderings_Oord__class_Oless(U_2056,U_2059,c_Groups_Oone__class_Oone(U_2056))
| ~ c_Orderings_Oord__class_Oless(U_2056,c_Groups_Ozero__class_Ozero(U_2056),U_2059)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2057,U_2058)
| ~ class_Rings_Olinordered__semidom(U_2056) ),
inference(definitional_conversion,[status(esa)],[f_650_2]) ).
cnf(f_650_4,plain,
( c_Orderings_Oord__class_Oless(U_2056,hAPP(hAPP(c_Power_Opower__class_Opower(U_2056),U_2059),U_2058),hAPP(hAPP(c_Power_Opower__class_Opower(U_2056),U_2059),U_2057))
| ~ c_Orderings_Oord__class_Oless(U_2056,U_2059,c_Groups_Oone__class_Oone(U_2056))
| ~ c_Orderings_Oord__class_Oless(U_2056,c_Groups_Ozero__class_Ozero(U_2056),U_2059)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2057,U_2058)
| ~ class_Rings_Olinordered__semidom(U_2056) ),
inference(clausify,[status(thm)],[f_650_3]) ).
fof(f_651_1,plain,
! [V_b,V_n,V_a,T_a] :
( V_a = V_b
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a)
| 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__eq__imp__eq__base]) ).
fof(f_651_2,plain,
! [U_2063,U_2062,U_2061,U_2060] :
( U_2061 = U_2063
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2062)
| ~ c_Orderings_Oord__class_Oless__eq(U_2060,c_Groups_Ozero__class_Ozero(U_2060),U_2063)
| ~ c_Orderings_Oord__class_Oless__eq(U_2060,c_Groups_Ozero__class_Ozero(U_2060),U_2061)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2060),U_2061),U_2062) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2060),U_2063),U_2062)
| ~ class_Rings_Olinordered__semidom(U_2060) ),
inference(variable_rename,[status(thm)],[f_651_1]) ).
fof(f_651_3,plain,
! [U_2060,U_2061,U_2062,U_2063] :
( U_2061 = U_2063
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2062)
| ~ c_Orderings_Oord__class_Oless__eq(U_2060,c_Groups_Ozero__class_Ozero(U_2060),U_2063)
| ~ c_Orderings_Oord__class_Oless__eq(U_2060,c_Groups_Ozero__class_Ozero(U_2060),U_2061)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2060),U_2061),U_2062) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2060),U_2063),U_2062)
| ~ class_Rings_Olinordered__semidom(U_2060) ),
inference(definitional_conversion,[status(esa)],[f_651_2]) ).
cnf(f_651_4,plain,
( U_2061 = U_2063
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2062)
| ~ c_Orderings_Oord__class_Oless__eq(U_2060,c_Groups_Ozero__class_Ozero(U_2060),U_2063)
| ~ c_Orderings_Oord__class_Oless__eq(U_2060,c_Groups_Ozero__class_Ozero(U_2060),U_2061)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2060),U_2061),U_2062) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2060),U_2063),U_2062)
| ~ class_Rings_Olinordered__semidom(U_2060) ),
inference(clausify,[status(thm)],[f_651_3]) ).
fof(f_652_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_652_2,plain,
! [U_2067,U_2066,U_2065,U_2064] :
( c_Orderings_Oord__class_Oless__eq(U_2064,hAPP(hAPP(c_Power_Opower__class_Opower(U_2064),U_2067),U_2066),hAPP(hAPP(c_Power_Opower__class_Opower(U_2064),U_2067),U_2065))
| ~ c_Orderings_Oord__class_Oless__eq(U_2064,U_2067,c_Groups_Oone__class_Oone(U_2064))
| ~ c_Orderings_Oord__class_Oless__eq(U_2064,c_Groups_Ozero__class_Ozero(U_2064),U_2067)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2065,U_2066)
| ~ class_Rings_Olinordered__semidom(U_2064) ),
inference(variable_rename,[status(thm)],[f_652_1]) ).
fof(f_652_3,plain,
! [U_2067,U_2064,U_2065,U_2066] :
( c_Orderings_Oord__class_Oless__eq(U_2064,hAPP(hAPP(c_Power_Opower__class_Opower(U_2064),U_2067),U_2066),hAPP(hAPP(c_Power_Opower__class_Opower(U_2064),U_2067),U_2065))
| ~ c_Orderings_Oord__class_Oless__eq(U_2064,U_2067,c_Groups_Oone__class_Oone(U_2064))
| ~ c_Orderings_Oord__class_Oless__eq(U_2064,c_Groups_Ozero__class_Ozero(U_2064),U_2067)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2065,U_2066)
| ~ class_Rings_Olinordered__semidom(U_2064) ),
inference(definitional_conversion,[status(esa)],[f_652_2]) ).
cnf(f_652_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2064,hAPP(hAPP(c_Power_Opower__class_Opower(U_2064),U_2067),U_2066),hAPP(hAPP(c_Power_Opower__class_Opower(U_2064),U_2067),U_2065))
| ~ c_Orderings_Oord__class_Oless__eq(U_2064,U_2067,c_Groups_Oone__class_Oone(U_2064))
| ~ c_Orderings_Oord__class_Oless__eq(U_2064,c_Groups_Ozero__class_Ozero(U_2064),U_2067)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2065,U_2066)
| ~ class_Rings_Olinordered__semidom(U_2064) ),
inference(clausify,[status(thm)],[f_652_3]) ).
fof(f_653_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_653_2,plain,
! [U_2071,U_2070,U_2069,U_2068] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2070,U_2071)
| ~ c_Orderings_Oord__class_Oless__eq(U_2068,hAPP(hAPP(c_Power_Opower__class_Opower(U_2068),U_2069),U_2070),hAPP(hAPP(c_Power_Opower__class_Opower(U_2068),U_2069),U_2071))
| ~ c_Orderings_Oord__class_Oless(U_2068,c_Groups_Oone__class_Oone(U_2068),U_2069)
| ~ class_Rings_Olinordered__semidom(U_2068) ),
inference(variable_rename,[status(thm)],[f_653_1]) ).
fof(f_653_3,plain,
! [U_2068,U_2071,U_2069,U_2070] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2070,U_2071)
| ~ c_Orderings_Oord__class_Oless__eq(U_2068,hAPP(hAPP(c_Power_Opower__class_Opower(U_2068),U_2069),U_2070),hAPP(hAPP(c_Power_Opower__class_Opower(U_2068),U_2069),U_2071))
| ~ c_Orderings_Oord__class_Oless(U_2068,c_Groups_Oone__class_Oone(U_2068),U_2069)
| ~ class_Rings_Olinordered__semidom(U_2068) ),
inference(definitional_conversion,[status(esa)],[f_653_2]) ).
cnf(f_653_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2070,U_2071)
| ~ c_Orderings_Oord__class_Oless__eq(U_2068,hAPP(hAPP(c_Power_Opower__class_Opower(U_2068),U_2069),U_2070),hAPP(hAPP(c_Power_Opower__class_Opower(U_2068),U_2069),U_2071))
| ~ c_Orderings_Oord__class_Oless(U_2068,c_Groups_Oone__class_Oone(U_2068),U_2069)
| ~ class_Rings_Olinordered__semidom(U_2068) ),
inference(clausify,[status(thm)],[f_653_3]) ).
fof(f_654_1,plain,
! [V_y_2,V_x_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_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(T_a,hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_x_2),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b_2),V_y_2)) ) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oone__class_Oone(T_a),V_b_2)
| ~ class_Rings_Olinordered__semidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_power__increasing__iff]) ).
fof(f_654_2,plain,
! [U_2075,U_2074,U_2073,U_2072] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2072,hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2074),hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2075))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2074,U_2075) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2074,U_2075)
| ~ c_Orderings_Oord__class_Oless__eq(U_2072,hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2074),hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2075)) ) )
| ~ c_Orderings_Oord__class_Oless(U_2072,c_Groups_Oone__class_Oone(U_2072),U_2073)
| ~ class_Rings_Olinordered__semidom(U_2072) ),
inference(variable_rename,[status(thm)],[f_654_1]) ).
fof(f_654_3,plain,
( ! [U_2072,U_2073,U_2074,U_2075] :
( c_Orderings_Oord__class_Oless__eq(U_2072,hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2074),hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2075))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2074,U_2075)
| ~ sP229(U_2072,U_2073,U_2074,U_2075) )
& ! [U_2072,U_2073,U_2074,U_2075] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2074,U_2075)
| ~ c_Orderings_Oord__class_Oless__eq(U_2072,hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2074),hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2075))
| ~ sP229(U_2072,U_2073,U_2074,U_2075) )
& ! [U_2072,U_2073,U_2074,U_2075] :
( sP229(U_2072,U_2073,U_2074,U_2075)
| ~ c_Orderings_Oord__class_Oless(U_2072,c_Groups_Oone__class_Oone(U_2072),U_2073)
| ~ class_Rings_Olinordered__semidom(U_2072) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP229])],[f_654_2]) ).
cnf(f_654_4,plain,
( sP229(U_2072,U_2073,U_2074,U_2075)
| ~ c_Orderings_Oord__class_Oless(U_2072,c_Groups_Oone__class_Oone(U_2072),U_2073)
| ~ class_Rings_Olinordered__semidom(U_2072) ),
inference(clausify,[status(thm)],[f_654_3]) ).
cnf(f_654_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2074,U_2075)
| ~ c_Orderings_Oord__class_Oless__eq(U_2072,hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2074),hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2075))
| ~ sP229(U_2072,U_2073,U_2074,U_2075) ),
inference(clausify,[status(thm)],[f_654_3]) ).
cnf(f_654_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2072,hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2074),hAPP(hAPP(c_Power_Opower__class_Opower(U_2072),U_2073),U_2075))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2074,U_2075)
| ~ sP229(U_2072,U_2073,U_2074,U_2075) ),
inference(clausify,[status(thm)],[f_654_3]) ).
fof(f_655_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_dvd__pos__nat]) ).
fof(f_655_2,plain,
! [U_2077,U_2076] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2077)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2077,U_2076)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2076) ),
inference(variable_rename,[status(thm)],[f_655_1]) ).
fof(f_655_3,plain,
! [U_2077,U_2076] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2077)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2077,U_2076)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2076) ),
inference(definitional_conversion,[status(esa)],[f_655_2]) ).
cnf(f_655_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2077)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2077,U_2076)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2076) ),
inference(clausify,[status(thm)],[f_655_3]) ).
fof(f_656_1,plain,
! [V_a,V_p,T_a] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)
& c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Polynomial_Oorder(T_a,V_a,V_p)),V_p) )
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order]) ).
fof(f_656_2,plain,
! [U_2080,U_2079,U_2078] :
( ( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2078),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2078)),c_Polynomial_OpCons(U_2078,c_Groups_Ouminus__class_Ouminus(U_2078,U_2080),c_Polynomial_OpCons(U_2078,c_Groups_Oone__class_Oone(U_2078),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2078))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2078,U_2080,U_2079))),U_2079)
& c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2078),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2078)),c_Polynomial_OpCons(U_2078,c_Groups_Ouminus__class_Ouminus(U_2078,U_2080),c_Polynomial_OpCons(U_2078,c_Groups_Oone__class_Oone(U_2078),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2078))))),c_Polynomial_Oorder(U_2078,U_2080,U_2079)),U_2079) )
| U_2079 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2078))
| ~ class_Rings_Oidom(U_2078) ),
inference(variable_rename,[status(thm)],[f_656_1]) ).
fof(f_656_3,plain,
( ! [U_2078,U_2080,U_2079] :
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2078),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2078)),c_Polynomial_OpCons(U_2078,c_Groups_Ouminus__class_Ouminus(U_2078,U_2080),c_Polynomial_OpCons(U_2078,c_Groups_Oone__class_Oone(U_2078),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2078))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2078,U_2080,U_2079))),U_2079)
| ~ sP230(U_2078,U_2080,U_2079) )
& ! [U_2078,U_2080,U_2079] :
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2078),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2078)),c_Polynomial_OpCons(U_2078,c_Groups_Ouminus__class_Ouminus(U_2078,U_2080),c_Polynomial_OpCons(U_2078,c_Groups_Oone__class_Oone(U_2078),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2078))))),c_Polynomial_Oorder(U_2078,U_2080,U_2079)),U_2079)
| ~ sP230(U_2078,U_2080,U_2079) )
& ! [U_2078,U_2080,U_2079] :
( sP230(U_2078,U_2080,U_2079)
| U_2079 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2078))
| ~ class_Rings_Oidom(U_2078) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP230])],[f_656_2]) ).
cnf(f_656_4,plain,
( sP230(U_2078,U_2080,U_2079)
| U_2079 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2078))
| ~ class_Rings_Oidom(U_2078) ),
inference(clausify,[status(thm)],[f_656_3]) ).
cnf(f_656_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2078),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2078)),c_Polynomial_OpCons(U_2078,c_Groups_Ouminus__class_Ouminus(U_2078,U_2080),c_Polynomial_OpCons(U_2078,c_Groups_Oone__class_Oone(U_2078),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2078))))),c_Polynomial_Oorder(U_2078,U_2080,U_2079)),U_2079)
| ~ sP230(U_2078,U_2080,U_2079) ),
inference(clausify,[status(thm)],[f_656_3]) ).
cnf(f_656_6,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2078),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2078)),c_Polynomial_OpCons(U_2078,c_Groups_Ouminus__class_Ouminus(U_2078,U_2080),c_Polynomial_OpCons(U_2078,c_Groups_Oone__class_Oone(U_2078),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2078))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2078,U_2080,U_2079))),U_2079)
| ~ sP230(U_2078,U_2080,U_2079) ),
inference(clausify,[status(thm)],[f_656_3]) ).
fof(f_657_1,plain,
! [V_a,V_p,T_a] :
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(T_a)),c_Polynomial_OpCons(T_a,c_Groups_Ouminus__class_Ouminus(T_a,V_a),c_Polynomial_OpCons(T_a,c_Groups_Oone__class_Oone(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))))),c_Nat_OSuc(c_Polynomial_Oorder(T_a,V_a,V_p))),V_p)
| V_p = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_order__2]) ).
fof(f_657_2,plain,
! [U_2083,U_2082,U_2081] :
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2081),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2081)),c_Polynomial_OpCons(U_2081,c_Groups_Ouminus__class_Ouminus(U_2081,U_2083),c_Polynomial_OpCons(U_2081,c_Groups_Oone__class_Oone(U_2081),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2081))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2081,U_2083,U_2082))),U_2082)
| U_2082 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2081))
| ~ class_Rings_Oidom(U_2081) ),
inference(variable_rename,[status(thm)],[f_657_1]) ).
fof(f_657_3,plain,
! [U_2082,U_2081,U_2083] :
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2081),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2081)),c_Polynomial_OpCons(U_2081,c_Groups_Ouminus__class_Ouminus(U_2081,U_2083),c_Polynomial_OpCons(U_2081,c_Groups_Oone__class_Oone(U_2081),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2081))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2081,U_2083,U_2082))),U_2082)
| U_2082 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2081))
| ~ class_Rings_Oidom(U_2081) ),
inference(definitional_conversion,[status(esa)],[f_657_2]) ).
cnf(f_657_4,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Polynomial_Opoly(U_2081),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Polynomial_Opoly(U_2081)),c_Polynomial_OpCons(U_2081,c_Groups_Ouminus__class_Ouminus(U_2081,U_2083),c_Polynomial_OpCons(U_2081,c_Groups_Oone__class_Oone(U_2081),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2081))))),c_Nat_OSuc(c_Polynomial_Oorder(U_2081,U_2083,U_2082))),U_2082)
| U_2082 = c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_2081))
| ~ class_Rings_Oidom(U_2081) ),
inference(clausify,[status(thm)],[f_657_3]) ).
fof(f_658_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_658_2,plain,
! [U_2084] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2084,c_Nat_OSuc(U_2084)),
inference(variable_rename,[status(thm)],[f_658_1]) ).
fof(f_658_3,plain,
! [U_2084] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2084,c_Nat_OSuc(U_2084)),
inference(definitional_conversion,[status(esa)],[f_658_2]) ).
cnf(f_658_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2084,c_Nat_OSuc(U_2084)),
inference(clausify,[status(thm)],[f_658_3]) ).
fof(f_659_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_659_2,plain,
! [U_2086,U_2085] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2085),c_Nat_OSuc(U_2086))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2085,U_2086) ),
inference(variable_rename,[status(thm)],[f_659_1]) ).
fof(f_659_3,plain,
! [U_2085,U_2086] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2085),c_Nat_OSuc(U_2086))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2085,U_2086) ),
inference(definitional_conversion,[status(esa)],[f_659_2]) ).
cnf(f_659_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2085),c_Nat_OSuc(U_2086))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2085,U_2086) ),
inference(clausify,[status(thm)],[f_659_3]) ).
fof(f_660_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_660_2,plain,
! [U_2087] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_2087)),
inference(variable_rename,[status(thm)],[f_660_1]) ).
fof(f_660_3,plain,
! [U_2087] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_2087)),
inference(definitional_conversion,[status(esa)],[f_660_2]) ).
cnf(f_660_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Nat_OSuc(U_2087)),
inference(clausify,[status(thm)],[f_660_3]) ).
fof(f_661_1,plain,
! [V_k] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k),
inference(fof_nnf,[status(thm)],[fact_dvd__1__left]) ).
fof(f_661_2,plain,
! [U_2088] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2088),
inference(variable_rename,[status(thm)],[f_661_1]) ).
fof(f_661_3,plain,
! [U_2088] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2088),
inference(definitional_conversion,[status(esa)],[f_661_2]) ).
cnf(f_661_4,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2088),
inference(clausify,[status(thm)],[f_661_3]) ).
fof(f_662_1,plain,
! [V_n,V_m] :
( V_m = V_n
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__nonneg]) ).
fof(f_662_2,plain,
! [U_2090,U_2089] :
( U_2089 = U_2090
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2090,U_2089)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2089,U_2090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2089) ),
inference(variable_rename,[status(thm)],[f_662_1]) ).
fof(f_662_3,plain,
! [U_2089,U_2090] :
( U_2089 = U_2090
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2090,U_2089)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2089,U_2090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2089) ),
inference(definitional_conversion,[status(esa)],[f_662_2]) ).
cnf(f_662_4,plain,
( U_2089 = U_2090
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2090,U_2089)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2089,U_2090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2090)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2089) ),
inference(clausify,[status(thm)],[f_662_3]) ).
fof(f_663_1,plain,
! [V_t_2,V_ma_2,V_k_2] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ma_2,V_t_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2)) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_t_2))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_ma_2,V_t_2) ) )
| V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mono]) ).
fof(f_663_2,plain,
! [U_2093,U_2092,U_2091] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2092,U_2093)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2093)) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2093))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2092,U_2093) ) )
| U_2091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_663_1]) ).
fof(f_663_3,plain,
( ! [U_2091,U_2092,U_2093] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2092,U_2093)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2093))
| ~ sP231(U_2091,U_2092,U_2093) )
& ! [U_2091,U_2092,U_2093] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2093))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2092,U_2093)
| ~ sP231(U_2091,U_2092,U_2093) )
& ! [U_2091,U_2092,U_2093] :
( sP231(U_2091,U_2092,U_2093)
| U_2091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231])],[f_663_2]) ).
cnf(f_663_4,plain,
( sP231(U_2091,U_2092,U_2093)
| U_2091 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_663_3]) ).
cnf(f_663_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2093))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2092,U_2093)
| ~ sP231(U_2091,U_2092,U_2093) ),
inference(clausify,[status(thm)],[f_663_3]) ).
cnf(f_663_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2092,U_2093)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2091),U_2093))
| ~ sP231(U_2091,U_2092,U_2093) ),
inference(clausify,[status(thm)],[f_663_3]) ).
fof(f_664_1,plain,
! [V_x_2] :
( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_x_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_x_2,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_zdvd1__eq]) ).
fof(f_664_2,plain,
! [U_2094] :
( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2094,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2094) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2094) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2094,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_664_1]) ).
fof(f_664_3,plain,
( ! [U_2096] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2096,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2096) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ! [U_2095] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2095) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2095,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_664_2]) ).
fof(f_664_4,plain,
( ! [U_2096] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2096,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2096) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ! [U_2095] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2095) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2095,c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa)],[f_664_3]) ).
cnf(f_664_5,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2095) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2095,c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_664_4]) ).
cnf(f_664_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2096,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2096) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_664_4]) ).
fof(f_665_1,plain,
! [V_ma_2,V_n_2,V_k_2] :
( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,V_n_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_n_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_ma_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__reduce]) ).
fof(f_665_2,plain,
! [U_2099,U_2098,U_2097] :
( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2097,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2097),U_2099)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2097,U_2098) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2097,U_2098)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2097,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2098,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2097),U_2099))) ) ),
inference(variable_rename,[status(thm)],[f_665_1]) ).
fof(f_665_3,plain,
( ! [U_2105,U_2103,U_2101] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2101,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2101),U_2105)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2101,U_2103) )
& ! [U_2104,U_2102,U_2100] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2100,U_2102)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2100,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2100),U_2104))) ) ),
inference(miniscope,[status(thm)],[f_665_2]) ).
fof(f_665_4,plain,
( ! [U_2103,U_2105,U_2101] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2101,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2101),U_2105)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2101,U_2103) )
& ! [U_2104,U_2100,U_2102] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2100,U_2102)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2100,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2100),U_2104))) ) ),
inference(definitional_conversion,[status(esa)],[f_665_3]) ).
cnf(f_665_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2100,U_2102)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2100,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2102,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2100),U_2104))) ),
inference(clausify,[status(thm)],[f_665_4]) ).
cnf(f_665_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2101,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2103,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2101),U_2105)))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2101,U_2103) ),
inference(clausify,[status(thm)],[f_665_4]) ).
fof(f_666_1,plain,
! [V_ca_2,V_t_2,V_x_2,V_d_2,V_a_2] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2)) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ca_2),V_d_2)),V_t_2))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x_2,V_t_2)) ) )
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_d_2) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__period]) ).
fof(f_666_2,plain,
! [U_2110,U_2109,U_2108,U_2107,U_2106] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,U_2109))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2110),U_2107)),U_2109)) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2110),U_2107)),U_2109))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,U_2109)) ) )
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,U_2107) ),
inference(variable_rename,[status(thm)],[f_666_1]) ).
fof(f_666_3,plain,
( ! [U_2106,U_2107,U_2108,U_2109,U_2110] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,U_2109))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2110),U_2107)),U_2109))
| ~ sP232(U_2106,U_2107,U_2108,U_2109,U_2110) )
& ! [U_2106,U_2107,U_2108,U_2109,U_2110] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2110),U_2107)),U_2109))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,U_2109))
| ~ sP232(U_2106,U_2107,U_2108,U_2109,U_2110) )
& ! [U_2106,U_2107,U_2108,U_2109,U_2110] :
( sP232(U_2106,U_2107,U_2108,U_2109,U_2110)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,U_2107) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP232])],[f_666_2]) ).
cnf(f_666_4,plain,
( sP232(U_2106,U_2107,U_2108,U_2109,U_2110)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,U_2107) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2110),U_2107)),U_2109))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,U_2109))
| ~ sP232(U_2106,U_2107,U_2108,U_2109,U_2110) ),
inference(clausify,[status(thm)],[f_666_3]) ).
cnf(f_666_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,U_2109))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2106,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2108,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2110),U_2107)),U_2109))
| ~ sP232(U_2106,U_2107,U_2108,U_2109,U_2110) ),
inference(clausify,[status(thm)],[f_666_3]) ).
fof(f_667_1,plain,
! [V_b,V_a] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_a) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_b)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_b,V_a)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__antisym__abs]) ).
fof(f_667_2,plain,
! [U_2112,U_2111] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2111) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2112)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2112,U_2111)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2111,U_2112) ),
inference(variable_rename,[status(thm)],[f_667_1]) ).
fof(f_667_3,plain,
! [U_2112,U_2111] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2111) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2112)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2112,U_2111)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2111,U_2112) ),
inference(definitional_conversion,[status(esa)],[f_667_2]) ).
cnf(f_667_4,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2111) = c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2112)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2112,U_2111)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2111,U_2112) ),
inference(clausify,[status(thm)],[f_667_3]) ).
fof(f_668_1,plain,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_m,V_n)
| V_k = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_m),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel]) ).
fof(f_668_2,plain,
! [U_2115,U_2114,U_2113] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2114,U_2115)
| U_2113 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2113),U_2114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2113),U_2115)) ),
inference(variable_rename,[status(thm)],[f_668_1]) ).
fof(f_668_3,plain,
! [U_2115,U_2113,U_2114] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2114,U_2115)
| U_2113 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2113),U_2114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2113),U_2115)) ),
inference(definitional_conversion,[status(esa)],[f_668_2]) ).
cnf(f_668_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2114,U_2115)
| U_2113 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2113),U_2114),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2113),U_2115)) ),
inference(clausify,[status(thm)],[f_668_3]) ).
fof(f_669_1,plain,
! [V_n,V_z] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_n)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_z,V_n) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__imp__le]) ).
fof(f_669_2,plain,
! [U_2117,U_2116] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2116,U_2117)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2117)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2116,U_2117) ),
inference(variable_rename,[status(thm)],[f_669_1]) ).
fof(f_669_3,plain,
! [U_2116,U_2117] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2116,U_2117)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2117)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2116,U_2117) ),
inference(definitional_conversion,[status(esa)],[f_669_2]) ).
cnf(f_669_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2116,U_2117)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2117)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2116,U_2117) ),
inference(clausify,[status(thm)],[f_669_3]) ).
fof(f_670_1,plain,
! [V_n,V_m] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_n,V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_m,V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_m) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__not__zless]) ).
fof(f_670_2,plain,
! [U_2119,U_2118] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2119,U_2118)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2118,U_2119)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2118) ),
inference(variable_rename,[status(thm)],[f_670_1]) ).
fof(f_670_3,plain,
! [U_2118,U_2119] :
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2119,U_2118)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2118,U_2119)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2118) ),
inference(definitional_conversion,[status(esa)],[f_670_2]) ).
cnf(f_670_4,plain,
( ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2119,U_2118)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2118,U_2119)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2118) ),
inference(clausify,[status(thm)],[f_670_3]) ).
fof(f_671_1,plain,
! [V_d,V_i] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_d),c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d,V_i)
| V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_dvd__imp__le__int]) ).
fof(f_671_2,plain,
! [U_2121,U_2120] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2121),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2120))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2121,U_2120)
| U_2120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_671_1]) ).
fof(f_671_3,plain,
! [U_2120,U_2121] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2121),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2120))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2121,U_2120)
| U_2120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_671_2]) ).
cnf(f_671_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2121),c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2120))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2121,U_2120)
| U_2120 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_671_3]) ).
fof(f_672_1,plain,
! [V_n_2,V_ma_2] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2),V_ma_2)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2),V_ma_2) ) )
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__mult__cancel1]) ).
fof(f_672_2,plain,
! [U_2123,U_2122] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2122),U_2123),U_2122)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2123) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2123) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2122),U_2123),U_2122) ) )
| U_2122 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_672_1]) ).
fof(f_672_3,plain,
( ! [U_2122,U_2123] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2122),U_2123),U_2122)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2123) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP233(U_2122,U_2123) )
& ! [U_2122,U_2123] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2123) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2122),U_2123),U_2122)
| ~ sP233(U_2122,U_2123) )
& ! [U_2122,U_2123] :
( sP233(U_2122,U_2123)
| U_2122 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP233])],[f_672_2]) ).
cnf(f_672_4,plain,
( sP233(U_2122,U_2123)
| U_2122 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_672_3]) ).
cnf(f_672_5,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2123) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2122),U_2123),U_2122)
| ~ sP233(U_2122,U_2123) ),
inference(clausify,[status(thm)],[f_672_3]) ).
cnf(f_672_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2122),U_2123),U_2122)
| c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2123) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP233(U_2122,U_2123) ),
inference(clausify,[status(thm)],[f_672_3]) ).
fof(f_673_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_673_2,plain,
! [U_2125,U_2124] : 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_2124)),U_2125)),
inference(variable_rename,[status(thm)],[f_673_1]) ).
fof(f_673_3,plain,
! [U_2124,U_2125] : 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_2124)),U_2125)),
inference(definitional_conversion,[status(esa)],[f_673_2]) ).
cnf(f_673_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_2124)),U_2125)),
inference(clausify,[status(thm)],[f_673_3]) ).
fof(f_674_1,plain,
! [V_ma_2,V_x_2] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_2) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( V_x_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( V_x_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_ma_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_674_2,plain,
! [U_2127,U_2126] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2126),U_2127) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_2126 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2127 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( U_2126 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2127 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2126),U_2127) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_674_1]) ).
fof(f_674_3,plain,
( ! [U_2131,U_2129] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2129),U_2131) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( U_2129 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2131 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2130,U_2128] :
( U_2128 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2128),U_2130) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_674_2]) ).
fof(f_674_4,plain,
( ! [U_2131,U_2129] :
( U_2129 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP234(U_2131,U_2129) )
& ! [U_2131,U_2129] :
( U_2131 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP234(U_2131,U_2129) )
& ! [U_2131,U_2129] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2129),U_2131) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP234(U_2131,U_2129) )
& ! [U_2130,U_2128] :
( U_2128 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2128),U_2130) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234])],[f_674_3]) ).
cnf(f_674_5,plain,
( U_2128 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2130 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2128),U_2130) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_674_4]) ).
cnf(f_674_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2129),U_2131) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP234(U_2131,U_2129) ),
inference(clausify,[status(thm)],[f_674_4]) ).
cnf(f_674_7,plain,
( U_2131 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP234(U_2131,U_2129) ),
inference(clausify,[status(thm)],[f_674_4]) ).
cnf(f_674_8,plain,
( U_2129 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP234(U_2131,U_2129) ),
inference(clausify,[status(thm)],[f_674_4]) ).
fof(f_675_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_675_2,plain,
! [U_2132] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2132) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_675_1]) ).
fof(f_675_3,plain,
! [U_2132] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2132) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_675_2]) ).
cnf(f_675_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_2132) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_675_3]) ).
fof(f_676_1,plain,
! [V_i] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_i) ) )
| V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(fof_nnf,[status(thm)],[fact_zsgn__def]) ).
fof(f_676_2,plain,
! [U_2133] :
( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2133) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2133) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2133) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2133) ) )
| U_2133 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2133) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2133 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(variable_rename,[status(thm)],[f_676_1]) ).
fof(f_676_3,plain,
( ! [U_2135] :
( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2135) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2135) )
& ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2135) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2135) ) )
| U_2135 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2134] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2134) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2134 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(miniscope,[status(thm)],[f_676_2]) ).
fof(f_676_4,plain,
( ! [U_2135] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2135) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2135)
| ~ sP235(U_2135) )
& ! [U_2135] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2135) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2135)
| ~ sP235(U_2135) )
& ! [U_2135] :
( sP235(U_2135)
| U_2135 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2134] :
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2134) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2134 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235])],[f_676_3]) ).
cnf(f_676_5,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2134) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| U_2134 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_676_4]) ).
cnf(f_676_6,plain,
( sP235(U_2135)
| U_2135 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_676_4]) ).
cnf(f_676_7,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2135) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2135)
| ~ sP235(U_2135) ),
inference(clausify,[status(thm)],[f_676_4]) ).
cnf(f_676_8,plain,
( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2135) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint))
| c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2135)
| ~ sP235(U_2135) ),
inference(clausify,[status(thm)],[f_676_4]) ).
fof(f_677_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_677_2,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_677_1]) ).
cnf(f_677_3,plain,
c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_677_2]) ).
fof(f_678_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_678_2,plain,
! [U_2136] : 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_2136),U_2136) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_678_1]) ).
fof(f_678_3,plain,
! [U_2136] : 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_2136),U_2136) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_678_2]) ).
cnf(f_678_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_2136),U_2136) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_678_3]) ).
fof(f_679_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_679_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_679_1]) ).
cnf(f_679_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_679_2]) ).
fof(f_680_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_680_2,plain,
! [U_2137] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2137) = U_2137,
inference(variable_rename,[status(thm)],[f_680_1]) ).
fof(f_680_3,plain,
! [U_2137] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2137) = U_2137,
inference(definitional_conversion,[status(esa)],[f_680_2]) ).
cnf(f_680_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2137) = U_2137,
inference(clausify,[status(thm)],[f_680_3]) ).
fof(f_681_1,plain,
! [V_z_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2) ) ),
inference(fof_nnf,[status(thm)],[fact_int__one__le__iff__zero__less]) ).
fof(f_681_2,plain,
! [U_2138] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2138)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2138) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2138)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2138) ) ),
inference(variable_rename,[status(thm)],[f_681_1]) ).
fof(f_681_3,plain,
( ! [U_2140] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2140)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2140) )
& ! [U_2139] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2139)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2139) ) ),
inference(miniscope,[status(thm)],[f_681_2]) ).
fof(f_681_4,plain,
( ! [U_2140] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2140)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2140) )
& ! [U_2139] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2139)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2139) ) ),
inference(definitional_conversion,[status(esa)],[f_681_3]) ).
cnf(f_681_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2139)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2139) ),
inference(clausify,[status(thm)],[f_681_4]) ).
cnf(f_681_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2140)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2140) ),
inference(clausify,[status(thm)],[f_681_4]) ).
fof(f_682_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_682_2,plain,
! [U_2141] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2141,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2141,
inference(variable_rename,[status(thm)],[f_682_1]) ).
fof(f_682_3,plain,
! [U_2141] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2141,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2141,
inference(definitional_conversion,[status(esa)],[f_682_2]) ).
cnf(f_682_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2141,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2141,
inference(clausify,[status(thm)],[f_682_3]) ).
fof(f_683_1,plain,
! [V_w_2,V_z_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2)
| V_z_2 = V_w_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) )
& ( ( V_z_2 != V_w_2
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_2,V_w_2) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,V_w_2) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__le]) ).
fof(f_683_2,plain,
! [U_2143,U_2142] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2142,U_2143)
| U_2142 = U_2143
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2142,U_2143) )
& ( ( U_2142 != U_2143
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2142,U_2143) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2142,U_2143) ) ),
inference(variable_rename,[status(thm)],[f_683_1]) ).
fof(f_683_3,plain,
( ! [U_2147,U_2145] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2145,U_2147)
| U_2145 = U_2147
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2145,U_2147) )
& ! [U_2146,U_2144] :
( ( U_2144 != U_2146
& c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2144,U_2146) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2144,U_2146) ) ),
inference(miniscope,[status(thm)],[f_683_2]) ).
fof(f_683_4,plain,
( ! [U_2144,U_2146] :
( U_2144 != U_2146
| ~ sP236(U_2144,U_2146) )
& ! [U_2144,U_2146] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2144,U_2146)
| ~ sP236(U_2144,U_2146) )
& ! [U_2147,U_2145] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2145,U_2147)
| U_2145 = U_2147
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2145,U_2147) )
& ! [U_2144,U_2146] :
( sP236(U_2144,U_2146)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2144,U_2146) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236])],[f_683_3]) ).
cnf(f_683_5,plain,
( sP236(U_2144,U_2146)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2144,U_2146) ),
inference(clausify,[status(thm)],[f_683_4]) ).
cnf(f_683_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2145,U_2147)
| U_2145 = U_2147
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2145,U_2147) ),
inference(clausify,[status(thm)],[f_683_4]) ).
cnf(f_683_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2144,U_2146)
| ~ sP236(U_2144,U_2146) ),
inference(clausify,[status(thm)],[f_683_4]) ).
cnf(f_683_8,plain,
( U_2144 != U_2146
| ~ sP236(U_2144,U_2146) ),
inference(clausify,[status(thm)],[f_683_4]) ).
fof(f_684_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__add1__eq__le]) ).
fof(f_684_2,plain,
! [U_2149,U_2148] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2148,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2149,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2148,U_2149) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2148,U_2149)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2148,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2149,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_684_1]) ).
fof(f_684_3,plain,
( ! [U_2153,U_2151] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2151,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2153,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2151,U_2153) )
& ! [U_2152,U_2150] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2150,U_2152)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2150,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2152,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_684_2]) ).
fof(f_684_4,plain,
( ! [U_2153,U_2151] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2151,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2153,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2151,U_2153) )
& ! [U_2150,U_2152] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2150,U_2152)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2150,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2152,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_684_3]) ).
cnf(f_684_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2150,U_2152)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2150,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2152,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_684_4]) ).
cnf(f_684_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2151,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2153,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2151,U_2153) ),
inference(clausify,[status(thm)],[f_684_4]) ).
fof(f_685_1,plain,
! [V_z_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint))
| V_z_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_z_2),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_zabs__less__one__iff]) ).
fof(f_685_2,plain,
! [U_2154] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2154),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_2154 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ( U_2154 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2154),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_685_1]) ).
fof(f_685_3,plain,
( ! [U_2156] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2156),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_2156 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2155] :
( U_2155 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2155),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_685_2]) ).
fof(f_685_4,plain,
( ! [U_2156] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2156),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_2156 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
& ! [U_2155] :
( U_2155 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2155),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa)],[f_685_3]) ).
cnf(f_685_5,plain,
( U_2155 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2155),c_Groups_Oone__class_Oone(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_685_4]) ).
cnf(f_685_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2156),c_Groups_Oone__class_Oone(tc_Int_Oint))
| U_2156 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_685_4]) ).
fof(f_686_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_2,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2) ) ),
inference(fof_nnf,[status(thm)],[fact_add1__zle__eq]) ).
fof(f_686_2,plain,
! [U_2158,U_2157] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2157,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2158)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2157,U_2158) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2157,U_2158)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2157,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2158) ) ),
inference(variable_rename,[status(thm)],[f_686_1]) ).
fof(f_686_3,plain,
( ! [U_2162,U_2160] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2160,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2162)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2160,U_2162) )
& ! [U_2161,U_2159] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2159,U_2161)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2159,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2161) ) ),
inference(miniscope,[status(thm)],[f_686_2]) ).
fof(f_686_4,plain,
( ! [U_2160,U_2162] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2160,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2162)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2160,U_2162) )
& ! [U_2159,U_2161] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2159,U_2161)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2159,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2161) ) ),
inference(definitional_conversion,[status(esa)],[f_686_3]) ).
cnf(f_686_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2159,U_2161)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2159,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2161) ),
inference(clausify,[status(thm)],[f_686_4]) ).
cnf(f_686_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2160,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2162)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2160,U_2162) ),
inference(clausify,[status(thm)],[f_686_4]) ).
fof(f_687_1,plain,
! [V_z_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z_2),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_odd__less__0]) ).
fof(f_687_2,plain,
! [U_2163] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2163),U_2163),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2163,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2163,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2163),U_2163),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_687_1]) ).
fof(f_687_3,plain,
( ! [U_2165] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2165),U_2165),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2165,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2164] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2164,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2164),U_2164),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_687_2]) ).
fof(f_687_4,plain,
( ! [U_2165] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2165),U_2165),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2165,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2164] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2164,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2164),U_2164),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa)],[f_687_3]) ).
cnf(f_687_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2164,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2164),U_2164),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_687_4]) ).
cnf(f_687_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2165),U_2165),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2165,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_687_4]) ).
fof(f_688_1,plain,
! [V_z] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) ),
inference(fof_nnf,[status(thm)],[fact_le__imp__0__less]) ).
fof(f_688_2,plain,
! [U_2166] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2166))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2166) ),
inference(variable_rename,[status(thm)],[f_688_1]) ).
fof(f_688_3,plain,
! [U_2166] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2166))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2166) ),
inference(definitional_conversion,[status(esa)],[f_688_2]) ).
cnf(f_688_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2166))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2166) ),
inference(clausify,[status(thm)],[f_688_3]) ).
fof(f_689_1,plain,
! [V_n_2,V_ma_2] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_n_2 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| V_ma_2 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& V_ma_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_ma_2),V_n_2) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_pos__zmult__eq__1__iff]) ).
fof(f_689_2,plain,
! [U_2168,U_2167] :
( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2167),U_2168) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2168 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2167 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
& ( ( U_2168 = c_Groups_Oone__class_Oone(tc_Int_Oint)
& U_2167 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2167),U_2168) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2167) ),
inference(variable_rename,[status(thm)],[f_689_1]) ).
fof(f_689_3,plain,
( ! [U_2167,U_2168] :
( U_2168 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP237(U_2167,U_2168) )
& ! [U_2167,U_2168] :
( U_2167 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP237(U_2167,U_2168) )
& ! [U_2167,U_2168] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2167),U_2168) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2168 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2167 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP238(U_2167,U_2168) )
& ! [U_2167,U_2168] :
( sP237(U_2167,U_2168)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2167),U_2168) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP238(U_2167,U_2168) )
& ! [U_2167,U_2168] :
( sP238(U_2167,U_2168)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2167) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP237,sP238])],[f_689_2]) ).
cnf(f_689_4,plain,
( sP238(U_2167,U_2168)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2167) ),
inference(clausify,[status(thm)],[f_689_3]) ).
cnf(f_689_5,plain,
( sP237(U_2167,U_2168)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2167),U_2168) != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP238(U_2167,U_2168) ),
inference(clausify,[status(thm)],[f_689_3]) ).
cnf(f_689_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2167),U_2168) = c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2168 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| U_2167 != c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP238(U_2167,U_2168) ),
inference(clausify,[status(thm)],[f_689_3]) ).
cnf(f_689_7,plain,
( U_2167 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP237(U_2167,U_2168) ),
inference(clausify,[status(thm)],[f_689_3]) ).
cnf(f_689_8,plain,
( U_2168 = c_Groups_Oone__class_Oone(tc_Int_Oint)
| ~ sP237(U_2167,U_2168) ),
inference(clausify,[status(thm)],[f_689_3]) ).
fof(f_690_1,plain,
! [V_z,V_w] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w,V_z) ),
inference(fof_nnf,[status(thm)],[fact_zless__imp__add1__zle]) ).
fof(f_690_2,plain,
! [U_2170,U_2169] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2169,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2170)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2169,U_2170) ),
inference(variable_rename,[status(thm)],[f_690_1]) ).
fof(f_690_3,plain,
! [U_2169,U_2170] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2169,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2170)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2169,U_2170) ),
inference(definitional_conversion,[status(esa)],[f_690_2]) ).
cnf(f_690_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2169,c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2170)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2169,U_2170) ),
inference(clausify,[status(thm)],[f_690_3]) ).
fof(f_691_1,plain,
! [V_k,V_j,V_i] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_i),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_j))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,V_j) ),
inference(fof_nnf,[status(thm)],[fact_zmult__zless__mono2]) ).
fof(f_691_2,plain,
! [U_2173,U_2172,U_2171] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2173),U_2171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2173),U_2172))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2173)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2171,U_2172) ),
inference(variable_rename,[status(thm)],[f_691_1]) ).
fof(f_691_3,plain,
! [U_2171,U_2173,U_2172] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2173),U_2171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2173),U_2172))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2173)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2171,U_2172) ),
inference(definitional_conversion,[status(esa)],[f_691_2]) ).
cnf(f_691_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2173),U_2171),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2173),U_2172))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2173)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2171,U_2172) ),
inference(clausify,[status(thm)],[f_691_3]) ).
fof(f_692_1,plain,
! [V_z,V_z_H,V_w,V_w_H] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w_H,V_z_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_z_H,V_z)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_H,V_w) ),
inference(fof_nnf,[status(thm)],[fact_zadd__zless__mono]) ).
fof(f_692_2,plain,
! [U_2177,U_2176,U_2175,U_2174] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2174,U_2176),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2175,U_2177))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2176,U_2177)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2174,U_2175) ),
inference(variable_rename,[status(thm)],[f_692_1]) ).
fof(f_692_3,plain,
! [U_2174,U_2177,U_2175,U_2176] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2174,U_2176),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2175,U_2177))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2176,U_2177)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2174,U_2175) ),
inference(definitional_conversion,[status(esa)],[f_692_2]) ).
cnf(f_692_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2174,U_2176),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2175,U_2177))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2176,U_2177)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2174,U_2175) ),
inference(clausify,[status(thm)],[f_692_3]) ).
fof(f_693_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_693_2,plain,
! [U_2179,U_2178] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2178) = 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_2178),U_2179)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(variable_rename,[status(thm)],[f_693_1]) ).
fof(f_693_3,plain,
! [U_2178,U_2179] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2178) = 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_2178),U_2179)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(definitional_conversion,[status(esa)],[f_693_2]) ).
cnf(f_693_4,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2178) = 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_2178),U_2179)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
inference(clausify,[status(thm)],[f_693_3]) ).
fof(f_694_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_694_2,plain,
! [U_2182,U_2181,U_2180] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2180,U_2182),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2181,U_2182))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2180,U_2181) ),
inference(variable_rename,[status(thm)],[f_694_1]) ).
fof(f_694_3,plain,
! [U_2180,U_2181,U_2182] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2180,U_2182),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2181,U_2182))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2180,U_2181) ),
inference(definitional_conversion,[status(esa)],[f_694_2]) ).
cnf(f_694_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2180,U_2182),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2181,U_2182))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2180,U_2181) ),
inference(clausify,[status(thm)],[f_694_3]) ).
fof(f_695_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_n_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_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_695_2,plain,
! [U_2185,U_2184,U_2183] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2183)),U_2184) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2183)),U_2185)
| U_2184 != U_2185 )
& ( U_2184 = U_2185
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2183)),U_2184) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2183)),U_2185) ) ),
inference(variable_rename,[status(thm)],[f_695_1]) ).
fof(f_695_3,plain,
( ! [U_2191,U_2189] :
( ! [U_2187] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2187)),U_2189) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2187)),U_2191)
| U_2189 != U_2191 )
& ! [U_2190,U_2188] :
( ! [U_2186] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2186)),U_2188) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2186)),U_2190)
| U_2188 = U_2190 ) ),
inference(miniscope,[status(thm)],[f_695_2]) ).
fof(f_695_4,plain,
( ! [U_2187,U_2189,U_2191] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2187)),U_2189) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2187)),U_2191)
| U_2189 != U_2191 )
& ! [U_2186,U_2190,U_2188] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2186)),U_2188) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2186)),U_2190)
| U_2188 = U_2190 ) ),
inference(definitional_conversion,[status(esa)],[f_695_3]) ).
cnf(f_695_5,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2186)),U_2188) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2186)),U_2190)
| U_2188 = U_2190 ),
inference(clausify,[status(thm)],[f_695_4]) ).
cnf(f_695_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2187)),U_2189) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2187)),U_2191)
| U_2189 != U_2191 ),
inference(clausify,[status(thm)],[f_695_4]) ).
fof(f_696_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_696_2,plain,
! [U_2194,U_2193,U_2192] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2192,U_2193)),U_2194) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2192),U_2194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2193),U_2194)),
inference(variable_rename,[status(thm)],[f_696_1]) ).
fof(f_696_3,plain,
! [U_2192,U_2193,U_2194] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2192,U_2193)),U_2194) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2192),U_2194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2193),U_2194)),
inference(definitional_conversion,[status(esa)],[f_696_2]) ).
cnf(f_696_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2192,U_2193)),U_2194) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2192),U_2194),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2193),U_2194)),
inference(clausify,[status(thm)],[f_696_3]) ).
fof(f_697_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_697_2,plain,
! [U_2197,U_2196,U_2195] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2195),U_2196)),U_2197) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2195),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2196),U_2197)),
inference(variable_rename,[status(thm)],[f_697_1]) ).
fof(f_697_3,plain,
! [U_2195,U_2196,U_2197] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2195),U_2196)),U_2197) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2195),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2196),U_2197)),
inference(definitional_conversion,[status(esa)],[f_697_2]) ).
cnf(f_697_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2195),U_2196)),U_2197) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2195),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2196),U_2197)),
inference(clausify,[status(thm)],[f_697_3]) ).
fof(f_698_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_698_2,plain,
! [U_2199,U_2198] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2198),U_2199) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2198,c_Nat_OSuc(U_2199)),
inference(variable_rename,[status(thm)],[f_698_1]) ).
fof(f_698_3,plain,
! [U_2199,U_2198] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2198),U_2199) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2198,c_Nat_OSuc(U_2199)),
inference(definitional_conversion,[status(esa)],[f_698_2]) ).
cnf(f_698_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2198),U_2199) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2198,c_Nat_OSuc(U_2199)),
inference(clausify,[status(thm)],[f_698_3]) ).
fof(f_699_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_699_2,plain,
! [U_2201,U_2200] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2200),U_2201) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2200,U_2201)),
inference(variable_rename,[status(thm)],[f_699_1]) ).
fof(f_699_3,plain,
! [U_2200,U_2201] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2200),U_2201) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2200,U_2201)),
inference(definitional_conversion,[status(esa)],[f_699_2]) ).
cnf(f_699_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Nat_OSuc(U_2200),U_2201) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2200,U_2201)),
inference(clausify,[status(thm)],[f_699_3]) ).
fof(f_700_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_700_2,plain,
! [U_2204,U_2203,U_2202] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2202),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2203,U_2204)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2202),U_2203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2202),U_2204)),
inference(variable_rename,[status(thm)],[f_700_1]) ).
fof(f_700_3,plain,
! [U_2202,U_2203,U_2204] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2202),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2203,U_2204)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2202),U_2203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2202),U_2204)),
inference(definitional_conversion,[status(esa)],[f_700_2]) ).
cnf(f_700_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2202),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2203,U_2204)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2202),U_2203),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2202),U_2204)),
inference(clausify,[status(thm)],[f_700_3]) ).
fof(f_701_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( V_w_2 != V_z_2
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) ) )
& ( V_w_2 = V_z_2
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zless__add1__eq]) ).
fof(f_701_2,plain,
! [U_2206,U_2205] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2205,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2206,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_2205 != U_2206
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2205,U_2206) ) )
& ( U_2205 = U_2206
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2205,U_2206)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2205,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2206,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_701_1]) ).
fof(f_701_3,plain,
( ! [U_2210,U_2208] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2208,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2210,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ( U_2208 != U_2210
& ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2208,U_2210) ) )
& ! [U_2209,U_2207] :
( U_2207 = U_2209
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2207,U_2209)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2207,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2209,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_701_2]) ).
fof(f_701_4,plain,
( ! [U_2210,U_2208] :
( U_2208 != U_2210
| ~ sP239(U_2210,U_2208) )
& ! [U_2210,U_2208] :
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2208,U_2210)
| ~ sP239(U_2210,U_2208) )
& ! [U_2210,U_2208] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2208,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2210,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| sP239(U_2210,U_2208) )
& ! [U_2207,U_2209] :
( U_2207 = U_2209
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2207,U_2209)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2207,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2209,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP239])],[f_701_3]) ).
cnf(f_701_5,plain,
( U_2207 = U_2209
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2207,U_2209)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2207,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2209,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_701_4]) ).
cnf(f_701_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2208,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2210,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| sP239(U_2210,U_2208) ),
inference(clausify,[status(thm)],[f_701_4]) ).
cnf(f_701_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2208,U_2210)
| ~ sP239(U_2210,U_2208) ),
inference(clausify,[status(thm)],[f_701_4]) ).
cnf(f_701_8,plain,
( U_2208 != U_2210
| ~ sP239(U_2210,U_2208) ),
inference(clausify,[status(thm)],[f_701_4]) ).
fof(f_702_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_702_2,plain,
! [U_2212,U_2211] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,c_Nat_OSuc(U_2212)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,U_2212)),
inference(variable_rename,[status(thm)],[f_702_1]) ).
fof(f_702_3,plain,
! [U_2212,U_2211] : c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,c_Nat_OSuc(U_2212)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,U_2212)),
inference(definitional_conversion,[status(esa)],[f_702_2]) ).
cnf(f_702_4,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,c_Nat_OSuc(U_2212)) = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2211,U_2212)),
inference(clausify,[status(thm)],[f_702_3]) ).
fof(f_703_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_703_2,plain,
! [U_2214,U_2213] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2214,U_2213)
| U_2213 = U_2214
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2213,U_2214) ),
inference(variable_rename,[status(thm)],[f_703_1]) ).
fof(f_703_3,plain,
! [U_2214,U_2213] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2214,U_2213)
| U_2213 = U_2214
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2213,U_2214) ),
inference(definitional_conversion,[status(esa)],[f_703_2]) ).
cnf(f_703_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2214,U_2213)
| U_2213 = U_2214
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2213,U_2214) ),
inference(clausify,[status(thm)],[f_703_3]) ).
fof(f_704_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_704_2,plain,
! [U_2216,U_2215] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2215),U_2216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2216),U_2215),
inference(variable_rename,[status(thm)],[f_704_1]) ).
fof(f_704_3,plain,
! [U_2215,U_2216] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2215),U_2216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2216),U_2215),
inference(definitional_conversion,[status(esa)],[f_704_2]) ).
cnf(f_704_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2215),U_2216) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2216),U_2215),
inference(clausify,[status(thm)],[f_704_3]) ).
fof(f_705_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_705_2,plain,
! [U_2217] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2217),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2217,
inference(variable_rename,[status(thm)],[f_705_1]) ).
fof(f_705_3,plain,
! [U_2217] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2217),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2217,
inference(definitional_conversion,[status(esa)],[f_705_2]) ).
cnf(f_705_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2217),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_2217,
inference(clausify,[status(thm)],[f_705_3]) ).
fof(f_706_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_706_2,plain,
! [U_2218] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2218) = U_2218,
inference(variable_rename,[status(thm)],[f_706_1]) ).
fof(f_706_3,plain,
! [U_2218] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2218) = U_2218,
inference(definitional_conversion,[status(esa)],[f_706_2]) ).
cnf(f_706_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2218) = U_2218,
inference(clausify,[status(thm)],[f_706_3]) ).
fof(f_707_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_707_2,plain,
! [U_2219] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2219),
inference(variable_rename,[status(thm)],[f_707_1]) ).
fof(f_707_3,plain,
! [U_2219] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2219),
inference(definitional_conversion,[status(esa)],[f_707_2]) ).
cnf(f_707_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2219),
inference(clausify,[status(thm)],[f_707_3]) ).
fof(f_708_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_708_2,plain,
! [U_2220] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2220),
inference(variable_rename,[status(thm)],[f_708_1]) ).
fof(f_708_3,plain,
! [U_2220] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2220),
inference(definitional_conversion,[status(esa)],[f_708_2]) ).
cnf(f_708_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2220),
inference(clausify,[status(thm)],[f_708_3]) ).
fof(f_709_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_709_2,plain,
! [U_2221] : c_Nat_OSuc(U_2221) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_709_1]) ).
fof(f_709_3,plain,
! [U_2221] : c_Nat_OSuc(U_2221) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_709_2]) ).
cnf(f_709_4,plain,
c_Nat_OSuc(U_2221) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_709_3]) ).
fof(f_710_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_710_2,plain,
! [U_2222] : c_Nat_OSuc(U_2222) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_710_1]) ).
fof(f_710_3,plain,
! [U_2222] : c_Nat_OSuc(U_2222) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_710_2]) ).
cnf(f_710_4,plain,
c_Nat_OSuc(U_2222) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_710_3]) ).
fof(f_711_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_711_2,plain,
! [U_2223] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2223),
inference(variable_rename,[status(thm)],[f_711_1]) ).
fof(f_711_3,plain,
! [U_2223] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2223),
inference(definitional_conversion,[status(esa)],[f_711_2]) ).
cnf(f_711_4,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != c_Nat_OSuc(U_2223),
inference(clausify,[status(thm)],[f_711_3]) ).
fof(f_712_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_712_2,plain,
! [U_2224] : c_Nat_OSuc(U_2224) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_712_1]) ).
fof(f_712_3,plain,
! [U_2224] : c_Nat_OSuc(U_2224) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_712_2]) ).
cnf(f_712_4,plain,
c_Nat_OSuc(U_2224) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_712_3]) ).
fof(f_713_1,plain,
! [V_n_2,V_ma_2] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq]) ).
fof(f_713_2,plain,
! [U_2226,U_2225] :
( ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2225,U_2226)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2226,c_Nat_OSuc(U_2225)) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2226,c_Nat_OSuc(U_2225))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2225,U_2226) ) ),
inference(variable_rename,[status(thm)],[f_713_1]) ).
fof(f_713_3,plain,
( ! [U_2230,U_2228] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2228,U_2230)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2230,c_Nat_OSuc(U_2228)) )
& ! [U_2229,U_2227] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2229,c_Nat_OSuc(U_2227))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2227,U_2229) ) ),
inference(miniscope,[status(thm)],[f_713_2]) ).
fof(f_713_4,plain,
( ! [U_2230,U_2228] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2228,U_2230)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2230,c_Nat_OSuc(U_2228)) )
& ! [U_2229,U_2227] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2229,c_Nat_OSuc(U_2227))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2227,U_2229) ) ),
inference(definitional_conversion,[status(esa)],[f_713_3]) ).
cnf(f_713_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2229,c_Nat_OSuc(U_2227))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2227,U_2229) ),
inference(clausify,[status(thm)],[f_713_4]) ).
cnf(f_713_6,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2228,U_2230)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2230,c_Nat_OSuc(U_2228)) ),
inference(clausify,[status(thm)],[f_713_4]) ).
fof(f_714_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
| ( V_ma_2 != V_n_2
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) )
& ( V_ma_2 = V_n_2
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq]) ).
fof(f_714_2,plain,
! [U_2232,U_2231] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2231,c_Nat_OSuc(U_2232))
| ( U_2231 != U_2232
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2231,U_2232) ) )
& ( U_2231 = U_2232
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2231,U_2232)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2231,c_Nat_OSuc(U_2232)) ) ),
inference(variable_rename,[status(thm)],[f_714_1]) ).
fof(f_714_3,plain,
( ! [U_2236,U_2234] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2234,c_Nat_OSuc(U_2236))
| ( U_2234 != U_2236
& ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2234,U_2236) ) )
& ! [U_2235,U_2233] :
( U_2233 = U_2235
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2233,U_2235)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2233,c_Nat_OSuc(U_2235)) ) ),
inference(miniscope,[status(thm)],[f_714_2]) ).
fof(f_714_4,plain,
( ! [U_2234,U_2236] :
( U_2234 != U_2236
| ~ sP240(U_2234,U_2236) )
& ! [U_2234,U_2236] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2234,U_2236)
| ~ sP240(U_2234,U_2236) )
& ! [U_2234,U_2236] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2234,c_Nat_OSuc(U_2236))
| sP240(U_2234,U_2236) )
& ! [U_2233,U_2235] :
( U_2233 = U_2235
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2233,U_2235)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2233,c_Nat_OSuc(U_2235)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240])],[f_714_3]) ).
cnf(f_714_5,plain,
( U_2233 = U_2235
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2233,U_2235)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2233,c_Nat_OSuc(U_2235)) ),
inference(clausify,[status(thm)],[f_714_4]) ).
cnf(f_714_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2234,c_Nat_OSuc(U_2236))
| sP240(U_2234,U_2236) ),
inference(clausify,[status(thm)],[f_714_4]) ).
cnf(f_714_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2234,U_2236)
| ~ sP240(U_2234,U_2236) ),
inference(clausify,[status(thm)],[f_714_4]) ).
cnf(f_714_8,plain,
( U_2234 != U_2236
| ~ sP240(U_2234,U_2236) ),
inference(clausify,[status(thm)],[f_714_4]) ).
fof(f_715_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__less__eq]) ).
fof(f_715_2,plain,
! [U_2238,U_2237] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2237),c_Nat_OSuc(U_2238))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2237,U_2238) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2237,U_2238)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2237),c_Nat_OSuc(U_2238)) ) ),
inference(variable_rename,[status(thm)],[f_715_1]) ).
fof(f_715_3,plain,
( ! [U_2242,U_2240] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2240),c_Nat_OSuc(U_2242))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2240,U_2242) )
& ! [U_2241,U_2239] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2239,U_2241)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2239),c_Nat_OSuc(U_2241)) ) ),
inference(miniscope,[status(thm)],[f_715_2]) ).
fof(f_715_4,plain,
( ! [U_2242,U_2240] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2240),c_Nat_OSuc(U_2242))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2240,U_2242) )
& ! [U_2239,U_2241] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2239,U_2241)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2239),c_Nat_OSuc(U_2241)) ) ),
inference(definitional_conversion,[status(esa)],[f_715_3]) ).
cnf(f_715_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2239,U_2241)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2239),c_Nat_OSuc(U_2241)) ),
inference(clausify,[status(thm)],[f_715_4]) ).
cnf(f_715_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2240),c_Nat_OSuc(U_2242))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2240,U_2242) ),
inference(clausify,[status(thm)],[f_715_4]) ).
fof(f_716_1,plain,
! [V_ma_2,V_n_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
| V_n_2 != V_ma_2 )
& ( V_n_2 = V_ma_2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_not__less__less__Suc__eq]) ).
fof(f_716_2,plain,
! [U_2244,U_2243] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2243,c_Nat_OSuc(U_2244))
| U_2243 != U_2244 )
& ( U_2243 = U_2244
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2243,c_Nat_OSuc(U_2244)) ) )
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2243,U_2244) ),
inference(variable_rename,[status(thm)],[f_716_1]) ).
fof(f_716_3,plain,
( ! [U_2244,U_2243] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2243,c_Nat_OSuc(U_2244))
| U_2243 != U_2244
| ~ sP241(U_2244,U_2243) )
& ! [U_2244,U_2243] :
( U_2243 = U_2244
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2243,c_Nat_OSuc(U_2244))
| ~ sP241(U_2244,U_2243) )
& ! [U_2244,U_2243] :
( sP241(U_2244,U_2243)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2243,U_2244) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP241])],[f_716_2]) ).
cnf(f_716_4,plain,
( sP241(U_2244,U_2243)
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2243,U_2244) ),
inference(clausify,[status(thm)],[f_716_3]) ).
cnf(f_716_5,plain,
( U_2243 = U_2244
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2243,c_Nat_OSuc(U_2244))
| ~ sP241(U_2244,U_2243) ),
inference(clausify,[status(thm)],[f_716_3]) ).
cnf(f_716_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2243,c_Nat_OSuc(U_2244))
| U_2243 != U_2244
| ~ sP241(U_2244,U_2243) ),
inference(clausify,[status(thm)],[f_716_3]) ).
fof(f_717_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_717_2,plain,
! [U_2246,U_2245] :
( U_2246 = U_2245
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2245,c_Nat_OSuc(U_2246))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2245,U_2246) ),
inference(variable_rename,[status(thm)],[f_717_1]) ).
fof(f_717_3,plain,
! [U_2245,U_2246] :
( U_2246 = U_2245
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2245,c_Nat_OSuc(U_2246))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2245,U_2246) ),
inference(definitional_conversion,[status(esa)],[f_717_2]) ).
cnf(f_717_4,plain,
( U_2246 = U_2245
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2245,c_Nat_OSuc(U_2246))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2245,U_2246) ),
inference(clausify,[status(thm)],[f_717_3]) ).
fof(f_718_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_718_2,plain,
! [U_2248,U_2247] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2247,c_Nat_OSuc(U_2248))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2247,U_2248) ),
inference(variable_rename,[status(thm)],[f_718_1]) ).
fof(f_718_3,plain,
! [U_2248,U_2247] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2247,c_Nat_OSuc(U_2248))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2247,U_2248) ),
inference(definitional_conversion,[status(esa)],[f_718_2]) ).
cnf(f_718_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2247,c_Nat_OSuc(U_2248))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2247,U_2248) ),
inference(clausify,[status(thm)],[f_718_3]) ).
fof(f_719_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_719_2,plain,
! [U_2250,U_2249] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2249),U_2250)
| c_Nat_OSuc(U_2249) = U_2250
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2249,U_2250) ),
inference(variable_rename,[status(thm)],[f_719_1]) ).
fof(f_719_3,plain,
! [U_2249,U_2250] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2249),U_2250)
| c_Nat_OSuc(U_2249) = U_2250
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2249,U_2250) ),
inference(definitional_conversion,[status(esa)],[f_719_2]) ).
cnf(f_719_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2249),U_2250)
| c_Nat_OSuc(U_2249) = U_2250
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2249,U_2250) ),
inference(clausify,[status(thm)],[f_719_3]) ).
fof(f_720_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_720_2,plain,
! [U_2253,U_2252,U_2251] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2251),U_2253)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2252,U_2253)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2251,U_2252) ),
inference(variable_rename,[status(thm)],[f_720_1]) ).
fof(f_720_3,plain,
! [U_2252,U_2251,U_2253] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2251),U_2253)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2252,U_2253)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2251,U_2252) ),
inference(definitional_conversion,[status(esa)],[f_720_2]) ).
cnf(f_720_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2251),U_2253)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2252,U_2253)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2251,U_2252) ),
inference(clausify,[status(thm)],[f_720_3]) ).
fof(f_721_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_721_2,plain,
! [U_2255,U_2254] :
( U_2254 = U_2255
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2254,U_2255)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2254,c_Nat_OSuc(U_2255)) ),
inference(variable_rename,[status(thm)],[f_721_1]) ).
fof(f_721_3,plain,
! [U_2254,U_2255] :
( U_2254 = U_2255
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2254,U_2255)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2254,c_Nat_OSuc(U_2255)) ),
inference(definitional_conversion,[status(esa)],[f_721_2]) ).
cnf(f_721_4,plain,
( U_2254 = U_2255
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2254,U_2255)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2254,c_Nat_OSuc(U_2255)) ),
inference(clausify,[status(thm)],[f_721_3]) ).
fof(f_722_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_722_2,plain,
! [U_2257,U_2256] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2256,U_2257)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2256),U_2257) ),
inference(variable_rename,[status(thm)],[f_722_1]) ).
fof(f_722_3,plain,
! [U_2257,U_2256] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2256,U_2257)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2256),U_2257) ),
inference(definitional_conversion,[status(esa)],[f_722_2]) ).
cnf(f_722_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2256,U_2257)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2256),U_2257) ),
inference(clausify,[status(thm)],[f_722_3]) ).
fof(f_723_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_723_2,plain,
! [U_2259,U_2258] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2258,U_2259)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2258),c_Nat_OSuc(U_2259)) ),
inference(variable_rename,[status(thm)],[f_723_1]) ).
fof(f_723_3,plain,
! [U_2258,U_2259] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2258,U_2259)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2258),c_Nat_OSuc(U_2259)) ),
inference(definitional_conversion,[status(esa)],[f_723_2]) ).
cnf(f_723_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2258,U_2259)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(U_2258),c_Nat_OSuc(U_2259)) ),
inference(clausify,[status(thm)],[f_723_3]) ).
fof(f_724_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_724_2,plain,
! [U_2260] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2260),U_2260),
inference(variable_rename,[status(thm)],[f_724_1]) ).
fof(f_724_3,plain,
! [U_2260] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2260),U_2260),
inference(definitional_conversion,[status(esa)],[f_724_2]) ).
cnf(f_724_4,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2260),U_2260),
inference(clausify,[status(thm)],[f_724_3]) ).
fof(f_725_1,plain,
! [V_n_2,V_ma_2] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_not__less__eq__eq]) ).
fof(f_725_2,plain,
! [U_2262,U_2261] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2261,U_2262)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2262),U_2261) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2262),U_2261)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2261,U_2262) ) ),
inference(variable_rename,[status(thm)],[f_725_1]) ).
fof(f_725_3,plain,
( ! [U_2266,U_2264] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2264,U_2266)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2266),U_2264) )
& ! [U_2265,U_2263] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2265),U_2263)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2263,U_2265) ) ),
inference(miniscope,[status(thm)],[f_725_2]) ).
fof(f_725_4,plain,
( ! [U_2264,U_2266] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2264,U_2266)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2266),U_2264) )
& ! [U_2263,U_2265] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2265),U_2263)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2263,U_2265) ) ),
inference(definitional_conversion,[status(esa)],[f_725_3]) ).
cnf(f_725_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2265),U_2263)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2263,U_2265) ),
inference(clausify,[status(thm)],[f_725_4]) ).
cnf(f_725_6,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2264,U_2266)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2266),U_2264) ),
inference(clausify,[status(thm)],[f_725_4]) ).
fof(f_726_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
| ( V_ma_2 != c_Nat_OSuc(V_n_2)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ) )
& ( V_ma_2 = c_Nat_OSuc(V_n_2)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__Suc__eq]) ).
fof(f_726_2,plain,
! [U_2268,U_2267] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2267,c_Nat_OSuc(U_2268))
| ( U_2267 != c_Nat_OSuc(U_2268)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2267,U_2268) ) )
& ( U_2267 = c_Nat_OSuc(U_2268)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2267,U_2268)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2267,c_Nat_OSuc(U_2268)) ) ),
inference(variable_rename,[status(thm)],[f_726_1]) ).
fof(f_726_3,plain,
( ! [U_2272,U_2270] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2270,c_Nat_OSuc(U_2272))
| ( U_2270 != c_Nat_OSuc(U_2272)
& ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2270,U_2272) ) )
& ! [U_2271,U_2269] :
( U_2269 = c_Nat_OSuc(U_2271)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2269,U_2271)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2269,c_Nat_OSuc(U_2271)) ) ),
inference(miniscope,[status(thm)],[f_726_2]) ).
fof(f_726_4,plain,
( ! [U_2270,U_2272] :
( U_2270 != c_Nat_OSuc(U_2272)
| ~ sP242(U_2270,U_2272) )
& ! [U_2270,U_2272] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2270,U_2272)
| ~ sP242(U_2270,U_2272) )
& ! [U_2270,U_2272] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2270,c_Nat_OSuc(U_2272))
| sP242(U_2270,U_2272) )
& ! [U_2271,U_2269] :
( U_2269 = c_Nat_OSuc(U_2271)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2269,U_2271)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2269,c_Nat_OSuc(U_2271)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP242])],[f_726_3]) ).
cnf(f_726_5,plain,
( U_2269 = c_Nat_OSuc(U_2271)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2269,U_2271)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2269,c_Nat_OSuc(U_2271)) ),
inference(clausify,[status(thm)],[f_726_4]) ).
cnf(f_726_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2270,c_Nat_OSuc(U_2272))
| sP242(U_2270,U_2272) ),
inference(clausify,[status(thm)],[f_726_4]) ).
cnf(f_726_7,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2270,U_2272)
| ~ sP242(U_2270,U_2272) ),
inference(clausify,[status(thm)],[f_726_4]) ).
cnf(f_726_8,plain,
( U_2270 != c_Nat_OSuc(U_2272)
| ~ sP242(U_2270,U_2272) ),
inference(clausify,[status(thm)],[f_726_4]) ).
fof(f_727_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),c_Nat_OSuc(V_ma_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__mono]) ).
fof(f_727_2,plain,
! [U_2274,U_2273] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2273),c_Nat_OSuc(U_2274))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2273,U_2274) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2273,U_2274)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2273),c_Nat_OSuc(U_2274)) ) ),
inference(variable_rename,[status(thm)],[f_727_1]) ).
fof(f_727_3,plain,
( ! [U_2278,U_2276] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2276),c_Nat_OSuc(U_2278))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2276,U_2278) )
& ! [U_2277,U_2275] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2275,U_2277)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2275),c_Nat_OSuc(U_2277)) ) ),
inference(miniscope,[status(thm)],[f_727_2]) ).
fof(f_727_4,plain,
( ! [U_2278,U_2276] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2276),c_Nat_OSuc(U_2278))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2276,U_2278) )
& ! [U_2275,U_2277] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2275,U_2277)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2275),c_Nat_OSuc(U_2277)) ) ),
inference(definitional_conversion,[status(esa)],[f_727_3]) ).
cnf(f_727_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2275,U_2277)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2275),c_Nat_OSuc(U_2277)) ),
inference(clausify,[status(thm)],[f_727_4]) ).
cnf(f_727_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2276),c_Nat_OSuc(U_2278))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2276,U_2278) ),
inference(clausify,[status(thm)],[f_727_4]) ).
fof(f_728_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_728_2,plain,
! [U_2280,U_2279] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2279,c_Nat_OSuc(U_2280))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2279,U_2280) ),
inference(variable_rename,[status(thm)],[f_728_1]) ).
fof(f_728_3,plain,
! [U_2280,U_2279] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2279,c_Nat_OSuc(U_2280))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2279,U_2280) ),
inference(definitional_conversion,[status(esa)],[f_728_2]) ).
cnf(f_728_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2279,c_Nat_OSuc(U_2280))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2279,U_2280) ),
inference(clausify,[status(thm)],[f_728_3]) ).
fof(f_729_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_729_2,plain,
! [U_2282,U_2281] :
( U_2281 = c_Nat_OSuc(U_2282)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2281,U_2282)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2281,c_Nat_OSuc(U_2282)) ),
inference(variable_rename,[status(thm)],[f_729_1]) ).
fof(f_729_3,plain,
! [U_2282,U_2281] :
( U_2281 = c_Nat_OSuc(U_2282)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2281,U_2282)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2281,c_Nat_OSuc(U_2282)) ),
inference(definitional_conversion,[status(esa)],[f_729_2]) ).
cnf(f_729_4,plain,
( U_2281 = c_Nat_OSuc(U_2282)
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2281,U_2282)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2281,c_Nat_OSuc(U_2282)) ),
inference(clausify,[status(thm)],[f_729_3]) ).
fof(f_730_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_730_2,plain,
! [U_2284,U_2283] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2283,U_2284)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2283),U_2284) ),
inference(variable_rename,[status(thm)],[f_730_1]) ).
fof(f_730_3,plain,
! [U_2284,U_2283] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2283,U_2284)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2283),U_2284) ),
inference(definitional_conversion,[status(esa)],[f_730_2]) ).
cnf(f_730_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2283,U_2284)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2283),U_2284) ),
inference(clausify,[status(thm)],[f_730_3]) ).
fof(f_731_1,plain,
! [V_n] : V_n != c_Nat_OSuc(V_n),
inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).
fof(f_731_2,plain,
! [U_2285] : U_2285 != c_Nat_OSuc(U_2285),
inference(variable_rename,[status(thm)],[f_731_1]) ).
fof(f_731_3,plain,
! [U_2285] : U_2285 != c_Nat_OSuc(U_2285),
inference(definitional_conversion,[status(esa)],[f_731_2]) ).
cnf(f_731_4,plain,
U_2285 != c_Nat_OSuc(U_2285),
inference(clausify,[status(thm)],[f_731_3]) ).
fof(f_732_1,plain,
! [V_n] : c_Nat_OSuc(V_n) != V_n,
inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).
fof(f_732_2,plain,
! [U_2286] : c_Nat_OSuc(U_2286) != U_2286,
inference(variable_rename,[status(thm)],[f_732_1]) ).
fof(f_732_3,plain,
! [U_2286] : c_Nat_OSuc(U_2286) != U_2286,
inference(definitional_conversion,[status(esa)],[f_732_2]) ).
cnf(f_732_4,plain,
c_Nat_OSuc(U_2286) != U_2286,
inference(clausify,[status(thm)],[f_732_3]) ).
fof(f_733_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_733_2,plain,
! [U_2288,U_2287] :
( ( c_Nat_OSuc(U_2287) = c_Nat_OSuc(U_2288)
| U_2287 != U_2288 )
& ( U_2287 = U_2288
| c_Nat_OSuc(U_2287) != c_Nat_OSuc(U_2288) ) ),
inference(variable_rename,[status(thm)],[f_733_1]) ).
fof(f_733_3,plain,
( ! [U_2292,U_2290] :
( c_Nat_OSuc(U_2290) = c_Nat_OSuc(U_2292)
| U_2290 != U_2292 )
& ! [U_2291,U_2289] :
( U_2289 = U_2291
| c_Nat_OSuc(U_2289) != c_Nat_OSuc(U_2291) ) ),
inference(miniscope,[status(thm)],[f_733_2]) ).
fof(f_733_4,plain,
( ! [U_2290,U_2292] :
( c_Nat_OSuc(U_2290) = c_Nat_OSuc(U_2292)
| U_2290 != U_2292 )
& ! [U_2289,U_2291] :
( U_2289 = U_2291
| c_Nat_OSuc(U_2289) != c_Nat_OSuc(U_2291) ) ),
inference(definitional_conversion,[status(esa)],[f_733_3]) ).
cnf(f_733_5,plain,
( U_2289 = U_2291
| c_Nat_OSuc(U_2289) != c_Nat_OSuc(U_2291) ),
inference(clausify,[status(thm)],[f_733_4]) ).
cnf(f_733_6,plain,
( c_Nat_OSuc(U_2290) = c_Nat_OSuc(U_2292)
| U_2290 != U_2292 ),
inference(clausify,[status(thm)],[f_733_4]) ).
fof(f_734_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_734_2,plain,
! [U_2294,U_2293] :
( U_2293 = U_2294
| c_Nat_OSuc(U_2293) != c_Nat_OSuc(U_2294) ),
inference(variable_rename,[status(thm)],[f_734_1]) ).
fof(f_734_3,plain,
! [U_2293,U_2294] :
( U_2293 = U_2294
| c_Nat_OSuc(U_2293) != c_Nat_OSuc(U_2294) ),
inference(definitional_conversion,[status(esa)],[f_734_2]) ).
cnf(f_734_4,plain,
( U_2293 = U_2294
| c_Nat_OSuc(U_2293) != c_Nat_OSuc(U_2294) ),
inference(clausify,[status(thm)],[f_734_3]) ).
fof(f_735_1,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zminus__0]) ).
fof(f_735_2,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_735_1]) ).
cnf(f_735_3,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_735_2]) ).
fof(f_736_1,plain,
! [V_w,V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)),V_w) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),V_w)),
inference(fof_nnf,[status(thm)],[fact_zmult__zminus]) ).
fof(f_736_2,plain,
! [U_2296,U_2295] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2295)),U_2296) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2295),U_2296)),
inference(variable_rename,[status(thm)],[f_736_1]) ).
fof(f_736_3,plain,
! [U_2295,U_2296] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2295)),U_2296) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2295),U_2296)),
inference(definitional_conversion,[status(esa)],[f_736_2]) ).
cnf(f_736_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2295)),U_2296) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2295),U_2296)),
inference(clausify,[status(thm)],[f_736_3]) ).
fof(f_737_1,plain,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),V_z) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[fact_zadd__zminus__inverse2]) ).
fof(f_737_2,plain,
! [U_2297] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2297),U_2297) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(variable_rename,[status(thm)],[f_737_1]) ).
fof(f_737_3,plain,
! [U_2297] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2297),U_2297) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_737_2]) ).
cnf(f_737_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2297),U_2297) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_737_3]) ).
fof(f_738_1,plain,
! [V_i] :
( ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = V_i
| c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,V_i) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_i)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_i,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(fof_nnf,[status(thm)],[fact_zabs__def]) ).
fof(f_738_2,plain,
! [U_2298] :
( ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2298) = U_2298
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2298,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2298) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2298)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2298,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(variable_rename,[status(thm)],[f_738_1]) ).
fof(f_738_3,plain,
( ! [U_2300] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2300) = U_2300
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2300,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2299] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2299) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2299)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2299,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(miniscope,[status(thm)],[f_738_2]) ).
fof(f_738_4,plain,
( ! [U_2300] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2300) = U_2300
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2300,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2299] :
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2299) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2299)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2299,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
inference(definitional_conversion,[status(esa)],[f_738_3]) ).
cnf(f_738_5,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2299) = c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2299)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2299,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_738_4]) ).
cnf(f_738_6,plain,
( c_Groups_Oabs__class_Oabs(tc_Int_Oint,U_2300) = U_2300
| c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2300,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_738_4]) ).
fof(f_739_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_739_2,plain,
! [U_2302,U_2301] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2301),c_Groups_Ozero__class_Ozero(U_2301)),c_Nat_OSuc(U_2302)) = c_Groups_Ozero__class_Ozero(U_2301)
| ~ class_Rings_Osemiring__0(U_2301)
| ~ class_Power_Opower(U_2301) ),
inference(variable_rename,[status(thm)],[f_739_1]) ).
fof(f_739_3,plain,
! [U_2302,U_2301] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2301),c_Groups_Ozero__class_Ozero(U_2301)),c_Nat_OSuc(U_2302)) = c_Groups_Ozero__class_Ozero(U_2301)
| ~ class_Rings_Osemiring__0(U_2301)
| ~ class_Power_Opower(U_2301) ),
inference(definitional_conversion,[status(esa)],[f_739_2]) ).
cnf(f_739_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2301),c_Groups_Ozero__class_Ozero(U_2301)),c_Nat_OSuc(U_2302)) = c_Groups_Ozero__class_Ozero(U_2301)
| ~ class_Rings_Osemiring__0(U_2301)
| ~ class_Power_Opower(U_2301) ),
inference(clausify,[status(thm)],[f_739_3]) ).
fof(f_740_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_740_2,plain,
! [U_2305,U_2304,U_2303] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),c_Nat_OSuc(U_2305)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2303),U_2304),hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),U_2305))
| ~ class_Rings_Ocomm__semiring__1(U_2303) ),
inference(variable_rename,[status(thm)],[f_740_1]) ).
fof(f_740_3,plain,
! [U_2303,U_2304,U_2305] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),c_Nat_OSuc(U_2305)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2303),U_2304),hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),U_2305))
| ~ class_Rings_Ocomm__semiring__1(U_2303) ),
inference(definitional_conversion,[status(esa)],[f_740_2]) ).
cnf(f_740_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),c_Nat_OSuc(U_2305)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2303),U_2304),hAPP(hAPP(c_Power_Opower__class_Opower(U_2303),U_2304),U_2305))
| ~ class_Rings_Ocomm__semiring__1(U_2303) ),
inference(clausify,[status(thm)],[f_740_3]) ).
fof(f_741_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_741_2,plain,
! [U_2308,U_2307,U_2306] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2306),U_2307),hAPP(hAPP(c_Power_Opower__class_Opower(U_2306),U_2307),U_2308)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2306),U_2307),c_Nat_OSuc(U_2308))
| ~ class_Rings_Ocomm__semiring__1(U_2306) ),
inference(variable_rename,[status(thm)],[f_741_1]) ).
fof(f_741_3,plain,
! [U_2306,U_2307,U_2308] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2306),U_2307),hAPP(hAPP(c_Power_Opower__class_Opower(U_2306),U_2307),U_2308)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2306),U_2307),c_Nat_OSuc(U_2308))
| ~ class_Rings_Ocomm__semiring__1(U_2306) ),
inference(definitional_conversion,[status(esa)],[f_741_2]) ).
cnf(f_741_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2306),U_2307),hAPP(hAPP(c_Power_Opower__class_Opower(U_2306),U_2307),U_2308)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2306),U_2307),c_Nat_OSuc(U_2308))
| ~ class_Rings_Ocomm__semiring__1(U_2306) ),
inference(clausify,[status(thm)],[f_741_3]) ).
fof(f_742_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_742_2,plain,
! [U_2311,U_2310,U_2309] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2309),hAPP(hAPP(c_Power_Opower__class_Opower(U_2309),U_2310),U_2311)),U_2310) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2309),U_2310),c_Nat_OSuc(U_2311))
| ~ class_Rings_Ocomm__semiring__1(U_2309) ),
inference(variable_rename,[status(thm)],[f_742_1]) ).
fof(f_742_3,plain,
! [U_2309,U_2310,U_2311] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2309),hAPP(hAPP(c_Power_Opower__class_Opower(U_2309),U_2310),U_2311)),U_2310) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2309),U_2310),c_Nat_OSuc(U_2311))
| ~ class_Rings_Ocomm__semiring__1(U_2309) ),
inference(definitional_conversion,[status(esa)],[f_742_2]) ).
cnf(f_742_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2309),hAPP(hAPP(c_Power_Opower__class_Opower(U_2309),U_2310),U_2311)),U_2310) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2309),U_2310),c_Nat_OSuc(U_2311))
| ~ class_Rings_Ocomm__semiring__1(U_2309) ),
inference(clausify,[status(thm)],[f_742_3]) ).
fof(f_743_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_743_2,plain,
! [U_2314,U_2313,U_2312] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2312),U_2313),c_Nat_OSuc(U_2314)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2312),hAPP(hAPP(c_Power_Opower__class_Opower(U_2312),U_2313),U_2314)),U_2313)
| ~ class_Groups_Omonoid__mult(U_2312) ),
inference(variable_rename,[status(thm)],[f_743_1]) ).
fof(f_743_3,plain,
! [U_2312,U_2313,U_2314] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2312),U_2313),c_Nat_OSuc(U_2314)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2312),hAPP(hAPP(c_Power_Opower__class_Opower(U_2312),U_2313),U_2314)),U_2313)
| ~ class_Groups_Omonoid__mult(U_2312) ),
inference(definitional_conversion,[status(esa)],[f_743_2]) ).
cnf(f_743_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2312),U_2313),c_Nat_OSuc(U_2314)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2312),hAPP(hAPP(c_Power_Opower__class_Opower(U_2312),U_2313),U_2314)),U_2313)
| ~ class_Groups_Omonoid__mult(U_2312) ),
inference(clausify,[status(thm)],[f_743_3]) ).
fof(f_744_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_744_2,plain,
! [U_2317,U_2316,U_2315] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),c_Nat_OSuc(U_2317)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2315),U_2316),hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),U_2317))
| ~ class_Power_Opower(U_2315) ),
inference(variable_rename,[status(thm)],[f_744_1]) ).
fof(f_744_3,plain,
! [U_2315,U_2316,U_2317] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),c_Nat_OSuc(U_2317)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2315),U_2316),hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),U_2317))
| ~ class_Power_Opower(U_2315) ),
inference(definitional_conversion,[status(esa)],[f_744_2]) ).
cnf(f_744_4,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),c_Nat_OSuc(U_2317)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2315),U_2316),hAPP(hAPP(c_Power_Opower__class_Opower(U_2315),U_2316),U_2317))
| ~ class_Power_Opower(U_2315) ),
inference(clausify,[status(thm)],[f_744_3]) ).
fof(f_745_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
| ( ! [B_j] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,B_j,V_n_2)
| V_ma_2 != c_Nat_OSuc(B_j) )
& V_ma_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_ma_2 = c_Nat_OSuc(B_j) )
| V_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__0__disj]) ).
fof(f_745_2,plain,
! [U_2321,U_2320] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2320,c_Nat_OSuc(U_2321))
| ( ! [U_2319] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2321)
| U_2320 != c_Nat_OSuc(U_2319) )
& U_2320 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( ? [U_2318] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2318,U_2321)
& U_2320 = c_Nat_OSuc(U_2318) )
| U_2320 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2320,c_Nat_OSuc(U_2321)) ) ),
inference(variable_rename,[status(thm)],[f_745_1]) ).
fof(f_745_3,plain,
( ! [U_2325,U_2323] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2323,c_Nat_OSuc(U_2325))
| ( ! [U_2319] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2325)
| U_2323 != c_Nat_OSuc(U_2319) )
& U_2323 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2324,U_2322] :
( ? [U_2318] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2318,U_2324)
& U_2322 = c_Nat_OSuc(U_2318) )
| U_2322 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2322,c_Nat_OSuc(U_2324)) ) ),
inference(miniscope,[status(thm)],[f_745_2]) ).
fof(f_745_4,plain,
( ! [U_2325,U_2323] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2323,c_Nat_OSuc(U_2325))
| ( ! [U_2319] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2325)
| U_2323 != c_Nat_OSuc(U_2319) )
& U_2323 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2324,U_2322] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK30(U_2324,U_2322),U_2324)
& U_2322 = c_Nat_OSuc(sK30(U_2324,U_2322)) )
| U_2322 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2322,c_Nat_OSuc(U_2324)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_2318,sK30(U_2324,U_2322))],[f_745_3]) ).
fof(f_745_5,plain,
( ! [U_2319,U_2323,U_2325] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2325)
| U_2323 != c_Nat_OSuc(U_2319)
| ~ sP244(U_2319,U_2323,U_2325) )
& ! [U_2319,U_2323,U_2325] :
( U_2323 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP244(U_2319,U_2323,U_2325) )
& ! [U_2322,U_2324] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK30(U_2324,U_2322),U_2324)
| ~ sP243(U_2322,U_2324) )
& ! [U_2322,U_2324] :
( U_2322 = c_Nat_OSuc(sK30(U_2324,U_2322))
| ~ sP243(U_2322,U_2324) )
& ! [U_2319,U_2323,U_2325] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2323,c_Nat_OSuc(U_2325))
| sP244(U_2319,U_2323,U_2325) )
& ! [U_2322,U_2324] :
( sP243(U_2322,U_2324)
| U_2322 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2322,c_Nat_OSuc(U_2324)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP243,sP244])],[f_745_4]) ).
cnf(f_745_6,plain,
( sP243(U_2322,U_2324)
| U_2322 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2322,c_Nat_OSuc(U_2324)) ),
inference(clausify,[status(thm)],[f_745_5]) ).
cnf(f_745_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2323,c_Nat_OSuc(U_2325))
| sP244(U_2319,U_2323,U_2325) ),
inference(clausify,[status(thm)],[f_745_5]) ).
cnf(f_745_8,plain,
( U_2322 = c_Nat_OSuc(sK30(U_2324,U_2322))
| ~ sP243(U_2322,U_2324) ),
inference(clausify,[status(thm)],[f_745_5]) ).
cnf(f_745_9,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,sK30(U_2324,U_2322),U_2324)
| ~ sP243(U_2322,U_2324) ),
inference(clausify,[status(thm)],[f_745_5]) ).
cnf(f_745_10,plain,
( U_2323 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP244(U_2319,U_2323,U_2325) ),
inference(clausify,[status(thm)],[f_745_5]) ).
cnf(f_745_11,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2319,U_2325)
| U_2323 != c_Nat_OSuc(U_2319)
| ~ sP244(U_2319,U_2323,U_2325) ),
inference(clausify,[status(thm)],[f_745_5]) ).
fof(f_746_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_746_2,plain,
! [U_2326] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2326,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2326 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2326 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2326,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_746_1]) ).
fof(f_746_3,plain,
( ! [U_2328] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2328,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2328 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2327] :
( U_2327 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2327,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_746_2]) ).
fof(f_746_4,plain,
( ! [U_2328] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2328,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2328 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2327] :
( U_2327 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2327,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa)],[f_746_3]) ).
cnf(f_746_5,plain,
( U_2327 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2327,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_746_4]) ).
cnf(f_746_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2328,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2328 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_746_4]) ).
fof(f_747_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_747_2,plain,
! [U_2331] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2331)
| ! [U_2330] : U_2331 != c_Nat_OSuc(U_2330) )
& ( ? [U_2329] : U_2331 = c_Nat_OSuc(U_2329)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2331) ) ),
inference(variable_rename,[status(thm)],[f_747_1]) ).
fof(f_747_3,plain,
( ! [U_2333] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2333)
| ! [U_2330] : U_2333 != c_Nat_OSuc(U_2330) )
& ! [U_2332] :
( ? [U_2329] : U_2332 = c_Nat_OSuc(U_2329)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2332) ) ),
inference(miniscope,[status(thm)],[f_747_2]) ).
fof(f_747_4,plain,
( ! [U_2333] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2333)
| ! [U_2330] : U_2333 != c_Nat_OSuc(U_2330) )
& ! [U_2332] :
( U_2332 = c_Nat_OSuc(sK31(U_2332))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2332) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_2329,sK31(U_2332))],[f_747_3]) ).
fof(f_747_5,plain,
( ! [U_2333,U_2330] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2333)
| U_2333 != c_Nat_OSuc(U_2330) )
& ! [U_2332] :
( U_2332 = c_Nat_OSuc(sK31(U_2332))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2332) ) ),
inference(definitional_conversion,[status(esa)],[f_747_4]) ).
cnf(f_747_6,plain,
( U_2332 = c_Nat_OSuc(sK31(U_2332))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2332) ),
inference(clausify,[status(thm)],[f_747_5]) ).
cnf(f_747_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2333)
| U_2333 != c_Nat_OSuc(U_2330) ),
inference(clausify,[status(thm)],[f_747_5]) ).
fof(f_748_1,plain,
! [V_ma_2] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| V_ma_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(fof_nnf,[status(thm)],[fact_dvd__1__iff__1]) ).
fof(f_748_2,plain,
! [U_2334] :
( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2334,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2334 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( U_2334 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2334,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(variable_rename,[status(thm)],[f_748_1]) ).
fof(f_748_3,plain,
( ! [U_2336] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2336,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2336 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_2335] :
( U_2335 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2335,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(miniscope,[status(thm)],[f_748_2]) ).
fof(f_748_4,plain,
( ! [U_2336] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2336,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2336 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_2335] :
( U_2335 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2335,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
inference(definitional_conversion,[status(esa)],[f_748_3]) ).
cnf(f_748_5,plain,
( U_2335 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2335,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
inference(clausify,[status(thm)],[f_748_4]) ).
cnf(f_748_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2336,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| U_2336 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_748_4]) ).
fof(f_749_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,V_n_2)
| ( ( V_n_2 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| V_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_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_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_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_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_one__is__add]) ).
fof(f_749_2,plain,
! [U_2338,U_2337] :
( ( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2337,U_2338)
| ( ( U_2338 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2337 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2338 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2337 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2338 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2337 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2338 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2337 = 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_2337,U_2338) ) ),
inference(variable_rename,[status(thm)],[f_749_1]) ).
fof(f_749_3,plain,
( ! [U_2342,U_2340] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2340,U_2342)
| ( ( U_2342 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2340 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2342 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2340 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2341,U_2339] :
( ( U_2341 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2339 = 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_2339,U_2341) ) ),
inference(miniscope,[status(thm)],[f_749_2]) ).
fof(f_749_4,plain,
( ! [U_2342,U_2340] :
( U_2342 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2340 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP247(U_2342,U_2340) )
& ! [U_2342,U_2340] :
( U_2342 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2340 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP247(U_2342,U_2340) )
& ! [U_2339,U_2341] :
( U_2341 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP246(U_2339,U_2341) )
& ! [U_2339,U_2341] :
( U_2339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP246(U_2339,U_2341) )
& ! [U_2339,U_2341] :
( U_2341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP245(U_2339,U_2341) )
& ! [U_2339,U_2341] :
( U_2339 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP245(U_2339,U_2341) )
& ! [U_2342,U_2340] :
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2340,U_2342)
| sP247(U_2342,U_2340) )
& ! [U_2339,U_2341] :
( sP246(U_2339,U_2341)
| sP245(U_2339,U_2341)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2339,U_2341) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP245,sP246,sP247])],[f_749_3]) ).
cnf(f_749_5,plain,
( sP246(U_2339,U_2341)
| sP245(U_2339,U_2341)
| c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2339,U_2341) ),
inference(clausify,[status(thm)],[f_749_4]) ).
cnf(f_749_6,plain,
( c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2340,U_2342)
| sP247(U_2342,U_2340) ),
inference(clausify,[status(thm)],[f_749_4]) ).
cnf(f_749_7,plain,
( U_2339 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP245(U_2339,U_2341) ),
inference(clausify,[status(thm)],[f_749_4]) ).
cnf(f_749_8,plain,
( U_2341 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP245(U_2339,U_2341) ),
inference(clausify,[status(thm)],[f_749_4]) ).
cnf(f_749_9,plain,
( U_2339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP246(U_2339,U_2341) ),
inference(clausify,[status(thm)],[f_749_4]) ).
cnf(f_749_10,plain,
( U_2341 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP246(U_2339,U_2341) ),
inference(clausify,[status(thm)],[f_749_4]) ).
cnf(f_749_11,plain,
( U_2342 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2340 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP247(U_2342,U_2340) ),
inference(clausify,[status(thm)],[f_749_4]) ).
cnf(f_749_12,plain,
( U_2342 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2340 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP247(U_2342,U_2340) ),
inference(clausify,[status(thm)],[f_749_4]) ).
fof(f_750_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_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_ma_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| V_ma_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_ma_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& V_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_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_750_2,plain,
! [U_2344,U_2343] :
( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2343,U_2344) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2344 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2343 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2344 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2343 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ( ( U_2344 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2343 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2344 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2343 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2343,U_2344) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_750_1]) ).
fof(f_750_3,plain,
( ! [U_2348,U_2346] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2346,U_2348) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ( ( U_2348 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2346 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2348 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2346 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
& ! [U_2347,U_2345] :
( ( U_2347 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
| ( U_2347 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
& U_2345 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2345,U_2347) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_750_2]) ).
fof(f_750_4,plain,
( ! [U_2346,U_2348] :
( U_2348 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2346 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP250(U_2346,U_2348) )
& ! [U_2346,U_2348] :
( U_2348 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2346 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP250(U_2346,U_2348) )
& ! [U_2345,U_2347] :
( U_2347 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP249(U_2345,U_2347) )
& ! [U_2345,U_2347] :
( U_2345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP249(U_2345,U_2347) )
& ! [U_2345,U_2347] :
( U_2347 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP248(U_2345,U_2347) )
& ! [U_2345,U_2347] :
( U_2345 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP248(U_2345,U_2347) )
& ! [U_2346,U_2348] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2346,U_2348) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP250(U_2346,U_2348) )
& ! [U_2345,U_2347] :
( sP249(U_2345,U_2347)
| sP248(U_2345,U_2347)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2345,U_2347) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248,sP249,sP250])],[f_750_3]) ).
cnf(f_750_5,plain,
( sP249(U_2345,U_2347)
| sP248(U_2345,U_2347)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2345,U_2347) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_750_4]) ).
cnf(f_750_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2346,U_2348) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| sP250(U_2346,U_2348) ),
inference(clausify,[status(thm)],[f_750_4]) ).
cnf(f_750_7,plain,
( U_2345 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP248(U_2345,U_2347) ),
inference(clausify,[status(thm)],[f_750_4]) ).
cnf(f_750_8,plain,
( U_2347 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP248(U_2345,U_2347) ),
inference(clausify,[status(thm)],[f_750_4]) ).
cnf(f_750_9,plain,
( U_2345 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP249(U_2345,U_2347) ),
inference(clausify,[status(thm)],[f_750_4]) ).
cnf(f_750_10,plain,
( U_2347 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP249(U_2345,U_2347) ),
inference(clausify,[status(thm)],[f_750_4]) ).
cnf(f_750_11,plain,
( U_2348 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| U_2346 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP250(U_2346,U_2348) ),
inference(clausify,[status(thm)],[f_750_4]) ).
cnf(f_750_12,plain,
( U_2348 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2346 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP250(U_2346,U_2348) ),
inference(clausify,[status(thm)],[f_750_4]) ).
fof(f_751_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_751_2,plain,
! [U_2350,U_2349] :
( 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_2349),U_2350))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2349) ),
inference(variable_rename,[status(thm)],[f_751_1]) ).
fof(f_751_3,plain,
! [U_2350,U_2349] :
( 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_2349),U_2350))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2349) ),
inference(definitional_conversion,[status(esa)],[f_751_2]) ).
cnf(f_751_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_2349),U_2350))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2349) ),
inference(clausify,[status(thm)],[f_751_3]) ).
fof(f_752_1,plain,
! [V_n_2,V_ma_2] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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_ma_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_ma_2 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_ma_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_752_2,plain,
! [U_2352,U_2351] :
( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2351),U_2352) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2352 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2351 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ( ( U_2352 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2351 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2351),U_2352) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(variable_rename,[status(thm)],[f_752_1]) ).
fof(f_752_3,plain,
( ! [U_2356,U_2354] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2354),U_2356) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2356 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2354 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_2355,U_2353] :
( ( U_2355 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
& U_2353 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2353),U_2355) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(miniscope,[status(thm)],[f_752_2]) ).
fof(f_752_4,plain,
( ! [U_2355,U_2353] :
( U_2355 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP251(U_2355,U_2353) )
& ! [U_2355,U_2353] :
( U_2353 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP251(U_2355,U_2353) )
& ! [U_2354,U_2356] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2354),U_2356) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2356 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2354 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
& ! [U_2355,U_2353] :
( sP251(U_2355,U_2353)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2353),U_2355) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP251])],[f_752_3]) ).
cnf(f_752_5,plain,
( sP251(U_2355,U_2353)
| hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2353),U_2355) != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_752_4]) ).
cnf(f_752_6,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2354),U_2356) = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2356 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2354 != c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
inference(clausify,[status(thm)],[f_752_4]) ).
cnf(f_752_7,plain,
( U_2353 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP251(U_2355,U_2353) ),
inference(clausify,[status(thm)],[f_752_4]) ).
cnf(f_752_8,plain,
( U_2355 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| ~ sP251(U_2355,U_2353) ),
inference(clausify,[status(thm)],[f_752_4]) ).
fof(f_753_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ! [B_k] : V_n_2 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k)) )
& ( ? [B_k] : V_n_2 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_ma_2,B_k))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__iff__Suc__add]) ).
fof(f_753_2,plain,
! [U_2360,U_2359] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2359,U_2360)
| ! [U_2358] : U_2360 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2359,U_2358)) )
& ( ? [U_2357] : U_2360 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2359,U_2357))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2359,U_2360) ) ),
inference(variable_rename,[status(thm)],[f_753_1]) ).
fof(f_753_3,plain,
( ! [U_2364,U_2362] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2362,U_2364)
| ! [U_2358] : U_2364 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2362,U_2358)) )
& ! [U_2363,U_2361] :
( ? [U_2357] : U_2363 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2361,U_2357))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2361,U_2363) ) ),
inference(miniscope,[status(thm)],[f_753_2]) ).
fof(f_753_4,plain,
( ! [U_2364,U_2362] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2362,U_2364)
| ! [U_2358] : U_2364 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2362,U_2358)) )
& ! [U_2363,U_2361] :
( U_2363 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2361,sK32(U_2363,U_2361)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2361,U_2363) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_2357,sK32(U_2363,U_2361))],[f_753_3]) ).
fof(f_753_5,plain,
( ! [U_2364,U_2358,U_2362] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2362,U_2364)
| U_2364 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2362,U_2358)) )
& ! [U_2361,U_2363] :
( U_2363 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2361,sK32(U_2363,U_2361)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2361,U_2363) ) ),
inference(definitional_conversion,[status(esa)],[f_753_4]) ).
cnf(f_753_6,plain,
( U_2363 = c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2361,sK32(U_2363,U_2361)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2361,U_2363) ),
inference(clausify,[status(thm)],[f_753_5]) ).
cnf(f_753_7,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2362,U_2364)
| U_2364 != c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2362,U_2358)) ),
inference(clausify,[status(thm)],[f_753_5]) ).
fof(f_754_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_754_2,plain,
! [U_2366,U_2365] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2365,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2366,U_2365))),
inference(variable_rename,[status(thm)],[f_754_1]) ).
fof(f_754_3,plain,
! [U_2365,U_2366] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2365,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2366,U_2365))),
inference(definitional_conversion,[status(esa)],[f_754_2]) ).
cnf(f_754_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2365,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2366,U_2365))),
inference(clausify,[status(thm)],[f_754_3]) ).
fof(f_755_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_755_2,plain,
! [U_2368,U_2367] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2367,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2367,U_2368))),
inference(variable_rename,[status(thm)],[f_755_1]) ).
fof(f_755_3,plain,
! [U_2367,U_2368] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2367,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2367,U_2368))),
inference(definitional_conversion,[status(esa)],[f_755_2]) ).
cnf(f_755_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2367,c_Nat_OSuc(c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2367,U_2368))),
inference(clausify,[status(thm)],[f_755_3]) ).
fof(f_756_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_n_2),V_ma_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__Suc__le]) ).
fof(f_756_2,plain,
! [U_2370,U_2369] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2369,U_2370)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2369),U_2370) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2369),U_2370)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2369,U_2370) ) ),
inference(variable_rename,[status(thm)],[f_756_1]) ).
fof(f_756_3,plain,
( ! [U_2374,U_2372] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2372,U_2374)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2372),U_2374) )
& ! [U_2373,U_2371] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2371),U_2373)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2371,U_2373) ) ),
inference(miniscope,[status(thm)],[f_756_2]) ).
fof(f_756_4,plain,
( ! [U_2372,U_2374] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2372,U_2374)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2372),U_2374) )
& ! [U_2373,U_2371] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2371),U_2373)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2371,U_2373) ) ),
inference(definitional_conversion,[status(esa)],[f_756_3]) ).
cnf(f_756_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2371),U_2373)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2371,U_2373) ),
inference(clausify,[status(thm)],[f_756_4]) ).
cnf(f_756_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2372,U_2374)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2372),U_2374) ),
inference(clausify,[status(thm)],[f_756_4]) ).
fof(f_757_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,c_Nat_OSuc(V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__Suc__eq__le]) ).
fof(f_757_2,plain,
! [U_2376,U_2375] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2375,c_Nat_OSuc(U_2376))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2375,U_2376) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2375,U_2376)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2375,c_Nat_OSuc(U_2376)) ) ),
inference(variable_rename,[status(thm)],[f_757_1]) ).
fof(f_757_3,plain,
( ! [U_2380,U_2378] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2378,c_Nat_OSuc(U_2380))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2378,U_2380) )
& ! [U_2379,U_2377] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2377,U_2379)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2377,c_Nat_OSuc(U_2379)) ) ),
inference(miniscope,[status(thm)],[f_757_2]) ).
fof(f_757_4,plain,
( ! [U_2378,U_2380] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2378,c_Nat_OSuc(U_2380))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2378,U_2380) )
& ! [U_2377,U_2379] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2377,U_2379)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2377,c_Nat_OSuc(U_2379)) ) ),
inference(definitional_conversion,[status(esa)],[f_757_3]) ).
cnf(f_757_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2377,U_2379)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2377,c_Nat_OSuc(U_2379)) ),
inference(clausify,[status(thm)],[f_757_4]) ).
cnf(f_757_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2378,c_Nat_OSuc(U_2380))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2378,U_2380) ),
inference(clausify,[status(thm)],[f_757_4]) ).
fof(f_758_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(V_ma_2),V_n_2) ) ),
inference(fof_nnf,[status(thm)],[fact_Suc__le__eq]) ).
fof(f_758_2,plain,
! [U_2382,U_2381] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2381),U_2382)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2381,U_2382) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2381,U_2382)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2381),U_2382) ) ),
inference(variable_rename,[status(thm)],[f_758_1]) ).
fof(f_758_3,plain,
( ! [U_2386,U_2384] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2384),U_2386)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2384,U_2386) )
& ! [U_2385,U_2383] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2383,U_2385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2383),U_2385) ) ),
inference(miniscope,[status(thm)],[f_758_2]) ).
fof(f_758_4,plain,
( ! [U_2384,U_2386] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2384),U_2386)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2384,U_2386) )
& ! [U_2383,U_2385] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2383,U_2385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2383),U_2385) ) ),
inference(definitional_conversion,[status(esa)],[f_758_3]) ).
cnf(f_758_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2383,U_2385)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2383),U_2385) ),
inference(clausify,[status(thm)],[f_758_4]) ).
cnf(f_758_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2384),U_2386)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2384,U_2386) ),
inference(clausify,[status(thm)],[f_758_4]) ).
fof(f_759_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_759_2,plain,
! [U_2388,U_2387] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2387,c_Nat_OSuc(U_2388))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2387,U_2388) ),
inference(variable_rename,[status(thm)],[f_759_1]) ).
fof(f_759_3,plain,
! [U_2388,U_2387] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2387,c_Nat_OSuc(U_2388))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2387,U_2388) ),
inference(definitional_conversion,[status(esa)],[f_759_2]) ).
cnf(f_759_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2387,c_Nat_OSuc(U_2388))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2387,U_2388) ),
inference(clausify,[status(thm)],[f_759_3]) ).
fof(f_760_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_760_2,plain,
! [U_2390,U_2389] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2389),U_2390)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2389,U_2390) ),
inference(variable_rename,[status(thm)],[f_760_1]) ).
fof(f_760_3,plain,
! [U_2389,U_2390] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2389),U_2390)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2389,U_2390) ),
inference(definitional_conversion,[status(esa)],[f_760_2]) ).
cnf(f_760_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2389),U_2390)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2389,U_2390) ),
inference(clausify,[status(thm)],[f_760_3]) ).
fof(f_761_1,plain,
! [V_n_2,V_ma_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2))
| V_n_2 != V_ma_2 )
& ( V_n_2 = V_ma_2
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,c_Nat_OSuc(V_ma_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) ),
inference(fof_nnf,[status(thm)],[fact_le__less__Suc__eq]) ).
fof(f_761_2,plain,
! [U_2392,U_2391] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,c_Nat_OSuc(U_2391))
| U_2392 != U_2391 )
& ( U_2392 = U_2391
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,c_Nat_OSuc(U_2391)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2391,U_2392) ),
inference(variable_rename,[status(thm)],[f_761_1]) ).
fof(f_761_3,plain,
( ! [U_2391,U_2392] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,c_Nat_OSuc(U_2391))
| U_2392 != U_2391
| ~ sP252(U_2391,U_2392) )
& ! [U_2391,U_2392] :
( U_2392 = U_2391
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,c_Nat_OSuc(U_2391))
| ~ sP252(U_2391,U_2392) )
& ! [U_2391,U_2392] :
( sP252(U_2391,U_2392)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2391,U_2392) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252])],[f_761_2]) ).
cnf(f_761_4,plain,
( sP252(U_2391,U_2392)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2391,U_2392) ),
inference(clausify,[status(thm)],[f_761_3]) ).
cnf(f_761_5,plain,
( U_2392 = U_2391
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,c_Nat_OSuc(U_2391))
| ~ sP252(U_2391,U_2392) ),
inference(clausify,[status(thm)],[f_761_3]) ).
cnf(f_761_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2392,c_Nat_OSuc(U_2391))
| U_2392 != U_2391
| ~ sP252(U_2391,U_2392) ),
inference(clausify,[status(thm)],[f_761_3]) ).
fof(f_762_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_762_2,plain,
! [U_2394,U_2393] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2393,U_2394)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2393),U_2394) ),
inference(variable_rename,[status(thm)],[f_762_1]) ).
fof(f_762_3,plain,
! [U_2393,U_2394] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2393,U_2394)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2393),U_2394) ),
inference(definitional_conversion,[status(esa)],[f_762_2]) ).
cnf(f_762_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2393,U_2394)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(U_2393),U_2394) ),
inference(clausify,[status(thm)],[f_762_3]) ).
fof(f_763_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_763_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_763_1]) ).
cnf(f_763_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_763_2]) ).
fof(f_764_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_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(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(V_k_2)),V_ma_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__less__cancel1]) ).
fof(f_764_2,plain,
! [U_2397,U_2396,U_2395] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2395)),U_2396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2395)),U_2397))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2396,U_2397) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2396,U_2397)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2395)),U_2396),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2395)),U_2397)) ) ),
inference(variable_rename,[status(thm)],[f_764_1]) ).
fof(f_764_3,plain,
( ! [U_2403,U_2401] :
( ! [U_2399] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2399)),U_2401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2399)),U_2403))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2401,U_2403) )
& ! [U_2402,U_2400] :
( ! [U_2398] : ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2398)),U_2400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2398)),U_2402))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2400,U_2402) ) ),
inference(miniscope,[status(thm)],[f_764_2]) ).
fof(f_764_4,plain,
( ! [U_2401,U_2403,U_2399] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2399)),U_2401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2399)),U_2403))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2401,U_2403) )
& ! [U_2402,U_2400,U_2398] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2398)),U_2400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2398)),U_2402))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2400,U_2402) ) ),
inference(definitional_conversion,[status(esa)],[f_764_3]) ).
cnf(f_764_5,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2398)),U_2400),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2398)),U_2402))
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2400,U_2402) ),
inference(clausify,[status(thm)],[f_764_4]) ).
cnf(f_764_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2399)),U_2401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2399)),U_2403))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2401,U_2403) ),
inference(clausify,[status(thm)],[f_764_4]) ).
fof(f_765_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_765_2,plain,
! [U_2405,U_2404] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),c_Nat_OSuc(U_2405)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),U_2405)),
inference(variable_rename,[status(thm)],[f_765_1]) ).
fof(f_765_3,plain,
! [U_2405,U_2404] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),c_Nat_OSuc(U_2405)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),U_2405)),
inference(definitional_conversion,[status(esa)],[f_765_2]) ).
cnf(f_765_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),c_Nat_OSuc(U_2405)) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2404,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2404),U_2405)),
inference(clausify,[status(thm)],[f_765_3]) ).
fof(f_766_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_766_2,plain,
! [U_2407,U_2406] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2406)),U_2407) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2407,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2406),U_2407)),
inference(variable_rename,[status(thm)],[f_766_1]) ).
fof(f_766_3,plain,
! [U_2406,U_2407] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2406)),U_2407) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2407,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2406),U_2407)),
inference(definitional_conversion,[status(esa)],[f_766_2]) ).
cnf(f_766_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2406)),U_2407) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2407,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2406),U_2407)),
inference(clausify,[status(thm)],[f_766_3]) ).
fof(f_767_1,plain,
! [V_n_2,V_ma_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_ma_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_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_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_ma_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_767_2,plain,
! [U_2410,U_2409,U_2408] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2408)),U_2409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2408)),U_2410))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2409,U_2410) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2409,U_2410)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2408)),U_2409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2408)),U_2410)) ) ),
inference(variable_rename,[status(thm)],[f_767_1]) ).
fof(f_767_3,plain,
( ! [U_2416,U_2414] :
( ! [U_2412] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2412)),U_2414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2412)),U_2416))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2414,U_2416) )
& ! [U_2415,U_2413] :
( ! [U_2411] : ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2411)),U_2413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2411)),U_2415))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2413,U_2415) ) ),
inference(miniscope,[status(thm)],[f_767_2]) ).
fof(f_767_4,plain,
( ! [U_2416,U_2412,U_2414] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2412)),U_2414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2412)),U_2416))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2414,U_2416) )
& ! [U_2415,U_2413,U_2411] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2411)),U_2413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2411)),U_2415))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2413,U_2415) ) ),
inference(definitional_conversion,[status(esa)],[f_767_3]) ).
cnf(f_767_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_2411)),U_2413),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2411)),U_2415))
| c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2413,U_2415) ),
inference(clausify,[status(thm)],[f_767_4]) ).
cnf(f_767_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_2412)),U_2414),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Nat_OSuc(U_2412)),U_2416))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2414,U_2416) ),
inference(clausify,[status(thm)],[f_767_4]) ).
fof(f_768_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_768_2,plain,
! [U_2417] : c_Nat_OSuc(U_2417) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2417),
inference(variable_rename,[status(thm)],[f_768_1]) ).
fof(f_768_3,plain,
! [U_2417] : c_Nat_OSuc(U_2417) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2417),
inference(definitional_conversion,[status(esa)],[f_768_2]) ).
cnf(f_768_4,plain,
c_Nat_OSuc(U_2417) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2417),
inference(clausify,[status(thm)],[f_768_3]) ).
fof(f_769_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_769_2,plain,
! [U_2418] : c_Nat_OSuc(U_2418) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2418,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_769_1]) ).
fof(f_769_3,plain,
! [U_2418] : c_Nat_OSuc(U_2418) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2418,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_769_2]) ).
cnf(f_769_4,plain,
c_Nat_OSuc(U_2418) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2418,c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_769_3]) ).
fof(f_770_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_770_2,plain,
! [U_2422,U_2421,U_2420,U_2419] :
( c_Orderings_Oord__class_Oless__eq(U_2419,U_2420,U_2422)
| ~ c_Orderings_Oord__class_Oless__eq(U_2419,c_Groups_Ozero__class_Ozero(U_2419),U_2422)
| ~ c_Orderings_Oord__class_Oless__eq(U_2419,hAPP(hAPP(c_Power_Opower__class_Opower(U_2419),U_2420),c_Nat_OSuc(U_2421)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2419),U_2422),c_Nat_OSuc(U_2421)))
| ~ class_Rings_Olinordered__semidom(U_2419) ),
inference(variable_rename,[status(thm)],[f_770_1]) ).
fof(f_770_3,plain,
! [U_2419,U_2420,U_2421,U_2422] :
( c_Orderings_Oord__class_Oless__eq(U_2419,U_2420,U_2422)
| ~ c_Orderings_Oord__class_Oless__eq(U_2419,c_Groups_Ozero__class_Ozero(U_2419),U_2422)
| ~ c_Orderings_Oord__class_Oless__eq(U_2419,hAPP(hAPP(c_Power_Opower__class_Opower(U_2419),U_2420),c_Nat_OSuc(U_2421)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2419),U_2422),c_Nat_OSuc(U_2421)))
| ~ class_Rings_Olinordered__semidom(U_2419) ),
inference(definitional_conversion,[status(esa)],[f_770_2]) ).
cnf(f_770_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2419,U_2420,U_2422)
| ~ c_Orderings_Oord__class_Oless__eq(U_2419,c_Groups_Ozero__class_Ozero(U_2419),U_2422)
| ~ c_Orderings_Oord__class_Oless__eq(U_2419,hAPP(hAPP(c_Power_Opower__class_Opower(U_2419),U_2420),c_Nat_OSuc(U_2421)),hAPP(hAPP(c_Power_Opower__class_Opower(U_2419),U_2422),c_Nat_OSuc(U_2421)))
| ~ class_Rings_Olinordered__semidom(U_2419) ),
inference(clausify,[status(thm)],[f_770_3]) ).
fof(f_771_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_771_2,plain,
! [U_2426,U_2425,U_2424,U_2423] :
( U_2424 = U_2426
| ~ c_Orderings_Oord__class_Oless__eq(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2426)
| ~ c_Orderings_Oord__class_Oless__eq(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2424)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2423),U_2424),c_Nat_OSuc(U_2425)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2423),U_2426),c_Nat_OSuc(U_2425))
| ~ class_Rings_Olinordered__semidom(U_2423) ),
inference(variable_rename,[status(thm)],[f_771_1]) ).
fof(f_771_3,plain,
! [U_2423,U_2424,U_2425,U_2426] :
( U_2424 = U_2426
| ~ c_Orderings_Oord__class_Oless__eq(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2426)
| ~ c_Orderings_Oord__class_Oless__eq(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2424)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2423),U_2424),c_Nat_OSuc(U_2425)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2423),U_2426),c_Nat_OSuc(U_2425))
| ~ class_Rings_Olinordered__semidom(U_2423) ),
inference(definitional_conversion,[status(esa)],[f_771_2]) ).
cnf(f_771_4,plain,
( U_2424 = U_2426
| ~ c_Orderings_Oord__class_Oless__eq(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2426)
| ~ c_Orderings_Oord__class_Oless__eq(U_2423,c_Groups_Ozero__class_Ozero(U_2423),U_2424)
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2423),U_2424),c_Nat_OSuc(U_2425)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2423),U_2426),c_Nat_OSuc(U_2425))
| ~ class_Rings_Olinordered__semidom(U_2423) ),
inference(clausify,[status(thm)],[f_771_3]) ).
fof(f_772_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_772_2,plain,
! [U_2429,U_2428,U_2427] :
( c_Orderings_Oord__class_Oless(U_2427,c_Groups_Oone__class_Oone(U_2427),hAPP(hAPP(c_Power_Opower__class_Opower(U_2427),U_2428),c_Nat_OSuc(U_2429)))
| ~ c_Orderings_Oord__class_Oless(U_2427,c_Groups_Oone__class_Oone(U_2427),U_2428)
| ~ class_Rings_Olinordered__semidom(U_2427) ),
inference(variable_rename,[status(thm)],[f_772_1]) ).
fof(f_772_3,plain,
! [U_2427,U_2428,U_2429] :
( c_Orderings_Oord__class_Oless(U_2427,c_Groups_Oone__class_Oone(U_2427),hAPP(hAPP(c_Power_Opower__class_Opower(U_2427),U_2428),c_Nat_OSuc(U_2429)))
| ~ c_Orderings_Oord__class_Oless(U_2427,c_Groups_Oone__class_Oone(U_2427),U_2428)
| ~ class_Rings_Olinordered__semidom(U_2427) ),
inference(definitional_conversion,[status(esa)],[f_772_2]) ).
cnf(f_772_4,plain,
( c_Orderings_Oord__class_Oless(U_2427,c_Groups_Oone__class_Oone(U_2427),hAPP(hAPP(c_Power_Opower__class_Opower(U_2427),U_2428),c_Nat_OSuc(U_2429)))
| ~ c_Orderings_Oord__class_Oless(U_2427,c_Groups_Oone__class_Oone(U_2427),U_2428)
| ~ class_Rings_Olinordered__semidom(U_2427) ),
inference(clausify,[status(thm)],[f_772_3]) ).
fof(f_773_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),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_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( V_x_2 != c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
& V_x_2 != V_y_2 ) )
& ( V_x_2 = c_Groups_Ouminus__class_Ouminus(T_a,V_y_2)
| V_x_2 = V_y_2
| hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x_2),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_2),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_realpow__two__disj]) ).
fof(f_773_2,plain,
! [U_2432,U_2431,U_2430] :
( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2431),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2432),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ( U_2431 != c_Groups_Ouminus__class_Ouminus(U_2430,U_2432)
& U_2431 != U_2432 ) )
& ( U_2431 = c_Groups_Ouminus__class_Ouminus(U_2430,U_2432)
| U_2431 = U_2432
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2431),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2432),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) )
| ~ class_Rings_Oidom(U_2430) ),
inference(variable_rename,[status(thm)],[f_773_1]) ).
fof(f_773_3,plain,
( ! [U_2430,U_2431,U_2432] :
( U_2431 != c_Groups_Ouminus__class_Ouminus(U_2430,U_2432)
| ~ sP253(U_2430,U_2431,U_2432) )
& ! [U_2430,U_2431,U_2432] :
( U_2431 != U_2432
| ~ sP253(U_2430,U_2431,U_2432) )
& ! [U_2430,U_2431,U_2432] :
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2431),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2432),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| sP253(U_2430,U_2431,U_2432)
| ~ sP254(U_2430,U_2431,U_2432) )
& ! [U_2430,U_2431,U_2432] :
( U_2431 = c_Groups_Ouminus__class_Ouminus(U_2430,U_2432)
| U_2431 = U_2432
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2431),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2432),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ sP254(U_2430,U_2431,U_2432) )
& ! [U_2430,U_2431,U_2432] :
( sP254(U_2430,U_2431,U_2432)
| ~ class_Rings_Oidom(U_2430) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP253,sP254])],[f_773_2]) ).
cnf(f_773_4,plain,
( sP254(U_2430,U_2431,U_2432)
| ~ class_Rings_Oidom(U_2430) ),
inference(clausify,[status(thm)],[f_773_3]) ).
cnf(f_773_5,plain,
( U_2431 = c_Groups_Ouminus__class_Ouminus(U_2430,U_2432)
| U_2431 = U_2432
| hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2431),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) != hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2432),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| ~ sP254(U_2430,U_2431,U_2432) ),
inference(clausify,[status(thm)],[f_773_3]) ).
cnf(f_773_6,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2431),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = hAPP(hAPP(c_Power_Opower__class_Opower(U_2430),U_2432),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
| sP253(U_2430,U_2431,U_2432)
| ~ sP254(U_2430,U_2431,U_2432) ),
inference(clausify,[status(thm)],[f_773_3]) ).
cnf(f_773_7,plain,
( U_2431 != U_2432
| ~ sP253(U_2430,U_2431,U_2432) ),
inference(clausify,[status(thm)],[f_773_3]) ).
cnf(f_773_8,plain,
( U_2431 != c_Groups_Ouminus__class_Ouminus(U_2430,U_2432)
| ~ sP253(U_2430,U_2431,U_2432) ),
inference(clausify,[status(thm)],[f_773_3]) ).
fof(f_774_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
inference(fof_nnf,[status(thm)],[fact_n__less__m__mult__n]) ).
fof(f_774_2,plain,
! [U_2434,U_2433] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2434),U_2433))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2434)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2433) ),
inference(variable_rename,[status(thm)],[f_774_1]) ).
fof(f_774_3,plain,
! [U_2433,U_2434] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2434),U_2433))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2434)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2433) ),
inference(definitional_conversion,[status(esa)],[f_774_2]) ).
cnf(f_774_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2433,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2434),U_2433))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2434)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2433) ),
inference(clausify,[status(thm)],[f_774_3]) ).
fof(f_775_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
inference(fof_nnf,[status(thm)],[fact_n__less__n__mult__m]) ).
fof(f_775_2,plain,
! [U_2436,U_2435] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2435,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2435),U_2436))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2436)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2435) ),
inference(variable_rename,[status(thm)],[f_775_1]) ).
fof(f_775_3,plain,
! [U_2435,U_2436] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2435,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2435),U_2436))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2436)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2435) ),
inference(definitional_conversion,[status(esa)],[f_775_2]) ).
cnf(f_775_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2435,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2435),U_2436))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2436)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2435) ),
inference(clausify,[status(thm)],[f_775_3]) ).
fof(f_776_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(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),V_n))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) ),
inference(fof_nnf,[status(thm)],[fact_one__less__mult]) ).
fof(f_776_2,plain,
! [U_2438,U_2437] :
( c_Orderings_Oord__class_Oless(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_2438),U_2437))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2438)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2437) ),
inference(variable_rename,[status(thm)],[f_776_1]) ).
fof(f_776_3,plain,
! [U_2437,U_2438] :
( c_Orderings_Oord__class_Oless(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_2438),U_2437))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2438)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2437) ),
inference(definitional_conversion,[status(esa)],[f_776_2]) ).
cnf(f_776_4,plain,
( c_Orderings_Oord__class_Oless(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_2438),U_2437))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2438)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2437) ),
inference(clausify,[status(thm)],[f_776_3]) ).
fof(f_777_1,plain,
! [V_n_2,V_ma_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_ma_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_ma_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_ma_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_ma_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_one__le__mult__iff]) ).
fof(f_777_2,plain,
! [U_2440,U_2439] :
( ( 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_2439),U_2440))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2440)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2439) )
& ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2440)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2439) )
| ~ 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_2439),U_2440)) ) ),
inference(variable_rename,[status(thm)],[f_777_1]) ).
fof(f_777_3,plain,
( ! [U_2444,U_2442] :
( 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_2442),U_2444))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2444)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2442) )
& ! [U_2443,U_2441] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2443)
& c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2441) )
| ~ 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_2441),U_2443)) ) ),
inference(miniscope,[status(thm)],[f_777_2]) ).
fof(f_777_4,plain,
( ! [U_2443,U_2441] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2443)
| ~ sP255(U_2443,U_2441) )
& ! [U_2443,U_2441] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2441)
| ~ sP255(U_2443,U_2441) )
& ! [U_2444,U_2442] :
( 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_2442),U_2444))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2444)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2442) )
& ! [U_2443,U_2441] :
( sP255(U_2443,U_2441)
| ~ 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_2441),U_2443)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255])],[f_777_3]) ).
cnf(f_777_5,plain,
( sP255(U_2443,U_2441)
| ~ 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_2441),U_2443)) ),
inference(clausify,[status(thm)],[f_777_4]) ).
cnf(f_777_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_2442),U_2444))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2444)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2442) ),
inference(clausify,[status(thm)],[f_777_4]) ).
cnf(f_777_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2441)
| ~ sP255(U_2443,U_2441) ),
inference(clausify,[status(thm)],[f_777_4]) ).
cnf(f_777_8,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2443)
| ~ sP255(U_2443,U_2441) ),
inference(clausify,[status(thm)],[f_777_4]) ).
fof(f_778_1,plain,
! [V_b,V_n,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a,V_b)
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__int]) ).
fof(f_778_2,plain,
! [U_2447,U_2446,U_2445] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2445,U_2447)
| U_2446 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2445),U_2446),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2447),U_2446)) ),
inference(variable_rename,[status(thm)],[f_778_1]) ).
fof(f_778_3,plain,
! [U_2446,U_2445,U_2447] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2445,U_2447)
| U_2446 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2445),U_2446),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2447),U_2446)) ),
inference(definitional_conversion,[status(esa)],[f_778_2]) ).
cnf(f_778_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2445,U_2447)
| U_2446 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2445),U_2446),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2447),U_2446)) ),
inference(clausify,[status(thm)],[f_778_3]) ).
fof(f_779_1,plain,
! [V_b_2,V_a_2,V_n_2] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_a_2,V_b_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_b_2),V_n_2)) ) )
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__int]) ).
fof(f_779_2,plain,
! [U_2450,U_2449,U_2448] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2449),U_2448),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2450),U_2448))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2449,U_2450) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2449,U_2450)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2449),U_2448),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2450),U_2448)) ) )
| U_2448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_779_1]) ).
fof(f_779_3,plain,
( ! [U_2450,U_2448,U_2449] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2449),U_2448),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2450),U_2448))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2449,U_2450)
| ~ sP256(U_2450,U_2448,U_2449) )
& ! [U_2450,U_2448,U_2449] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2449,U_2450)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2449),U_2448),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2450),U_2448))
| ~ sP256(U_2450,U_2448,U_2449) )
& ! [U_2450,U_2448,U_2449] :
( sP256(U_2450,U_2448,U_2449)
| U_2448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP256])],[f_779_2]) ).
cnf(f_779_4,plain,
( sP256(U_2450,U_2448,U_2449)
| U_2448 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_779_3]) ).
cnf(f_779_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2449,U_2450)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2449),U_2448),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2450),U_2448))
| ~ sP256(U_2450,U_2448,U_2449) ),
inference(clausify,[status(thm)],[f_779_3]) ).
cnf(f_779_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2449),U_2448),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_2450),U_2448))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2449,U_2450)
| ~ sP256(U_2450,U_2448,U_2449) ),
inference(clausify,[status(thm)],[f_779_3]) ).
fof(f_780_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_780_2,plain,
! [U_2453,U_2452,U_2451] :
( c_Orderings_Oord__class_Oless__eq(U_2451,hAPP(hAPP(c_Power_Opower__class_Opower(U_2451),U_2452),c_Nat_OSuc(U_2453)),U_2452)
| ~ c_Orderings_Oord__class_Oless__eq(U_2451,U_2452,c_Groups_Oone__class_Oone(U_2451))
| ~ c_Orderings_Oord__class_Oless__eq(U_2451,c_Groups_Ozero__class_Ozero(U_2451),U_2452)
| ~ class_Rings_Olinordered__semidom(U_2451) ),
inference(variable_rename,[status(thm)],[f_780_1]) ).
fof(f_780_3,plain,
! [U_2453,U_2452,U_2451] :
( c_Orderings_Oord__class_Oless__eq(U_2451,hAPP(hAPP(c_Power_Opower__class_Opower(U_2451),U_2452),c_Nat_OSuc(U_2453)),U_2452)
| ~ c_Orderings_Oord__class_Oless__eq(U_2451,U_2452,c_Groups_Oone__class_Oone(U_2451))
| ~ c_Orderings_Oord__class_Oless__eq(U_2451,c_Groups_Ozero__class_Ozero(U_2451),U_2452)
| ~ class_Rings_Olinordered__semidom(U_2451) ),
inference(definitional_conversion,[status(esa)],[f_780_2]) ).
cnf(f_780_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2451,hAPP(hAPP(c_Power_Opower__class_Opower(U_2451),U_2452),c_Nat_OSuc(U_2453)),U_2452)
| ~ c_Orderings_Oord__class_Oless__eq(U_2451,U_2452,c_Groups_Oone__class_Oone(U_2451))
| ~ c_Orderings_Oord__class_Oless__eq(U_2451,c_Groups_Ozero__class_Ozero(U_2451),U_2452)
| ~ class_Rings_Olinordered__semidom(U_2451) ),
inference(clausify,[status(thm)],[f_780_3]) ).
fof(f_781_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_781_2,plain,
! [U_2456,U_2455,U_2454] :
( c_Orderings_Oord__class_Oless(U_2454,hAPP(hAPP(c_Power_Opower__class_Opower(U_2454),U_2455),c_Nat_OSuc(U_2456)),c_Groups_Oone__class_Oone(U_2454))
| ~ c_Orderings_Oord__class_Oless(U_2454,U_2455,c_Groups_Oone__class_Oone(U_2454))
| ~ c_Orderings_Oord__class_Oless(U_2454,c_Groups_Ozero__class_Ozero(U_2454),U_2455)
| ~ class_Rings_Olinordered__semidom(U_2454) ),
inference(variable_rename,[status(thm)],[f_781_1]) ).
fof(f_781_3,plain,
! [U_2454,U_2455,U_2456] :
( c_Orderings_Oord__class_Oless(U_2454,hAPP(hAPP(c_Power_Opower__class_Opower(U_2454),U_2455),c_Nat_OSuc(U_2456)),c_Groups_Oone__class_Oone(U_2454))
| ~ c_Orderings_Oord__class_Oless(U_2454,U_2455,c_Groups_Oone__class_Oone(U_2454))
| ~ c_Orderings_Oord__class_Oless(U_2454,c_Groups_Ozero__class_Ozero(U_2454),U_2455)
| ~ class_Rings_Olinordered__semidom(U_2454) ),
inference(definitional_conversion,[status(esa)],[f_781_2]) ).
cnf(f_781_4,plain,
( c_Orderings_Oord__class_Oless(U_2454,hAPP(hAPP(c_Power_Opower__class_Opower(U_2454),U_2455),c_Nat_OSuc(U_2456)),c_Groups_Oone__class_Oone(U_2454))
| ~ c_Orderings_Oord__class_Oless(U_2454,U_2455,c_Groups_Oone__class_Oone(U_2454))
| ~ c_Orderings_Oord__class_Oless(U_2454,c_Groups_Ozero__class_Ozero(U_2454),U_2455)
| ~ class_Rings_Olinordered__semidom(U_2454) ),
inference(clausify,[status(thm)],[f_781_3]) ).
fof(f_782_1,plain,
! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_x,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(fof_nnf,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Otop__greatest]) ).
fof(f_782_2,plain,
! [U_2457] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2457,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(variable_rename,[status(thm)],[f_782_1]) ).
fof(f_782_3,plain,
! [U_2457] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2457,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(definitional_conversion,[status(esa)],[f_782_2]) ).
cnf(f_782_4,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2457,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
inference(clausify,[status(thm)],[f_782_3]) ).
fof(f_783_1,plain,
! [V_b,V_n,V_a] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a,V_b)
| V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a),V_n),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b),V_n)) ),
inference(fof_nnf,[status(thm)],[fact_pow__divides__pow__nat]) ).
fof(f_783_2,plain,
! [U_2460,U_2459,U_2458] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2458,U_2460)
| U_2459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2458),U_2459),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2460),U_2459)) ),
inference(variable_rename,[status(thm)],[f_783_1]) ).
fof(f_783_3,plain,
! [U_2458,U_2459,U_2460] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2458,U_2460)
| U_2459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2458),U_2459),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2460),U_2459)) ),
inference(definitional_conversion,[status(esa)],[f_783_2]) ).
cnf(f_783_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2458,U_2460)
| U_2459 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2458),U_2459),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2460),U_2459)) ),
inference(clausify,[status(thm)],[f_783_3]) ).
fof(f_784_1,plain,
! [V_b_2,V_a_2,V_n_2] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_a_2,V_b_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_a_2),V_n_2),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_b_2),V_n_2)) ) )
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(fof_nnf,[status(thm)],[fact_pow__divides__eq__nat]) ).
fof(f_784_2,plain,
! [U_2463,U_2462,U_2461] :
( ( ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2462),U_2461),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2463),U_2461))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2462,U_2463) )
& ( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2462,U_2463)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2462),U_2461),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2463),U_2461)) ) )
| U_2461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_784_1]) ).
fof(f_784_3,plain,
( ! [U_2461,U_2462,U_2463] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2462),U_2461),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2463),U_2461))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2462,U_2463)
| ~ sP257(U_2461,U_2462,U_2463) )
& ! [U_2461,U_2462,U_2463] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2462,U_2463)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2462),U_2461),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2463),U_2461))
| ~ sP257(U_2461,U_2462,U_2463) )
& ! [U_2461,U_2462,U_2463] :
( sP257(U_2461,U_2462,U_2463)
| U_2461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP257])],[f_784_2]) ).
cnf(f_784_4,plain,
( sP257(U_2461,U_2462,U_2463)
| U_2461 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_784_3]) ).
cnf(f_784_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2462,U_2463)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2462),U_2461),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2463),U_2461))
| ~ sP257(U_2461,U_2462,U_2463) ),
inference(clausify,[status(thm)],[f_784_3]) ).
cnf(f_784_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2462),U_2461),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2463),U_2461))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2462,U_2463)
| ~ sP257(U_2461,U_2462,U_2463) ),
inference(clausify,[status(thm)],[f_784_3]) ).
fof(f_785_1,plain,
! [V_x] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),V_x),
inference(fof_nnf,[status(thm)],[fact_gcd__lcm__complete__lattice__nat_Obot__least]) ).
fof(f_785_2,plain,
! [U_2464] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2464),
inference(variable_rename,[status(thm)],[f_785_1]) ).
fof(f_785_3,plain,
! [U_2464] : c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2464),
inference(definitional_conversion,[status(esa)],[f_785_2]) ).
cnf(f_785_4,plain,
c_Rings_Odvd__class_Odvd(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_2464),
inference(clausify,[status(thm)],[f_785_3]) ).
fof(f_786_1,plain,
! [V_n_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
& V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x_2)
| V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__power__nat__eq]) ).
fof(f_786_2,plain,
! [U_2466,U_2465] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2465),U_2466))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2465)
& U_2466 != 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_2465)
| U_2466 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2465),U_2466)) ) ),
inference(variable_rename,[status(thm)],[f_786_1]) ).
fof(f_786_3,plain,
( ! [U_2470,U_2468] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2468),U_2470))
| ( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2468)
& U_2470 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
& ! [U_2469,U_2467] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2467)
| U_2469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2467),U_2469)) ) ),
inference(miniscope,[status(thm)],[f_786_2]) ).
fof(f_786_4,plain,
( ! [U_2470,U_2468] :
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2468)
| ~ sP258(U_2470,U_2468) )
& ! [U_2470,U_2468] :
( U_2470 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP258(U_2470,U_2468) )
& ! [U_2470,U_2468] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2468),U_2470))
| sP258(U_2470,U_2468) )
& ! [U_2469,U_2467] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2467)
| U_2469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2467),U_2469)) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP258])],[f_786_3]) ).
cnf(f_786_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2467)
| U_2469 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2467),U_2469)) ),
inference(clausify,[status(thm)],[f_786_4]) ).
cnf(f_786_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2468),U_2470))
| sP258(U_2470,U_2468) ),
inference(clausify,[status(thm)],[f_786_4]) ).
cnf(f_786_7,plain,
( U_2470 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ sP258(U_2470,U_2468) ),
inference(clausify,[status(thm)],[f_786_4]) ).
cnf(f_786_8,plain,
( ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2468)
| ~ sP258(U_2470,U_2468) ),
inference(clausify,[status(thm)],[f_786_4]) ).
fof(f_787_1,plain,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
| V_a != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
inference(fof_nnf,[status(thm)],[fact_self__quotient__aux2]) ).
fof(f_787_2,plain,
! [U_2473,U_2472,U_2471] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2473,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2472)
| U_2471 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2472,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2471),U_2473))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2471) ),
inference(variable_rename,[status(thm)],[f_787_1]) ).
fof(f_787_3,plain,
! [U_2471,U_2472,U_2473] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2473,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2472)
| U_2471 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2472,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2471),U_2473))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2471) ),
inference(definitional_conversion,[status(esa)],[f_787_2]) ).
cnf(f_787_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2473,c_Groups_Oone__class_Oone(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2472)
| U_2471 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2472,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2471),U_2473))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2471) ),
inference(clausify,[status(thm)],[f_787_3]) ).
fof(f_788_1,plain,
! [V_q,V_r,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_q)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_a)
| V_a != c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_r,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_a) ),
inference(fof_nnf,[status(thm)],[fact_self__quotient__aux1]) ).
fof(f_788_2,plain,
! [U_2476,U_2475,U_2474] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2476)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2475,U_2474)
| U_2474 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2475,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2474),U_2476))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2474) ),
inference(variable_rename,[status(thm)],[f_788_1]) ).
fof(f_788_3,plain,
! [U_2474,U_2475,U_2476] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2476)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2475,U_2474)
| U_2474 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2475,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2474),U_2476))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2474) ),
inference(definitional_conversion,[status(esa)],[f_788_2]) ).
cnf(f_788_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_2476)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2475,U_2474)
| U_2474 != c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2475,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2474),U_2476))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2474) ),
inference(clausify,[status(thm)],[f_788_3]) ).
fof(f_789_1,plain,
! [V_w,V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_zminus__zadd__distrib]) ).
fof(f_789_2,plain,
! [U_2478,U_2477] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2477,U_2478)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2477),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2478)),
inference(variable_rename,[status(thm)],[f_789_1]) ).
fof(f_789_3,plain,
! [U_2477,U_2478] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2477,U_2478)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2477),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2478)),
inference(definitional_conversion,[status(esa)],[f_789_2]) ).
cnf(f_789_4,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2477,U_2478)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2477),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2478)),
inference(clausify,[status(thm)],[f_789_3]) ).
fof(f_790_1,plain,
! [V_z] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_z)) = V_z,
inference(fof_nnf,[status(thm)],[fact_zminus__zminus]) ).
fof(f_790_2,plain,
! [U_2479] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2479)) = U_2479,
inference(variable_rename,[status(thm)],[f_790_1]) ).
fof(f_790_3,plain,
! [U_2479] : c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2479)) = U_2479,
inference(definitional_conversion,[status(esa)],[f_790_2]) ).
cnf(f_790_4,plain,
c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2479)) = U_2479,
inference(clausify,[status(thm)],[f_790_3]) ).
fof(f_791_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_791_2,plain,
! [U_2481,U_2480] :
( U_2480 = U_2481
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2481,U_2480)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2480,U_2481) ),
inference(variable_rename,[status(thm)],[f_791_1]) ).
fof(f_791_3,plain,
! [U_2480,U_2481] :
( U_2480 = U_2481
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2481,U_2480)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2480,U_2481) ),
inference(definitional_conversion,[status(esa)],[f_791_2]) ).
cnf(f_791_4,plain,
( U_2480 = U_2481
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2481,U_2480)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2480,U_2481) ),
inference(clausify,[status(thm)],[f_791_3]) ).
fof(f_792_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_792_2,plain,
! [U_2484,U_2483,U_2482] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2482,U_2484)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2483,U_2484)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2482,U_2483) ),
inference(variable_rename,[status(thm)],[f_792_1]) ).
fof(f_792_3,plain,
! [U_2484,U_2483,U_2482] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2482,U_2484)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2483,U_2484)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2482,U_2483) ),
inference(definitional_conversion,[status(esa)],[f_792_2]) ).
cnf(f_792_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2482,U_2484)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2483,U_2484)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2482,U_2483) ),
inference(clausify,[status(thm)],[f_792_3]) ).
fof(f_793_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_793_2,plain,
! [U_2486,U_2485] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2486,U_2485)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2485,U_2486) ),
inference(variable_rename,[status(thm)],[f_793_1]) ).
fof(f_793_3,plain,
! [U_2486,U_2485] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2486,U_2485)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2485,U_2486) ),
inference(definitional_conversion,[status(esa)],[f_793_2]) ).
cnf(f_793_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2486,U_2485)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2485,U_2486) ),
inference(clausify,[status(thm)],[f_793_3]) ).
fof(f_794_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_794_2,plain,
! [U_2487] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2487,U_2487),
inference(variable_rename,[status(thm)],[f_794_1]) ).
fof(f_794_3,plain,
! [U_2487] : c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2487,U_2487),
inference(definitional_conversion,[status(esa)],[f_794_2]) ).
cnf(f_794_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2487,U_2487),
inference(clausify,[status(thm)],[f_794_3]) ).
fof(f_795_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_795_2,plain,
! [U_2489,U_2488] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2488,U_2489) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2489,U_2488),
inference(variable_rename,[status(thm)],[f_795_1]) ).
fof(f_795_3,plain,
! [U_2489,U_2488] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2488,U_2489) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2489,U_2488),
inference(definitional_conversion,[status(esa)],[f_795_2]) ).
cnf(f_795_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2488,U_2489) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2489,U_2488),
inference(clausify,[status(thm)],[f_795_3]) ).
fof(f_796_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_796_2,plain,
! [U_2492,U_2491,U_2490] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2490,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2491,U_2492)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2491,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2490,U_2492)),
inference(variable_rename,[status(thm)],[f_796_1]) ).
fof(f_796_3,plain,
! [U_2490,U_2491,U_2492] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2490,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2491,U_2492)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2491,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2490,U_2492)),
inference(definitional_conversion,[status(esa)],[f_796_2]) ).
cnf(f_796_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2490,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2491,U_2492)) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2491,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2490,U_2492)),
inference(clausify,[status(thm)],[f_796_3]) ).
fof(f_797_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_797_2,plain,
! [U_2495,U_2494,U_2493] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2493,U_2494),U_2495) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2493,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2494,U_2495)),
inference(variable_rename,[status(thm)],[f_797_1]) ).
fof(f_797_3,plain,
! [U_2494,U_2493,U_2495] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2493,U_2494),U_2495) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2493,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2494,U_2495)),
inference(definitional_conversion,[status(esa)],[f_797_2]) ).
cnf(f_797_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2493,U_2494),U_2495) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2493,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2494,U_2495)),
inference(clausify,[status(thm)],[f_797_3]) ).
fof(f_798_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_798_2,plain,
! [U_2498,U_2497,U_2496] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2498,U_2496),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2498,U_2497))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2496,U_2497) ),
inference(variable_rename,[status(thm)],[f_798_1]) ).
fof(f_798_3,plain,
! [U_2497,U_2496,U_2498] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2498,U_2496),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2498,U_2497))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2496,U_2497) ),
inference(definitional_conversion,[status(esa)],[f_798_2]) ).
cnf(f_798_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2498,U_2496),c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2498,U_2497))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2496,U_2497) ),
inference(clausify,[status(thm)],[f_798_3]) ).
fof(f_799_1,plain,
! [V_t_2,V_d_2] :
( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2)) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_t_2))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2) ) ),
inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I2_J]) ).
fof(f_799_2,plain,
! [U_2500,U_2499] :
( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2499,U_2500)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2499,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2500)) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2499,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2500))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2499,U_2500) ) ),
inference(variable_rename,[status(thm)],[f_799_1]) ).
fof(f_799_3,plain,
( ! [U_2504,U_2502] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2502,U_2504)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2502,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2504)) )
& ! [U_2503,U_2501] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2501,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2503))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2501,U_2503) ) ),
inference(miniscope,[status(thm)],[f_799_2]) ).
fof(f_799_4,plain,
( ! [U_2502,U_2504] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2502,U_2504)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2502,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2504)) )
& ! [U_2501,U_2503] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2501,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2503))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2501,U_2503) ) ),
inference(definitional_conversion,[status(esa)],[f_799_3]) ).
cnf(f_799_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2501,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2503))
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2501,U_2503) ),
inference(clausify,[status(thm)],[f_799_4]) ).
cnf(f_799_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2502,U_2504)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2502,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2504)) ),
inference(clausify,[status(thm)],[f_799_4]) ).
fof(f_800_1,plain,
! [V_t_2,V_d_2] :
( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_d_2),V_t_2)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_d_2,V_t_2) ) ),
inference(fof_nnf,[status(thm)],[fact_uminus__dvd__conv_I1_J]) ).
fof(f_800_2,plain,
! [U_2506,U_2505] :
( ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2505,U_2506)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2505),U_2506) )
& ( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2505),U_2506)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2505,U_2506) ) ),
inference(variable_rename,[status(thm)],[f_800_1]) ).
fof(f_800_3,plain,
( ! [U_2510,U_2508] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2508,U_2510)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2508),U_2510) )
& ! [U_2509,U_2507] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2507),U_2509)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2507,U_2509) ) ),
inference(miniscope,[status(thm)],[f_800_2]) ).
fof(f_800_4,plain,
( ! [U_2510,U_2508] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2508,U_2510)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2508),U_2510) )
& ! [U_2507,U_2509] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2507),U_2509)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2507,U_2509) ) ),
inference(definitional_conversion,[status(esa)],[f_800_3]) ).
cnf(f_800_5,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2507),U_2509)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2507,U_2509) ),
inference(clausify,[status(thm)],[f_800_4]) ).
cnf(f_800_6,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2508,U_2510)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2508),U_2510) ),
inference(clausify,[status(thm)],[f_800_4]) ).
fof(f_801_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_801_2,plain,
! [U_2511] :
( U_2511 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2511,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(variable_rename,[status(thm)],[f_801_1]) ).
fof(f_801_3,plain,
! [U_2511] :
( U_2511 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2511,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(definitional_conversion,[status(esa)],[f_801_2]) ).
cnf(f_801_4,plain,
( U_2511 = c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
| U_2511 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2511,c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
inference(clausify,[status(thm)],[f_801_3]) ).
fof(f_802_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__neg__lemma]) ).
fof(f_802_2,plain,
! [U_2517,U_2516,U_2515,U_2514,U_2513,U_2512] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2516,U_2513)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2515,U_2512)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2515)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2517)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2514,U_2512)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2515),U_2516),U_2517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2512),U_2513),U_2514) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2515),U_2516),U_2517) ),
inference(variable_rename,[status(thm)],[f_802_1]) ).
fof(f_802_3,plain,
! [U_2513,U_2512,U_2514,U_2515,U_2516,U_2517] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2516,U_2513)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2515,U_2512)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2515)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2517)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2514,U_2512)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2515),U_2516),U_2517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2512),U_2513),U_2514) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2515),U_2516),U_2517) ),
inference(definitional_conversion,[status(esa)],[f_802_2]) ).
cnf(f_802_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2516,U_2513)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2515,U_2512)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2515)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2517)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2514,U_2512)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2515),U_2516),U_2517),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2512),U_2513),U_2514) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2515),U_2516),U_2517) ),
inference(clausify,[status(thm)],[f_802_3]) ).
fof(f_803_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_b,V_r)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_r,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)) ),
inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma__neg]) ).
fof(f_803_2,plain,
! [U_2522,U_2521,U_2520,U_2519,U_2518] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2521,U_2519)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2518,U_2520)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2518,U_2522)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2522,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2518),U_2519),U_2520),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2518),U_2521),U_2522)) ),
inference(variable_rename,[status(thm)],[f_803_1]) ).
fof(f_803_3,plain,
! [U_2521,U_2519,U_2518,U_2520,U_2522] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2521,U_2519)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2518,U_2520)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2518,U_2522)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2522,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2518),U_2519),U_2520),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2518),U_2521),U_2522)) ),
inference(definitional_conversion,[status(esa)],[f_803_2]) ).
cnf(f_803_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2521,U_2519)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2518,U_2520)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2518,U_2522)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2522,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2518),U_2519),U_2520),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2518),U_2521),U_2522)) ),
inference(clausify,[status(thm)],[f_803_3]) ).
fof(f_804_1,plain,
! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q,V_q_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_b_H,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H) ),
inference(fof_nnf,[status(thm)],[fact_zdiv__mono2__lemma]) ).
fof(f_804_2,plain,
! [U_2528,U_2527,U_2526,U_2525,U_2524,U_2523] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2524,U_2527)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2526,U_2523)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2526)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2525)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2528,U_2526)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2526),U_2527),U_2528))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2523),U_2524),U_2525) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2526),U_2527),U_2528) ),
inference(variable_rename,[status(thm)],[f_804_1]) ).
fof(f_804_3,plain,
! [U_2525,U_2528,U_2524,U_2526,U_2523,U_2527] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2524,U_2527)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2526,U_2523)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2526)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2525)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2528,U_2526)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2526),U_2527),U_2528))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2523),U_2524),U_2525) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2526),U_2527),U_2528) ),
inference(definitional_conversion,[status(esa)],[f_804_2]) ).
cnf(f_804_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2524,U_2527)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2526,U_2523)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2526)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2525)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2528,U_2526)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2526),U_2527),U_2528))
| c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2523),U_2524),U_2525) != c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2526),U_2527),U_2528) ),
inference(clausify,[status(thm)],[f_804_3]) ).
fof(f_805_1,plain,
! [V_r,V_q,V_r_H,V_q_H,V_b] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,V_q)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r,V_b)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q_H),V_r_H),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q),V_r)) ),
inference(fof_nnf,[status(thm)],[fact_unique__quotient__lemma]) ).
fof(f_805_2,plain,
! [U_2533,U_2532,U_2531,U_2530,U_2529] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2530,U_2532)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2533,U_2529)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2531,U_2529)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2531)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2529),U_2530),U_2531),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2529),U_2532),U_2533)) ),
inference(variable_rename,[status(thm)],[f_805_1]) ).
fof(f_805_3,plain,
! [U_2530,U_2529,U_2531,U_2533,U_2532] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2530,U_2532)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2533,U_2529)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2531,U_2529)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2531)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2529),U_2530),U_2531),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2529),U_2532),U_2533)) ),
inference(definitional_conversion,[status(esa)],[f_805_2]) ).
cnf(f_805_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2530,U_2532)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2533,U_2529)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2531,U_2529)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2531)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2529),U_2530),U_2531),c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2529),U_2532),U_2533)) ),
inference(clausify,[status(thm)],[f_805_3]) ).
fof(f_806_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_q_H,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_r_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(fof_nnf,[status(thm)],[fact_q__neg__lemma]) ).
fof(f_806_2,plain,
! [U_2536,U_2535,U_2534] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2535,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2534)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2536)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2534),U_2535),U_2536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(variable_rename,[status(thm)],[f_806_1]) ).
fof(f_806_3,plain,
! [U_2536,U_2534,U_2535] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2535,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2534)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2536)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2534),U_2535),U_2536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(definitional_conversion,[status(esa)],[f_806_2]) ).
cnf(f_806_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2535,c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2534)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2536)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2534),U_2535),U_2536),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_806_3]) ).
fof(f_807_1,plain,
! [V_r_H,V_q_H,V_b_H] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_q_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b_H)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_r_H,V_b_H)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H),V_r_H)) ),
inference(fof_nnf,[status(thm)],[fact_q__pos__lemma]) ).
fof(f_807_2,plain,
! [U_2539,U_2538,U_2537] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2538)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2537)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2539,U_2537)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2537),U_2538),U_2539)) ),
inference(variable_rename,[status(thm)],[f_807_1]) ).
fof(f_807_3,plain,
! [U_2538,U_2537,U_2539] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2538)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2537)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2539,U_2537)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2537),U_2538),U_2539)) ),
inference(definitional_conversion,[status(esa)],[f_807_2]) ).
cnf(f_807_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2538)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2537)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2539,U_2537)
| ~ 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,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2537),U_2538),U_2539)) ),
inference(clausify,[status(thm)],[f_807_3]) ).
fof(f_808_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_808_2,plain,
! [U_2541,U_2540] :
( 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_2540),U_2541))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2540) ),
inference(variable_rename,[status(thm)],[f_808_1]) ).
fof(f_808_3,plain,
! [U_2540,U_2541] :
( 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_2540),U_2541))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2540) ),
inference(definitional_conversion,[status(esa)],[f_808_2]) ).
cnf(f_808_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_2540),U_2541))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2540) ),
inference(clausify,[status(thm)],[f_808_3]) ).
fof(f_809_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_809_2,plain,
! [U_2543,U_2542] :
( 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_2542),U_2543))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2543)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2542) ),
inference(variable_rename,[status(thm)],[f_809_1]) ).
fof(f_809_3,plain,
! [U_2542,U_2543] :
( 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_2542),U_2543))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2543)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2542) ),
inference(definitional_conversion,[status(esa)],[f_809_2]) ).
cnf(f_809_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_2542),U_2543))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2543)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2542) ),
inference(clausify,[status(thm)],[f_809_3]) ).
fof(f_810_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_810_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_810_1]) ).
cnf(f_810_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_810_2]) ).
fof(f_811_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_811_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_811_1]) ).
cnf(f_811_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_811_2]) ).
fof(f_812_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_812_2,plain,
! [U_2545,U_2544] :
( 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_2544,U_2545))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2545)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2544) ),
inference(variable_rename,[status(thm)],[f_812_1]) ).
fof(f_812_3,plain,
! [U_2545,U_2544] :
( 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_2544,U_2545))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2545)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2544) ),
inference(definitional_conversion,[status(esa)],[f_812_2]) ).
cnf(f_812_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_2544,U_2545))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2545)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2544) ),
inference(clausify,[status(thm)],[f_812_3]) ).
fof(f_813_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_813_2,plain,
! [U_2546] :
( c_Power_Opower__class_Opower(U_2546) = c_Power_Opower_Opower(U_2546,c_Groups_Oone__class_Oone(U_2546),c_Groups_Otimes__class_Otimes(U_2546))
| ~ class_Power_Opower(U_2546) ),
inference(variable_rename,[status(thm)],[f_813_1]) ).
fof(f_813_3,plain,
! [U_2546] :
( c_Power_Opower__class_Opower(U_2546) = c_Power_Opower_Opower(U_2546,c_Groups_Oone__class_Oone(U_2546),c_Groups_Otimes__class_Otimes(U_2546))
| ~ class_Power_Opower(U_2546) ),
inference(definitional_conversion,[status(esa)],[f_813_2]) ).
cnf(f_813_4,plain,
( c_Power_Opower__class_Opower(U_2546) = c_Power_Opower_Opower(U_2546,c_Groups_Oone__class_Oone(U_2546),c_Groups_Otimes__class_Otimes(U_2546))
| ~ class_Power_Opower(U_2546) ),
inference(clausify,[status(thm)],[f_813_3]) ).
fof(f_814_1,plain,
! [V_x] :
( c_RComplete_Onatfloor(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_Onatfloor(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_natfloor__add__one]) ).
fof(f_814_2,plain,
! [U_2547] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2547,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2547),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_2547) ),
inference(variable_rename,[status(thm)],[f_814_1]) ).
fof(f_814_3,plain,
! [U_2547] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2547,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2547),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_2547) ),
inference(definitional_conversion,[status(esa)],[f_814_2]) ).
cnf(f_814_4,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2547,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2547),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_2547) ),
inference(clausify,[status(thm)],[f_814_3]) ).
fof(f_815_1,plain,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_natfloor__one]) ).
fof(f_815_2,plain,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_815_1]) ).
cnf(f_815_3,plain,
c_RComplete_Onatfloor(c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_815_2]) ).
fof(f_816_1,plain,
! [V_y,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),c_RComplete_Onatfloor(V_y))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,V_y) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__mono]) ).
fof(f_816_2,plain,
! [U_2549,U_2548] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_2548),c_RComplete_Onatfloor(U_2549))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2548,U_2549) ),
inference(variable_rename,[status(thm)],[f_816_1]) ).
fof(f_816_3,plain,
! [U_2548,U_2549] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_2548),c_RComplete_Onatfloor(U_2549))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2548,U_2549) ),
inference(definitional_conversion,[status(esa)],[f_816_2]) ).
cnf(f_816_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatfloor(U_2548),c_RComplete_Onatfloor(U_2549))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2548,U_2549) ),
inference(clausify,[status(thm)],[f_816_3]) ).
fof(f_817_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),
inference(fof_nnf,[status(thm)],[fact_zero__le__natfloor]) ).
fof(f_817_2,plain,
! [U_2550] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_2550)),
inference(variable_rename,[status(thm)],[f_817_1]) ).
fof(f_817_3,plain,
! [U_2550] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_2550)),
inference(definitional_conversion,[status(esa)],[f_817_2]) ).
cnf(f_817_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_RComplete_Onatfloor(U_2550)),
inference(clausify,[status(thm)],[f_817_3]) ).
fof(f_818_1,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[fact_natfloor__zero]) ).
fof(f_818_2,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_818_1]) ).
cnf(f_818_3,plain,
c_RComplete_Onatfloor(c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_818_2]) ).
fof(f_819_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_819_2,plain,
! [U_2554,U_2553,U_2552,U_2551] : hAPP(hAPP(c_Power_Opower_Opower(U_2551,U_2552,U_2553),U_2554),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2552,
inference(variable_rename,[status(thm)],[f_819_1]) ).
fof(f_819_3,plain,
! [U_2551,U_2552,U_2553,U_2554] : hAPP(hAPP(c_Power_Opower_Opower(U_2551,U_2552,U_2553),U_2554),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2552,
inference(definitional_conversion,[status(esa)],[f_819_2]) ).
cnf(f_819_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_2551,U_2552,U_2553),U_2554),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_2552,
inference(clausify,[status(thm)],[f_819_3]) ).
fof(f_820_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_820_2,plain,
! [U_2559,U_2558,U_2557,U_2556,U_2555] : hAPP(hAPP(c_Power_Opower_Opower(U_2555,U_2556,U_2557),U_2558),c_Nat_OSuc(U_2559)) = hAPP(hAPP(U_2557,U_2558),hAPP(hAPP(c_Power_Opower_Opower(U_2555,U_2556,U_2557),U_2558),U_2559)),
inference(variable_rename,[status(thm)],[f_820_1]) ).
fof(f_820_3,plain,
! [U_2555,U_2556,U_2557,U_2558,U_2559] : hAPP(hAPP(c_Power_Opower_Opower(U_2555,U_2556,U_2557),U_2558),c_Nat_OSuc(U_2559)) = hAPP(hAPP(U_2557,U_2558),hAPP(hAPP(c_Power_Opower_Opower(U_2555,U_2556,U_2557),U_2558),U_2559)),
inference(definitional_conversion,[status(esa)],[f_820_2]) ).
cnf(f_820_4,plain,
hAPP(hAPP(c_Power_Opower_Opower(U_2555,U_2556,U_2557),U_2558),c_Nat_OSuc(U_2559)) = hAPP(hAPP(U_2557,U_2558),hAPP(hAPP(c_Power_Opower_Opower(U_2555,U_2556,U_2557),U_2558),U_2559)),
inference(clausify,[status(thm)],[f_820_3]) ).
fof(f_821_1,plain,
! [V_x] :
( c_RComplete_Onatfloor(V_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__neg]) ).
fof(f_821_2,plain,
! [U_2560] :
( c_RComplete_Onatfloor(U_2560) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2560,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(variable_rename,[status(thm)],[f_821_1]) ).
fof(f_821_3,plain,
! [U_2560] :
( c_RComplete_Onatfloor(U_2560) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2560,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(definitional_conversion,[status(esa)],[f_821_2]) ).
cnf(f_821_4,plain,
( c_RComplete_Onatfloor(U_2560) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2560,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_821_3]) ).
fof(f_822_1,plain,
! [V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(V_x_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq__one]) ).
fof(f_822_2,plain,
! [U_2561] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2561))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2561) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2561)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2561)) ) ),
inference(variable_rename,[status(thm)],[f_822_1]) ).
fof(f_822_3,plain,
( ! [U_2563] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2563))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2563) )
& ! [U_2562] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2562)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2562)) ) ),
inference(miniscope,[status(thm)],[f_822_2]) ).
fof(f_822_4,plain,
( ! [U_2563] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2563))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2563) )
& ! [U_2562] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2562)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2562)) ) ),
inference(definitional_conversion,[status(esa)],[f_822_3]) ).
cnf(f_822_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2562)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2562)) ),
inference(clausify,[status(thm)],[f_822_4]) ).
cnf(f_822_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_RComplete_Onatfloor(U_2563))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),U_2563) ),
inference(clausify,[status(thm)],[f_822_4]) ).
fof(f_823_1,plain,
! [V_b,V_a] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(V_a)),c_RComplete_Onatfloor(V_b)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),V_a),V_b)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_b)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a) ),
inference(fof_nnf,[status(thm)],[fact_le__mult__natfloor]) ).
fof(f_823_2,plain,
! [U_2565,U_2564] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_2564)),c_RComplete_Onatfloor(U_2565)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2564),U_2565)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2565)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2564) ),
inference(variable_rename,[status(thm)],[f_823_1]) ).
fof(f_823_3,plain,
! [U_2564,U_2565] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_2564)),c_RComplete_Onatfloor(U_2565)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2564),U_2565)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2565)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2564) ),
inference(definitional_conversion,[status(esa)],[f_823_2]) ).
cnf(f_823_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_RComplete_Onatfloor(U_2564)),c_RComplete_Onatfloor(U_2565)),c_RComplete_Onatfloor(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),U_2564),U_2565)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2565)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2564) ),
inference(clausify,[status(thm)],[f_823_3]) ).
fof(f_824_1,plain,
! [V_x,V_n] :
( c_RComplete_Onatceiling(V_x) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__eq]) ).
fof(f_824_2,plain,
! [U_2567,U_2566] :
( c_RComplete_Onatceiling(U_2567) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2566,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2567,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2566),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2566),U_2567) ),
inference(variable_rename,[status(thm)],[f_824_1]) ).
fof(f_824_3,plain,
! [U_2566,U_2567] :
( c_RComplete_Onatceiling(U_2567) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2566,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2567,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2566),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2566),U_2567) ),
inference(definitional_conversion,[status(esa)],[f_824_2]) ).
cnf(f_824_4,plain,
( c_RComplete_Onatceiling(U_2567) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2566,c_Groups_Oone__class_Oone(tc_Nat_Onat))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2567,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2566),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2566),U_2567) ),
inference(clausify,[status(thm)],[f_824_3]) ).
fof(f_825_1,plain,
! [V_k_2,V_P_2,V_d_2] :
( ! [B_x] :
( hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_d_2))))
| ~ hBOOL(hAPP(V_P_2,B_x)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_k_2)
| ? [B_x] :
( ~ hBOOL(hAPP(V_P_2,c_Groups_Oplus__class_Oplus(tc_Int_Oint,B_x,V_d_2)))
& hBOOL(hAPP(V_P_2,B_x)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d_2) ),
inference(fof_nnf,[status(thm)],[fact_incr__mult__lemma]) ).
fof(f_825_2,plain,
! [U_2572,U_2571,U_2570] :
( ! [U_2569] :
( hBOOL(hAPP(U_2571,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2569,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2572),U_2570))))
| ~ hBOOL(hAPP(U_2571,U_2569)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2572)
| ? [U_2568] :
( ~ hBOOL(hAPP(U_2571,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2568,U_2570)))
& hBOOL(hAPP(U_2571,U_2568)) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2570) ),
inference(variable_rename,[status(thm)],[f_825_1]) ).
fof(f_825_3,plain,
! [U_2572,U_2571,U_2570] :
( ! [U_2569] :
( hBOOL(hAPP(U_2571,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2569,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2572),U_2570))))
| ~ hBOOL(hAPP(U_2571,U_2569)) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2572)
| ( ~ hBOOL(hAPP(U_2571,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK33(U_2572,U_2571,U_2570),U_2570)))
& hBOOL(hAPP(U_2571,sK33(U_2572,U_2571,U_2570))) )
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2570) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_2568,sK33(U_2572,U_2571,U_2570))],[f_825_2]) ).
fof(f_825_4,plain,
( ! [U_2570,U_2571,U_2572] :
( ~ hBOOL(hAPP(U_2571,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK33(U_2572,U_2571,U_2570),U_2570)))
| ~ sP259(U_2570,U_2571,U_2572) )
& ! [U_2570,U_2571,U_2572] :
( hBOOL(hAPP(U_2571,sK33(U_2572,U_2571,U_2570)))
| ~ sP259(U_2570,U_2571,U_2572) )
& ! [U_2569,U_2570,U_2571,U_2572] :
( hBOOL(hAPP(U_2571,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2569,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2572),U_2570))))
| ~ hBOOL(hAPP(U_2571,U_2569))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2572)
| sP259(U_2570,U_2571,U_2572)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2570) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP259])],[f_825_3]) ).
cnf(f_825_5,plain,
( hBOOL(hAPP(U_2571,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2569,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2572),U_2570))))
| ~ hBOOL(hAPP(U_2571,U_2569))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2572)
| sP259(U_2570,U_2571,U_2572)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2570) ),
inference(clausify,[status(thm)],[f_825_4]) ).
cnf(f_825_6,plain,
( hBOOL(hAPP(U_2571,sK33(U_2572,U_2571,U_2570)))
| ~ sP259(U_2570,U_2571,U_2572) ),
inference(clausify,[status(thm)],[f_825_4]) ).
cnf(f_825_7,plain,
( ~ hBOOL(hAPP(U_2571,c_Groups_Oplus__class_Oplus(tc_Int_Oint,sK33(U_2572,U_2571,U_2570),U_2570)))
| ~ sP259(U_2570,U_2571,U_2572) ),
inference(clausify,[status(thm)],[f_825_4]) ).
fof(f_826_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__ge__zero]) ).
fof(f_826_2,plain,
! [U_2573] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2573)),
inference(variable_rename,[status(thm)],[f_826_1]) ).
fof(f_826_3,plain,
! [U_2573] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2573)),
inference(definitional_conversion,[status(esa)],[f_826_2]) ).
cnf(f_826_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2573)),
inference(clausify,[status(thm)],[f_826_3]) ).
fof(f_827_1,plain,
! [V_n] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
inference(fof_nnf,[status(thm)],[fact_natfloor__real__of__nat]) ).
fof(f_827_2,plain,
! [U_2574] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_2574)) = U_2574,
inference(variable_rename,[status(thm)],[f_827_1]) ).
fof(f_827_3,plain,
! [U_2574] : c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_2574)) = U_2574,
inference(definitional_conversion,[status(esa)],[f_827_2]) ).
cnf(f_827_4,plain,
c_RComplete_Onatfloor(c_RealDef_Oreal(tc_Nat_Onat,U_2574)) = U_2574,
inference(clausify,[status(thm)],[f_827_3]) ).
fof(f_828_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__iff]) ).
fof(f_828_2,plain,
! [U_2576,U_2575] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2575),c_RealDef_Oreal(tc_Nat_Onat,U_2576))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2575,U_2576) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2575,U_2576)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2575),c_RealDef_Oreal(tc_Nat_Onat,U_2576)) ) ),
inference(variable_rename,[status(thm)],[f_828_1]) ).
fof(f_828_3,plain,
( ! [U_2580,U_2578] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2578),c_RealDef_Oreal(tc_Nat_Onat,U_2580))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2578,U_2580) )
& ! [U_2579,U_2577] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2577,U_2579)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2577),c_RealDef_Oreal(tc_Nat_Onat,U_2579)) ) ),
inference(miniscope,[status(thm)],[f_828_2]) ).
fof(f_828_4,plain,
( ! [U_2580,U_2578] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2578),c_RealDef_Oreal(tc_Nat_Onat,U_2580))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2578,U_2580) )
& ! [U_2577,U_2579] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2577,U_2579)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2577),c_RealDef_Oreal(tc_Nat_Onat,U_2579)) ) ),
inference(definitional_conversion,[status(esa)],[f_828_3]) ).
cnf(f_828_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2577,U_2579)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2577),c_RealDef_Oreal(tc_Nat_Onat,U_2579)) ),
inference(clausify,[status(thm)],[f_828_4]) ).
cnf(f_828_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2578),c_RealDef_Oreal(tc_Nat_Onat,U_2580))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2578,U_2580) ),
inference(clausify,[status(thm)],[f_828_4]) ).
fof(f_829_1,plain,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__mult]) ).
fof(f_829_2,plain,
! [U_2582,U_2581] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2581),U_2582)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2581)),c_RealDef_Oreal(tc_Nat_Onat,U_2582)),
inference(variable_rename,[status(thm)],[f_829_1]) ).
fof(f_829_3,plain,
! [U_2581,U_2582] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2581),U_2582)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2581)),c_RealDef_Oreal(tc_Nat_Onat,U_2582)),
inference(definitional_conversion,[status(esa)],[f_829_2]) ).
cnf(f_829_4,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2581),U_2582)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2581)),c_RealDef_Oreal(tc_Nat_Onat,U_2582)),
inference(clausify,[status(thm)],[f_829_3]) ).
fof(f_830_1,plain,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__add]) ).
fof(f_830_2,plain,
! [U_2584,U_2583] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2583,U_2584)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2583),c_RealDef_Oreal(tc_Nat_Onat,U_2584)),
inference(variable_rename,[status(thm)],[f_830_1]) ).
fof(f_830_3,plain,
! [U_2583,U_2584] : c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2583,U_2584)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2583),c_RealDef_Oreal(tc_Nat_Onat,U_2584)),
inference(definitional_conversion,[status(esa)],[f_830_2]) ).
cnf(f_830_4,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2583,U_2584)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2583),c_RealDef_Oreal(tc_Nat_Onat,U_2584)),
inference(clausify,[status(thm)],[f_830_3]) ).
fof(f_831_1,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__1]) ).
fof(f_831_2,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_831_1]) ).
cnf(f_831_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_831_2]) ).
fof(f_832_1,plain,
! [V_n,V_m] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)),
inference(fof_nnf,[status(thm)],[fact_power__real__of__nat]) ).
fof(f_832_2,plain,
! [U_2586,U_2585] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2585)),U_2586) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2585),U_2586)),
inference(variable_rename,[status(thm)],[f_832_1]) ).
fof(f_832_3,plain,
! [U_2585,U_2586] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2585)),U_2586) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2585),U_2586)),
inference(definitional_conversion,[status(esa)],[f_832_2]) ).
cnf(f_832_4,plain,
hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2585)),U_2586) = c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2585),U_2586)),
inference(clausify,[status(thm)],[f_832_3]) ).
fof(f_833_1,plain,
! [V_n,V_m] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_m)),V_n),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__power]) ).
fof(f_833_2,plain,
! [U_2588,U_2587] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2587),U_2588)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2587)),U_2588),
inference(variable_rename,[status(thm)],[f_833_1]) ).
fof(f_833_3,plain,
! [U_2587,U_2588] : c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2587),U_2588)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2587)),U_2588),
inference(definitional_conversion,[status(esa)],[f_833_2]) ).
cnf(f_833_4,plain,
c_RealDef_Oreal(tc_Nat_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_2587),U_2588)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2587)),U_2588),
inference(clausify,[status(thm)],[f_833_3]) ).
fof(f_834_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(V_x))),
inference(fof_nnf,[status(thm)],[fact_real__natceiling__ge]) ).
fof(f_834_2,plain,
! [U_2589] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2589,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_2589))),
inference(variable_rename,[status(thm)],[f_834_1]) ).
fof(f_834_3,plain,
! [U_2589] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2589,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_2589))),
inference(definitional_conversion,[status(esa)],[f_834_2]) ).
cnf(f_834_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2589,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatceiling(U_2589))),
inference(clausify,[status(thm)],[f_834_3]) ).
fof(f_835_1,plain,
! [V_ma_2,V_n_2] :
( ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)
| V_n_2 != V_ma_2 )
& ( V_n_2 = V_ma_2
| c_RealDef_Oreal(tc_Nat_Onat,V_n_2) != c_RealDef_Oreal(tc_Nat_Onat,V_ma_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__inject]) ).
fof(f_835_2,plain,
! [U_2591,U_2590] :
( ( c_RealDef_Oreal(tc_Nat_Onat,U_2590) = c_RealDef_Oreal(tc_Nat_Onat,U_2591)
| U_2590 != U_2591 )
& ( U_2590 = U_2591
| c_RealDef_Oreal(tc_Nat_Onat,U_2590) != c_RealDef_Oreal(tc_Nat_Onat,U_2591) ) ),
inference(variable_rename,[status(thm)],[f_835_1]) ).
fof(f_835_3,plain,
( ! [U_2595,U_2593] :
( c_RealDef_Oreal(tc_Nat_Onat,U_2593) = c_RealDef_Oreal(tc_Nat_Onat,U_2595)
| U_2593 != U_2595 )
& ! [U_2594,U_2592] :
( U_2592 = U_2594
| c_RealDef_Oreal(tc_Nat_Onat,U_2592) != c_RealDef_Oreal(tc_Nat_Onat,U_2594) ) ),
inference(miniscope,[status(thm)],[f_835_2]) ).
fof(f_835_4,plain,
( ! [U_2593,U_2595] :
( c_RealDef_Oreal(tc_Nat_Onat,U_2593) = c_RealDef_Oreal(tc_Nat_Onat,U_2595)
| U_2593 != U_2595 )
& ! [U_2594,U_2592] :
( U_2592 = U_2594
| c_RealDef_Oreal(tc_Nat_Onat,U_2592) != c_RealDef_Oreal(tc_Nat_Onat,U_2594) ) ),
inference(definitional_conversion,[status(esa)],[f_835_3]) ).
cnf(f_835_5,plain,
( U_2592 = U_2594
| c_RealDef_Oreal(tc_Nat_Onat,U_2592) != c_RealDef_Oreal(tc_Nat_Onat,U_2594) ),
inference(clausify,[status(thm)],[f_835_4]) ).
cnf(f_835_6,plain,
( c_RealDef_Oreal(tc_Nat_Onat,U_2593) = c_RealDef_Oreal(tc_Nat_Onat,U_2595)
| U_2593 != U_2595 ),
inference(clausify,[status(thm)],[f_835_4]) ).
fof(f_836_1,plain,
! [V_n] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,V_n)) = V_n,
inference(fof_nnf,[status(thm)],[fact_natceiling__real__of__nat]) ).
fof(f_836_2,plain,
! [U_2596] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_2596)) = U_2596,
inference(variable_rename,[status(thm)],[f_836_1]) ).
fof(f_836_3,plain,
! [U_2596] : c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_2596)) = U_2596,
inference(definitional_conversion,[status(esa)],[f_836_2]) ).
cnf(f_836_4,plain,
c_RComplete_Onatceiling(c_RealDef_Oreal(tc_Nat_Onat,U_2596)) = U_2596,
inference(clausify,[status(thm)],[f_836_3]) ).
fof(f_837_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__less__iff]) ).
fof(f_837_2,plain,
! [U_2598,U_2597] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2597),c_RealDef_Oreal(tc_Nat_Onat,U_2598))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2597,U_2598) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2597,U_2598)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2597),c_RealDef_Oreal(tc_Nat_Onat,U_2598)) ) ),
inference(variable_rename,[status(thm)],[f_837_1]) ).
fof(f_837_3,plain,
( ! [U_2602,U_2600] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2600),c_RealDef_Oreal(tc_Nat_Onat,U_2602))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2600,U_2602) )
& ! [U_2601,U_2599] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2599,U_2601)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2599),c_RealDef_Oreal(tc_Nat_Onat,U_2601)) ) ),
inference(miniscope,[status(thm)],[f_837_2]) ).
fof(f_837_4,plain,
( ! [U_2600,U_2602] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2600),c_RealDef_Oreal(tc_Nat_Onat,U_2602))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2600,U_2602) )
& ! [U_2601,U_2599] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2599,U_2601)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2599),c_RealDef_Oreal(tc_Nat_Onat,U_2601)) ) ),
inference(definitional_conversion,[status(esa)],[f_837_3]) ).
cnf(f_837_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2599,U_2601)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2599),c_RealDef_Oreal(tc_Nat_Onat,U_2601)) ),
inference(clausify,[status(thm)],[f_837_4]) ).
cnf(f_837_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2600),c_RealDef_Oreal(tc_Nat_Onat,U_2602))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2600,U_2602) ),
inference(clausify,[status(thm)],[f_837_4]) ).
fof(f_838_1,plain,
! [V_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_not__real__of__nat__less__zero]) ).
fof(f_838_2,plain,
! [U_2603] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2603),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_838_1]) ).
fof(f_838_3,plain,
! [U_2603] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2603),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_838_2]) ).
cnf(f_838_4,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2603),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_838_3]) ).
fof(f_839_1,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero]) ).
fof(f_839_2,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_839_1]) ).
cnf(f_839_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_839_2]) ).
fof(f_840_1,plain,
! [V_n_2] :
( ( c_RealDef_Oreal(tc_Nat_Onat,V_n_2) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,V_n_2) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__zero__iff]) ).
fof(f_840_2,plain,
! [U_2604] :
( ( c_RealDef_Oreal(tc_Nat_Onat,U_2604) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2604 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2604 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_2604) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(variable_rename,[status(thm)],[f_840_1]) ).
fof(f_840_3,plain,
( ! [U_2606] :
( c_RealDef_Oreal(tc_Nat_Onat,U_2606) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2606 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2605] :
( U_2605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_2605) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(miniscope,[status(thm)],[f_840_2]) ).
fof(f_840_4,plain,
( ! [U_2606] :
( c_RealDef_Oreal(tc_Nat_Onat,U_2606) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2606 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2605] :
( U_2605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_2605) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ) ),
inference(definitional_conversion,[status(esa)],[f_840_3]) ).
cnf(f_840_5,plain,
( U_2605 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_RealDef_Oreal(tc_Nat_Onat,U_2605) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal) ),
inference(clausify,[status(thm)],[f_840_4]) ).
cnf(f_840_6,plain,
( c_RealDef_Oreal(tc_Nat_Onat,U_2606) = c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)
| U_2606 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_840_4]) ).
fof(f_841_1,plain,
! [V_x] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x)) = c_RealDef_Oreal(tc_Nat_Onat,V_x),
inference(fof_nnf,[status(thm)],[fact_abs__real__of__nat__cancel]) ).
fof(f_841_2,plain,
! [U_2607] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2607)) = c_RealDef_Oreal(tc_Nat_Onat,U_2607),
inference(variable_rename,[status(thm)],[f_841_1]) ).
fof(f_841_3,plain,
! [U_2607] : c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2607)) = c_RealDef_Oreal(tc_Nat_Onat,U_2607),
inference(definitional_conversion,[status(esa)],[f_841_2]) ).
cnf(f_841_4,plain,
c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2607)) = c_RealDef_Oreal(tc_Nat_Onat,U_2607),
inference(clausify,[status(thm)],[f_841_3]) ).
fof(f_842_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__le__zero__cancel__iff]) ).
fof(f_842_2,plain,
! [U_2608] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2608),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_2608 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ( U_2608 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2608),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(variable_rename,[status(thm)],[f_842_1]) ).
fof(f_842_3,plain,
( ! [U_2610] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2610),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_2610 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2609] :
( U_2609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2609),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(miniscope,[status(thm)],[f_842_2]) ).
fof(f_842_4,plain,
( ! [U_2610] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2610),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_2610 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
& ! [U_2609] :
( U_2609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2609),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ) ),
inference(definitional_conversion,[status(esa)],[f_842_3]) ).
cnf(f_842_5,plain,
( U_2609 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2609),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_842_4]) ).
cnf(f_842_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2610),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| U_2610 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_842_4]) ).
fof(f_843_1,plain,
! [V_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n))),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__Suc__gt__zero]) ).
fof(f_843_2,plain,
! [U_2611] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2611))),
inference(variable_rename,[status(thm)],[f_843_1]) ).
fof(f_843_3,plain,
! [U_2611] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2611))),
inference(definitional_conversion,[status(esa)],[f_843_2]) ).
cnf(f_843_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2611))),
inference(clausify,[status(thm)],[f_843_3]) ).
fof(f_844_1,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__one]) ).
fof(f_844_2,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_844_1]) ).
cnf(f_844_3,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Oone__class_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_844_2]) ).
fof(f_845_1,plain,
! [V_n] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(V_n)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__Suc]) ).
fof(f_845_2,plain,
! [U_2612] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2612)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2612),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(variable_rename,[status(thm)],[f_845_1]) ).
fof(f_845_3,plain,
! [U_2612] : c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2612)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2612),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(definitional_conversion,[status(esa)],[f_845_2]) ).
cnf(f_845_4,plain,
c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2612)) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2612),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(clausify,[status(thm)],[f_845_3]) ).
fof(f_846_1,plain,
! [V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),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__natfloor__le]) ).
fof(f_846_2,plain,
! [U_2613] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2613)),U_2613)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2613) ),
inference(variable_rename,[status(thm)],[f_846_1]) ).
fof(f_846_3,plain,
! [U_2613] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2613)),U_2613)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2613) ),
inference(definitional_conversion,[status(esa)],[f_846_2]) ).
cnf(f_846_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2613)),U_2613)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2613) ),
inference(clausify,[status(thm)],[f_846_3]) ).
fof(f_847_1,plain,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_x,c_RComplete_Onatfloor(V_a))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_x),V_a) ),
inference(fof_nnf,[status(thm)],[fact_le__natfloor]) ).
fof(f_847_2,plain,
! [U_2615,U_2614] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2614,c_RComplete_Onatfloor(U_2615))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2614),U_2615) ),
inference(variable_rename,[status(thm)],[f_847_1]) ).
fof(f_847_3,plain,
! [U_2614,U_2615] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2614,c_RComplete_Onatfloor(U_2615))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2614),U_2615) ),
inference(definitional_conversion,[status(esa)],[f_847_2]) ).
cnf(f_847_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2614,c_RComplete_Onatfloor(U_2615))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2614),U_2615) ),
inference(clausify,[status(thm)],[f_847_3]) ).
fof(f_848_1,plain,
! [V_a,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a)) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__le]) ).
fof(f_848_2,plain,
! [U_2617,U_2616] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2616),U_2617)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2616,c_RealDef_Oreal(tc_Nat_Onat,U_2617)) ),
inference(variable_rename,[status(thm)],[f_848_1]) ).
fof(f_848_3,plain,
! [U_2616,U_2617] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2616),U_2617)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2616,c_RealDef_Oreal(tc_Nat_Onat,U_2617)) ),
inference(definitional_conversion,[status(esa)],[f_848_2]) ).
cnf(f_848_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2616),U_2617)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2616,c_RealDef_Oreal(tc_Nat_Onat,U_2617)) ),
inference(clausify,[status(thm)],[f_848_3]) ).
fof(f_849_1,plain,
! [V_n,V_x] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),V_x),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(V_x)),V_n)
| V_x != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__power]) ).
fof(f_849_2,plain,
! [U_2619,U_2618] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2618),U_2619)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_2618)),U_2619)
| U_2618 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2618)) ),
inference(variable_rename,[status(thm)],[f_849_1]) ).
fof(f_849_3,plain,
! [U_2618,U_2619] :
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2618),U_2619)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_2618)),U_2619)
| U_2618 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2618)) ),
inference(definitional_conversion,[status(esa)],[f_849_2]) ).
cnf(f_849_4,plain,
( c_RComplete_Onatfloor(hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2618),U_2619)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_RComplete_Onatfloor(U_2618)),U_2619)
| U_2618 != c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2618)) ),
inference(clausify,[status(thm)],[f_849_3]) ).
fof(f_850_1,plain,
! [V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__gt__zero__cancel__iff]) ).
fof(f_850_2,plain,
! [U_2620] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2620))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2620) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2620)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2620)) ) ),
inference(variable_rename,[status(thm)],[f_850_1]) ).
fof(f_850_3,plain,
( ! [U_2622] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2622))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2622) )
& ! [U_2621] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2621)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2621)) ) ),
inference(miniscope,[status(thm)],[f_850_2]) ).
fof(f_850_4,plain,
( ! [U_2622] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2622))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2622) )
& ! [U_2621] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2621)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2621)) ) ),
inference(definitional_conversion,[status(esa)],[f_850_3]) ).
cnf(f_850_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2621)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2621)) ),
inference(clausify,[status(thm)],[f_850_4]) ).
cnf(f_850_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2622))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2622) ),
inference(clausify,[status(thm)],[f_850_4]) ).
fof(f_851_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,V_ma_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_n_2,V_ma_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__less__real__le]) ).
fof(f_851_2,plain,
! [U_2624,U_2623] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2623,U_2624)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2623),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2624)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2623),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2624))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2623,U_2624) ) ),
inference(variable_rename,[status(thm)],[f_851_1]) ).
fof(f_851_3,plain,
( ! [U_2628,U_2626] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2626,U_2628)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2626),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2628)) )
& ! [U_2627,U_2625] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2625),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2627))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2625,U_2627) ) ),
inference(miniscope,[status(thm)],[f_851_2]) ).
fof(f_851_4,plain,
( ! [U_2626,U_2628] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2626,U_2628)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2626),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2628)) )
& ! [U_2625,U_2627] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2625),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2627))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2625,U_2627) ) ),
inference(definitional_conversion,[status(esa)],[f_851_3]) ).
cnf(f_851_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2625),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2627))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2625,U_2627) ),
inference(clausify,[status(thm)],[f_851_4]) ).
cnf(f_851_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2626,U_2628)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2626),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealDef_Oreal(tc_Nat_Onat,U_2628)) ),
inference(clausify,[status(thm)],[f_851_4]) ).
fof(f_852_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n_2),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_ma_2),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n_2,V_ma_2) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__le__real__less]) ).
fof(f_852_2,plain,
! [U_2630,U_2629] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2629,U_2630)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2629),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2630),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2629),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2630),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2629,U_2630) ) ),
inference(variable_rename,[status(thm)],[f_852_1]) ).
fof(f_852_3,plain,
( ! [U_2634,U_2632] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2632,U_2634)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2632),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2634),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ! [U_2633,U_2631] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2631),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2633),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2631,U_2633) ) ),
inference(miniscope,[status(thm)],[f_852_2]) ).
fof(f_852_4,plain,
( ! [U_2632,U_2634] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2632,U_2634)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2632),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2634),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) )
& ! [U_2633,U_2631] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2631),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2633),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2631,U_2633) ) ),
inference(definitional_conversion,[status(esa)],[f_852_3]) ).
cnf(f_852_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2631),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2633),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2631,U_2633) ),
inference(clausify,[status(thm)],[f_852_4]) ).
cnf(f_852_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2632,U_2634)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2632),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2634),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(clausify,[status(thm)],[f_852_4]) ).
fof(f_853_1,plain,
! [V_a_2,V_x_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a_2),V_x_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_a_2,c_RComplete_Onatfloor(V_x_2)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_le__natfloor__eq]) ).
fof(f_853_2,plain,
! [U_2636,U_2635] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2636,c_RComplete_Onatfloor(U_2635))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2636),U_2635) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2636),U_2635)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2636,c_RComplete_Onatfloor(U_2635)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2635) ),
inference(variable_rename,[status(thm)],[f_853_1]) ).
fof(f_853_3,plain,
( ! [U_2636,U_2635] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2636,c_RComplete_Onatfloor(U_2635))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2636),U_2635)
| ~ sP260(U_2636,U_2635) )
& ! [U_2636,U_2635] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2636),U_2635)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2636,c_RComplete_Onatfloor(U_2635))
| ~ sP260(U_2636,U_2635) )
& ! [U_2636,U_2635] :
( sP260(U_2636,U_2635)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2635) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260])],[f_853_2]) ).
cnf(f_853_4,plain,
( sP260(U_2636,U_2635)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2635) ),
inference(clausify,[status(thm)],[f_853_3]) ).
cnf(f_853_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2636),U_2635)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2636,c_RComplete_Onatfloor(U_2635))
| ~ sP260(U_2636,U_2635) ),
inference(clausify,[status(thm)],[f_853_3]) ).
cnf(f_853_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2636,c_RComplete_Onatfloor(U_2635))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2636),U_2635)
| ~ sP260(U_2636,U_2635) ),
inference(clausify,[status(thm)],[f_853_3]) ).
fof(f_854_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__iff]) ).
fof(f_854_2,plain,
! [U_2642,U_2641] :
( ( ( c_SEQ_OBseq(U_2641,U_2642)
| ! [U_2640] :
? [U_2639] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,U_2639)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2640))) )
& ( ? [U_2638] :
! [U_2637] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,U_2637)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2638)))
| ~ c_SEQ_OBseq(U_2641,U_2642) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2641) ),
inference(variable_rename,[status(thm)],[f_854_1]) ).
fof(f_854_3,plain,
! [U_2642,U_2641] :
( ( ( c_SEQ_OBseq(U_2641,U_2642)
| ! [U_2640] :
? [U_2639] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,U_2639)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2640))) )
& ( ! [U_2637] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,U_2637)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK34(U_2642,U_2641))))
| ~ c_SEQ_OBseq(U_2641,U_2642) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2641) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_2638,sK34(U_2642,U_2641))],[f_854_2]) ).
fof(f_854_4,plain,
! [U_2642,U_2641] :
( ( ( c_SEQ_OBseq(U_2641,U_2642)
| ! [U_2640] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,sK35(U_2642,U_2641,U_2640))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2640))) )
& ( ! [U_2637] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,U_2637)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK34(U_2642,U_2641))))
| ~ c_SEQ_OBseq(U_2641,U_2642) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2641) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_2639,sK35(U_2642,U_2641,U_2640))],[f_854_3]) ).
fof(f_854_5,plain,
( ! [U_2641,U_2642,U_2640,U_2637] :
( c_SEQ_OBseq(U_2641,U_2642)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,sK35(U_2642,U_2641,U_2640))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2640)))
| ~ sP261(U_2641,U_2642,U_2640,U_2637) )
& ! [U_2641,U_2642,U_2640,U_2637] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,U_2637)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK34(U_2642,U_2641))))
| ~ c_SEQ_OBseq(U_2641,U_2642)
| ~ sP261(U_2641,U_2642,U_2640,U_2637) )
& ! [U_2641,U_2642,U_2640,U_2637] :
( sP261(U_2641,U_2642,U_2640,U_2637)
| ~ class_RealVector_Oreal__normed__vector(U_2641) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP261])],[f_854_4]) ).
cnf(f_854_6,plain,
( sP261(U_2641,U_2642,U_2640,U_2637)
| ~ class_RealVector_Oreal__normed__vector(U_2641) ),
inference(clausify,[status(thm)],[f_854_5]) ).
cnf(f_854_7,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,U_2637)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK34(U_2642,U_2641))))
| ~ c_SEQ_OBseq(U_2641,U_2642)
| ~ sP261(U_2641,U_2642,U_2640,U_2637) ),
inference(clausify,[status(thm)],[f_854_5]) ).
cnf(f_854_8,plain,
( c_SEQ_OBseq(U_2641,U_2642)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2641,hAPP(U_2642,sK35(U_2642,U_2641,U_2640))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2640)))
| ~ sP261(U_2641,U_2642,U_2640,U_2637) ),
inference(clausify,[status(thm)],[f_854_5]) ).
fof(f_855_1,plain,
! [V_X_2,T_a] :
( ( ( c_SEQ_OBseq(T_a,V_X_2)
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_a,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ~ c_SEQ_OBseq(T_a,V_X_2) ) )
| ~ class_RealVector_Oreal__normed__vector(T_a) ),
inference(fof_nnf,[status(thm)],[fact_Bseq__iff1a]) ).
fof(f_855_2,plain,
! [U_2648,U_2647] :
( ( ( c_SEQ_OBseq(U_2647,U_2648)
| ! [U_2646] :
? [U_2645] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,U_2645)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2646))) )
& ( ? [U_2644] :
! [U_2643] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,U_2643)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2644)))
| ~ c_SEQ_OBseq(U_2647,U_2648) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2647) ),
inference(variable_rename,[status(thm)],[f_855_1]) ).
fof(f_855_3,plain,
! [U_2648,U_2647] :
( ( ( c_SEQ_OBseq(U_2647,U_2648)
| ! [U_2646] :
? [U_2645] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,U_2645)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2646))) )
& ( ! [U_2643] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,U_2643)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK36(U_2648,U_2647))))
| ~ c_SEQ_OBseq(U_2647,U_2648) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2647) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_2644,sK36(U_2648,U_2647))],[f_855_2]) ).
fof(f_855_4,plain,
! [U_2648,U_2647] :
( ( ( c_SEQ_OBseq(U_2647,U_2648)
| ! [U_2646] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,sK37(U_2648,U_2647,U_2646))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2646))) )
& ( ! [U_2643] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,U_2643)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK36(U_2648,U_2647))))
| ~ c_SEQ_OBseq(U_2647,U_2648) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2647) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_2645,sK37(U_2648,U_2647,U_2646))],[f_855_3]) ).
fof(f_855_5,plain,
( ! [U_2646,U_2648,U_2643,U_2647] :
( c_SEQ_OBseq(U_2647,U_2648)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,sK37(U_2648,U_2647,U_2646))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2646)))
| ~ sP262(U_2646,U_2648,U_2643,U_2647) )
& ! [U_2646,U_2648,U_2643,U_2647] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,U_2643)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK36(U_2648,U_2647))))
| ~ c_SEQ_OBseq(U_2647,U_2648)
| ~ sP262(U_2646,U_2648,U_2643,U_2647) )
& ! [U_2646,U_2648,U_2643,U_2647] :
( sP262(U_2646,U_2648,U_2643,U_2647)
| ~ class_RealVector_Oreal__normed__vector(U_2647) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP262])],[f_855_4]) ).
cnf(f_855_6,plain,
( sP262(U_2646,U_2648,U_2643,U_2647)
| ~ class_RealVector_Oreal__normed__vector(U_2647) ),
inference(clausify,[status(thm)],[f_855_5]) ).
cnf(f_855_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,U_2643)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK36(U_2648,U_2647))))
| ~ c_SEQ_OBseq(U_2647,U_2648)
| ~ sP262(U_2646,U_2648,U_2643,U_2647) ),
inference(clausify,[status(thm)],[f_855_5]) ).
cnf(f_855_8,plain,
( c_SEQ_OBseq(U_2647,U_2648)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2647,hAPP(U_2648,sK37(U_2648,U_2647,U_2646))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2646)))
| ~ sP262(U_2646,U_2648,U_2643,U_2647) ),
inference(clausify,[status(thm)],[f_855_5]) ).
fof(f_856_1,plain,
! [V_a_2,V_x_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,c_RealDef_Oreal(tc_Nat_Onat,V_a_2))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(V_x_2),V_a_2) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_x_2) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__le__eq]) ).
fof(f_856_2,plain,
! [U_2650,U_2649] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2649),U_2650)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2649,c_RealDef_Oreal(tc_Nat_Onat,U_2650)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2649,c_RealDef_Oreal(tc_Nat_Onat,U_2650))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2649),U_2650) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2649) ),
inference(variable_rename,[status(thm)],[f_856_1]) ).
fof(f_856_3,plain,
( ! [U_2650,U_2649] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2649),U_2650)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2649,c_RealDef_Oreal(tc_Nat_Onat,U_2650))
| ~ sP263(U_2650,U_2649) )
& ! [U_2650,U_2649] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2649,c_RealDef_Oreal(tc_Nat_Onat,U_2650))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2649),U_2650)
| ~ sP263(U_2650,U_2649) )
& ! [U_2650,U_2649] :
( sP263(U_2650,U_2649)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2649) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263])],[f_856_2]) ).
cnf(f_856_4,plain,
( sP263(U_2650,U_2649)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2649) ),
inference(clausify,[status(thm)],[f_856_3]) ).
cnf(f_856_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2649,c_RealDef_Oreal(tc_Nat_Onat,U_2650))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2649),U_2650)
| ~ sP263(U_2650,U_2649) ),
inference(clausify,[status(thm)],[f_856_3]) ).
cnf(f_856_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_RComplete_Onatceiling(U_2649),U_2650)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2649,c_RealDef_Oreal(tc_Nat_Onat,U_2650))
| ~ sP263(U_2650,U_2649) ),
inference(clausify,[status(thm)],[f_856_3]) ).
fof(f_857_1,plain,
! [V_x] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(V_x)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(fof_nnf,[status(thm)],[fact_real__natfloor__add__one__gt]) ).
fof(f_857_2,plain,
! [U_2651] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2651,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2651)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(variable_rename,[status(thm)],[f_857_1]) ).
fof(f_857_3,plain,
! [U_2651] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2651,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2651)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(definitional_conversion,[status(esa)],[f_857_2]) ).
cnf(f_857_4,plain,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2651,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,c_RComplete_Onatfloor(U_2651)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(clausify,[status(thm)],[f_857_3]) ).
fof(f_858_1,plain,
! [V_X_2,T_b] :
( ( ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ! [B_K] :
( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) )
| ~ class_RealVector_Oreal__normed__vector(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def2]) ).
fof(f_858_2,plain,
! [U_2661,U_2660] :
( ( ( ? [U_2659] :
( ! [U_2658] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2658)),U_2659)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2659) )
| ! [U_2657] :
? [U_2656] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2656)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2657))) )
& ( ? [U_2655] :
! [U_2654] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2654)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2655)))
| ! [U_2653] :
( ? [U_2652] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2652)),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2653) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2660) ),
inference(variable_rename,[status(thm)],[f_858_1]) ).
fof(f_858_3,plain,
! [U_2661,U_2660] :
( ( ( ? [U_2659] :
( ! [U_2658] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2658)),U_2659)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2659) )
| ! [U_2657] :
? [U_2656] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2656)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2657))) )
& ( ? [U_2655] :
! [U_2654] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2654)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2655)))
| ! [U_2653] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK38(U_2661,U_2660,U_2653))),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2653) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2660) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_2652,sK38(U_2661,U_2660,U_2653))],[f_858_2]) ).
fof(f_858_4,plain,
! [U_2661,U_2660] :
( ( ( ? [U_2659] :
( ! [U_2658] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2658)),U_2659)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2659) )
| ! [U_2657] :
? [U_2656] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2656)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2657))) )
& ( ! [U_2654] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2654)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK39(U_2661,U_2660))))
| ! [U_2653] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK38(U_2661,U_2660,U_2653))),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2653) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2660) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2655,sK39(U_2661,U_2660))],[f_858_3]) ).
fof(f_858_5,plain,
! [U_2661,U_2660] :
( ( ( ? [U_2659] :
( ! [U_2658] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2658)),U_2659)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2659) )
| ! [U_2657] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK40(U_2661,U_2660,U_2657))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2657))) )
& ( ! [U_2654] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2654)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK39(U_2661,U_2660))))
| ! [U_2653] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK38(U_2661,U_2660,U_2653))),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2653) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2660) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2656,sK40(U_2661,U_2660,U_2657))],[f_858_4]) ).
fof(f_858_6,plain,
! [U_2661,U_2660] :
( ( ( ( ! [U_2658] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2658)),sK41(U_2661,U_2660))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(U_2661,U_2660)) )
| ! [U_2657] : ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK40(U_2661,U_2660,U_2657))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2657))) )
& ( ! [U_2654] : c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2654)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK39(U_2661,U_2660))))
| ! [U_2653] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK38(U_2661,U_2660,U_2653))),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2653) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2660) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2659,sK41(U_2661,U_2660))],[f_858_5]) ).
fof(f_858_7,plain,
( ! [U_2658,U_2660,U_2661] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2658)),sK41(U_2661,U_2660))
| ~ sP264(U_2658,U_2660,U_2661) )
& ! [U_2658,U_2660,U_2661] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(U_2661,U_2660))
| ~ sP264(U_2658,U_2660,U_2661) )
& ! [U_2653,U_2654,U_2657,U_2658,U_2660,U_2661] :
( sP264(U_2658,U_2660,U_2661)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK40(U_2661,U_2660,U_2657))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2657)))
| ~ sP265(U_2653,U_2654,U_2657,U_2658,U_2660,U_2661) )
& ! [U_2653,U_2654,U_2657,U_2658,U_2660,U_2661] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2654)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK39(U_2661,U_2660))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK38(U_2661,U_2660,U_2653))),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2653)
| ~ sP265(U_2653,U_2654,U_2657,U_2658,U_2660,U_2661) )
& ! [U_2653,U_2654,U_2657,U_2658,U_2660,U_2661] :
( sP265(U_2653,U_2654,U_2657,U_2658,U_2660,U_2661)
| ~ class_RealVector_Oreal__normed__vector(U_2660) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP264,sP265])],[f_858_6]) ).
cnf(f_858_8,plain,
( sP265(U_2653,U_2654,U_2657,U_2658,U_2660,U_2661)
| ~ class_RealVector_Oreal__normed__vector(U_2660) ),
inference(clausify,[status(thm)],[f_858_7]) ).
cnf(f_858_9,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2654)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK39(U_2661,U_2660))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK38(U_2661,U_2660,U_2653))),U_2653)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2653)
| ~ sP265(U_2653,U_2654,U_2657,U_2658,U_2660,U_2661) ),
inference(clausify,[status(thm)],[f_858_7]) ).
cnf(f_858_10,plain,
( sP264(U_2658,U_2660,U_2661)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,sK40(U_2661,U_2660,U_2657))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2657)))
| ~ sP265(U_2653,U_2654,U_2657,U_2658,U_2660,U_2661) ),
inference(clausify,[status(thm)],[f_858_7]) ).
cnf(f_858_11,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK41(U_2661,U_2660))
| ~ sP264(U_2658,U_2660,U_2661) ),
inference(clausify,[status(thm)],[f_858_7]) ).
cnf(f_858_12,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2660,hAPP(U_2661,U_2658)),sK41(U_2661,U_2660))
| ~ sP264(U_2658,U_2660,U_2661) ),
inference(clausify,[status(thm)],[f_858_7]) ).
fof(f_859_1,plain,
! [V_X_2,T_b] :
( ( ( ? [B_K] :
( ! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) )
| ! [B_N] :
? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N))) )
& ( ? [B_N] :
! [B_n] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_N)))
| ! [B_K] :
( ? [B_n] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),B_K)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_K) ) ) )
| ~ class_RealVector_Oreal__normed__vector(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lemma__NBseq__def]) ).
fof(f_859_2,plain,
! [U_2671,U_2670] :
( ( ( ? [U_2669] :
( ! [U_2668] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2668)),U_2669)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2669) )
| ! [U_2667] :
? [U_2666] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2666)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2667))) )
& ( ? [U_2665] :
! [U_2664] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2664)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2665)))
| ! [U_2663] :
( ? [U_2662] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2662)),U_2663)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2663) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2670) ),
inference(variable_rename,[status(thm)],[f_859_1]) ).
fof(f_859_3,plain,
! [U_2671,U_2670] :
( ( ( ? [U_2669] :
( ! [U_2668] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2668)),U_2669)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2669) )
| ! [U_2667] :
? [U_2666] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2666)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2667))) )
& ( ? [U_2665] :
! [U_2664] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2664)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2665)))
| ! [U_2663] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK42(U_2671,U_2670,U_2663))),U_2663)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2663) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2670) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2662,sK42(U_2671,U_2670,U_2663))],[f_859_2]) ).
fof(f_859_4,plain,
! [U_2671,U_2670] :
( ( ( ? [U_2669] :
( ! [U_2668] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2668)),U_2669)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2669) )
| ! [U_2667] :
? [U_2666] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2666)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2667))) )
& ( ! [U_2664] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2664)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK43(U_2671,U_2670))))
| ! [U_2663] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK42(U_2671,U_2670,U_2663))),U_2663)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2663) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2670) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_2665,sK43(U_2671,U_2670))],[f_859_3]) ).
fof(f_859_5,plain,
! [U_2671,U_2670] :
( ( ( ? [U_2669] :
( ! [U_2668] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2668)),U_2669)
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2669) )
| ! [U_2667] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK44(U_2671,U_2670,U_2667))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2667))) )
& ( ! [U_2664] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2664)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK43(U_2671,U_2670))))
| ! [U_2663] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK42(U_2671,U_2670,U_2663))),U_2663)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2663) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2670) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_2666,sK44(U_2671,U_2670,U_2667))],[f_859_4]) ).
fof(f_859_6,plain,
! [U_2671,U_2670] :
( ( ( ( ! [U_2668] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2668)),sK45(U_2671,U_2670))
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45(U_2671,U_2670)) )
| ! [U_2667] : ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK44(U_2671,U_2670,U_2667))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2667))) )
& ( ! [U_2664] : c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2664)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK43(U_2671,U_2670))))
| ! [U_2663] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK42(U_2671,U_2670,U_2663))),U_2663)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2663) ) ) )
| ~ class_RealVector_Oreal__normed__vector(U_2670) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_2669,sK45(U_2671,U_2670))],[f_859_5]) ).
fof(f_859_7,plain,
( ! [U_2670,U_2668,U_2671] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2668)),sK45(U_2671,U_2670))
| ~ sP266(U_2670,U_2668,U_2671) )
& ! [U_2670,U_2668,U_2671] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45(U_2671,U_2670))
| ~ sP266(U_2670,U_2668,U_2671) )
& ! [U_2667,U_2670,U_2668,U_2671,U_2663,U_2664] :
( sP266(U_2670,U_2668,U_2671)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK44(U_2671,U_2670,U_2667))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2667)))
| ~ sP267(U_2667,U_2670,U_2668,U_2671,U_2663,U_2664) )
& ! [U_2667,U_2670,U_2668,U_2671,U_2663,U_2664] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2664)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK43(U_2671,U_2670))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK42(U_2671,U_2670,U_2663))),U_2663)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2663)
| ~ sP267(U_2667,U_2670,U_2668,U_2671,U_2663,U_2664) )
& ! [U_2667,U_2670,U_2668,U_2671,U_2663,U_2664] :
( sP267(U_2667,U_2670,U_2668,U_2671,U_2663,U_2664)
| ~ class_RealVector_Oreal__normed__vector(U_2670) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP266,sP267])],[f_859_6]) ).
cnf(f_859_8,plain,
( sP267(U_2667,U_2670,U_2668,U_2671,U_2663,U_2664)
| ~ class_RealVector_Oreal__normed__vector(U_2670) ),
inference(clausify,[status(thm)],[f_859_7]) ).
cnf(f_859_9,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2664)),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK43(U_2671,U_2670))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK42(U_2671,U_2670,U_2663))),U_2663)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2663)
| ~ sP267(U_2667,U_2670,U_2668,U_2671,U_2663,U_2664) ),
inference(clausify,[status(thm)],[f_859_7]) ).
cnf(f_859_10,plain,
( sP266(U_2670,U_2668,U_2671)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,sK44(U_2671,U_2670,U_2667))),c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2667)))
| ~ sP267(U_2667,U_2670,U_2668,U_2671,U_2663,U_2664) ),
inference(clausify,[status(thm)],[f_859_7]) ).
cnf(f_859_11,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK45(U_2671,U_2670))
| ~ sP266(U_2670,U_2668,U_2671) ),
inference(clausify,[status(thm)],[f_859_7]) ).
cnf(f_859_12,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2670,hAPP(U_2671,U_2668)),sK45(U_2671,U_2670))
| ~ sP266(U_2670,U_2668,U_2671) ),
inference(clausify,[status(thm)],[f_859_7]) ).
fof(f_860_1,plain,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_n))
| ~ 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_less__natfloor]) ).
fof(f_860_2,plain,
! [U_2673,U_2672] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_2672),U_2673)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2672,c_RealDef_Oreal(tc_Nat_Onat,U_2673))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2672) ),
inference(variable_rename,[status(thm)],[f_860_1]) ).
fof(f_860_3,plain,
! [U_2672,U_2673] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_2672),U_2673)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2672,c_RealDef_Oreal(tc_Nat_Onat,U_2673))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2672) ),
inference(definitional_conversion,[status(esa)],[f_860_2]) ).
cnf(f_860_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_RComplete_Onatfloor(U_2672),U_2673)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2672,c_RealDef_Oreal(tc_Nat_Onat,U_2673))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2672) ),
inference(clausify,[status(thm)],[f_860_3]) ).
fof(f_861_1,plain,
! [V_a,V_x] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)
| ~ 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_natfloor__add]) ).
fof(f_861_2,plain,
! [U_2675,U_2674] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2674,c_RealDef_Oreal(tc_Nat_Onat,U_2675))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2674),U_2675)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2674) ),
inference(variable_rename,[status(thm)],[f_861_1]) ).
fof(f_861_3,plain,
! [U_2674,U_2675] :
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2674,c_RealDef_Oreal(tc_Nat_Onat,U_2675))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2674),U_2675)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2674) ),
inference(definitional_conversion,[status(esa)],[f_861_2]) ).
cnf(f_861_4,plain,
( c_RComplete_Onatfloor(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2674,c_RealDef_Oreal(tc_Nat_Onat,U_2675))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2674),U_2675)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2674) ),
inference(clausify,[status(thm)],[f_861_3]) ).
fof(f_862_1,plain,
! [V_n,V_z] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_z,c_RealDef_Oreal(tc_Nat_Onat,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(V_z),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) ),
inference(fof_nnf,[status(thm)],[fact_ge__natfloor__plus__one__imp__gt]) ).
fof(f_862_2,plain,
! [U_2677,U_2676] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2676,c_RealDef_Oreal(tc_Nat_Onat,U_2677))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2676),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2677) ),
inference(variable_rename,[status(thm)],[f_862_1]) ).
fof(f_862_3,plain,
! [U_2677,U_2676] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2676,c_RealDef_Oreal(tc_Nat_Onat,U_2677))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2676),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2677) ),
inference(definitional_conversion,[status(esa)],[f_862_2]) ).
cnf(f_862_4,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2676,c_RealDef_Oreal(tc_Nat_Onat,U_2677))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatfloor(U_2676),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2677) ),
inference(clausify,[status(thm)],[f_862_3]) ).
fof(f_863_1,plain,
! [V_x,V_n] :
( c_RComplete_Onatfloor(V_x) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_x,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_n),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__eq]) ).
fof(f_863_2,plain,
! [U_2679,U_2678] :
( c_RComplete_Onatfloor(U_2679) = U_2678
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2679,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2678),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2678),U_2679) ),
inference(variable_rename,[status(thm)],[f_863_1]) ).
fof(f_863_3,plain,
! [U_2678,U_2679] :
( c_RComplete_Onatfloor(U_2679) = U_2678
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2679,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2678),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2678),U_2679) ),
inference(definitional_conversion,[status(esa)],[f_863_2]) ).
cnf(f_863_4,plain,
( c_RComplete_Onatfloor(U_2679) = U_2678
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2679,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2678),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2678),U_2679) ),
inference(clausify,[status(thm)],[f_863_3]) ).
fof(f_864_1,plain,
! [V_a,V_x] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)
| ~ 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]) ).
fof(f_864_2,plain,
! [U_2681,U_2680] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2680,c_RealDef_Oreal(tc_Nat_Onat,U_2681))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2680),U_2681)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2680) ),
inference(variable_rename,[status(thm)],[f_864_1]) ).
fof(f_864_3,plain,
! [U_2681,U_2680] :
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2680,c_RealDef_Oreal(tc_Nat_Onat,U_2681))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2680),U_2681)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2680) ),
inference(definitional_conversion,[status(esa)],[f_864_2]) ).
cnf(f_864_4,plain,
( c_RComplete_Onatceiling(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2680,c_RealDef_Oreal(tc_Nat_Onat,U_2681))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_RComplete_Onatceiling(U_2680),U_2681)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2680) ),
inference(clausify,[status(thm)],[f_864_3]) ).
fof(f_865_1,plain,
! [V_n,V_x] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,V_n)),V_x),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),V_n))
| ~ 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_LIMSEQ__inverse__realpow__zero__lemma]) ).
fof(f_865_2,plain,
! [U_2683,U_2682] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2683)),U_2682),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2682,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_2683))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2682) ),
inference(variable_rename,[status(thm)],[f_865_1]) ).
fof(f_865_3,plain,
! [U_2683,U_2682] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2683)),U_2682),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2682,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_2683))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2682) ),
inference(definitional_conversion,[status(esa)],[f_865_2]) ).
cnf(f_865_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_RealDef_Oreal(tc_Nat_Onat,U_2683)),U_2682),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_2682,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),U_2683))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2682) ),
inference(clausify,[status(thm)],[f_865_3]) ).
fof(f_866_1,plain,
! [V_r] :
( ? [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,V_r,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(B_n)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,B_n),V_r) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_r) ),
inference(fof_nnf,[status(thm)],[fact_reals__Archimedean6a]) ).
fof(f_866_2,plain,
! [U_2685] :
( ? [U_2684] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2685,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(U_2684)))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_2684),U_2685) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2685) ),
inference(variable_rename,[status(thm)],[f_866_1]) ).
fof(f_866_3,plain,
! [U_2685] :
( ( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2685,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK46(U_2685))))
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK46(U_2685)),U_2685) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2685) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_2684,sK46(U_2685))],[f_866_2]) ).
fof(f_866_4,plain,
( ! [U_2685] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2685,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK46(U_2685))))
| ~ sP268(U_2685) )
& ! [U_2685] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK46(U_2685)),U_2685)
| ~ sP268(U_2685) )
& ! [U_2685] :
( sP268(U_2685)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2685) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268])],[f_866_3]) ).
cnf(f_866_5,plain,
( sP268(U_2685)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2685) ),
inference(clausify,[status(thm)],[f_866_4]) ).
cnf(f_866_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,sK46(U_2685)),U_2685)
| ~ sP268(U_2685) ),
inference(clausify,[status(thm)],[f_866_4]) ).
cnf(f_866_7,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,U_2685,c_RealDef_Oreal(tc_Nat_Onat,c_Nat_OSuc(sK46(U_2685))))
| ~ sP268(U_2685) ),
inference(clausify,[status(thm)],[f_866_4]) ).
fof(f_867_1,plain,
! [V_a,V_n] :
( ? [B_x] :
( ! [B_y] :
( B_y = B_x
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_y),V_n) != V_a
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_y) )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_x),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_x) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth__unique]) ).
fof(f_867_2,plain,
! [U_2689,U_2688] :
( ? [U_2687] :
( ! [U_2686] :
( U_2686 = U_2687
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2686),U_2688) != U_2689
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2686) )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2687),U_2688) = U_2689
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2687) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2689)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2688) ),
inference(variable_rename,[status(thm)],[f_867_1]) ).
fof(f_867_3,plain,
! [U_2689,U_2688] :
( ( ! [U_2686] :
( U_2686 = sK47(U_2689,U_2688)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2686),U_2688) != U_2689
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2686) )
& hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK47(U_2689,U_2688)),U_2688) = U_2689
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK47(U_2689,U_2688)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2689)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2688) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_2687,sK47(U_2689,U_2688))],[f_867_2]) ).
fof(f_867_4,plain,
( ! [U_2686,U_2688,U_2689] :
( U_2686 = sK47(U_2689,U_2688)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2686),U_2688) != U_2689
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2686)
| ~ sP269(U_2686,U_2688,U_2689) )
& ! [U_2686,U_2688,U_2689] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK47(U_2689,U_2688)),U_2688) = U_2689
| ~ sP269(U_2686,U_2688,U_2689) )
& ! [U_2686,U_2688,U_2689] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK47(U_2689,U_2688))
| ~ sP269(U_2686,U_2688,U_2689) )
& ! [U_2686,U_2688,U_2689] :
( sP269(U_2686,U_2688,U_2689)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2689)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2688) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP269])],[f_867_3]) ).
cnf(f_867_5,plain,
( sP269(U_2686,U_2688,U_2689)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2689)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2688) ),
inference(clausify,[status(thm)],[f_867_4]) ).
cnf(f_867_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK47(U_2689,U_2688))
| ~ sP269(U_2686,U_2688,U_2689) ),
inference(clausify,[status(thm)],[f_867_4]) ).
cnf(f_867_7,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK47(U_2689,U_2688)),U_2688) = U_2689
| ~ sP269(U_2686,U_2688,U_2689) ),
inference(clausify,[status(thm)],[f_867_4]) ).
cnf(f_867_8,plain,
( U_2686 = sK47(U_2689,U_2688)
| hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2686),U_2688) != U_2689
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2686)
| ~ sP269(U_2686,U_2688,U_2689) ),
inference(clausify,[status(thm)],[f_867_4]) ).
fof(f_868_1,plain,
! [V_a,V_n] :
( ? [B_r] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),B_r),V_n) = V_a
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_realpow__pos__nth]) ).
fof(f_868_2,plain,
! [U_2692,U_2691] :
( ? [U_2690] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),U_2690),U_2691) = U_2692
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2690) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2692)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2691) ),
inference(variable_rename,[status(thm)],[f_868_1]) ).
fof(f_868_3,plain,
! [U_2692,U_2691] :
( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK48(U_2692,U_2691)),U_2691) = U_2692
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK48(U_2692,U_2691)) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2692)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2691) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_2690,sK48(U_2692,U_2691))],[f_868_2]) ).
fof(f_868_4,plain,
( ! [U_2692,U_2691] :
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK48(U_2692,U_2691)),U_2691) = U_2692
| ~ sP270(U_2692,U_2691) )
& ! [U_2692,U_2691] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK48(U_2692,U_2691))
| ~ sP270(U_2692,U_2691) )
& ! [U_2692,U_2691] :
( sP270(U_2692,U_2691)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2692)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2691) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP270])],[f_868_3]) ).
cnf(f_868_5,plain,
( sP270(U_2692,U_2691)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_2692)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2691) ),
inference(clausify,[status(thm)],[f_868_4]) ).
cnf(f_868_6,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),sK48(U_2692,U_2691))
| ~ sP270(U_2692,U_2691) ),
inference(clausify,[status(thm)],[f_868_4]) ).
cnf(f_868_7,plain,
( hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),sK48(U_2692,U_2691)),U_2691) = U_2692
| ~ sP270(U_2692,U_2691) ),
inference(clausify,[status(thm)],[f_868_4]) ).
fof(f_869_1,plain,
! [V_x,V_z,V_d] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_z,c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) ),
inference(fof_nnf,[status(thm)],[fact_incr__lemma]) ).
fof(f_869_2,plain,
! [U_2695,U_2694,U_2693] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2694,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2695,U_2694)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2693)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2693) ),
inference(variable_rename,[status(thm)],[f_869_1]) ).
fof(f_869_3,plain,
! [U_2693,U_2694,U_2695] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2694,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2695,U_2694)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2693)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2693) ),
inference(definitional_conversion,[status(esa)],[f_869_2]) ).
cnf(f_869_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2694,c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2695,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2695,U_2694)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2693)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2693) ),
inference(clausify,[status(thm)],[f_869_3]) ).
fof(f_870_1,plain,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_870_2,plain,
! [U_2701,U_2700,U_2699,U_2698,U_2697,U_2696] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2697),U_2698),U_2699),c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2700),U_2698),U_2701))
| ~ c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),c_Groups_Ominus__class_Ominus(U_2696,U_2697,U_2700)),U_2698),U_2699),U_2701) )
& ( c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),c_Groups_Ominus__class_Ominus(U_2696,U_2697,U_2700)),U_2698),U_2699),U_2701)
| ~ c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2697),U_2698),U_2699),c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2700),U_2698),U_2701)) ) )
| ~ class_Rings_Oordered__ring(U_2696) ),
inference(variable_rename,[status(thm)],[f_870_1]) ).
fof(f_870_3,plain,
( ! [U_2696,U_2697,U_2698,U_2699,U_2700,U_2701] :
( c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2697),U_2698),U_2699),c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2700),U_2698),U_2701))
| ~ c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),c_Groups_Ominus__class_Ominus(U_2696,U_2697,U_2700)),U_2698),U_2699),U_2701)
| ~ sP271(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701) )
& ! [U_2696,U_2697,U_2698,U_2699,U_2700,U_2701] :
( c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),c_Groups_Ominus__class_Ominus(U_2696,U_2697,U_2700)),U_2698),U_2699),U_2701)
| ~ c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2697),U_2698),U_2699),c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2700),U_2698),U_2701))
| ~ sP271(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701) )
& ! [U_2696,U_2697,U_2698,U_2699,U_2700,U_2701] :
( sP271(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701)
| ~ class_Rings_Oordered__ring(U_2696) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271])],[f_870_2]) ).
cnf(f_870_4,plain,
( sP271(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701)
| ~ class_Rings_Oordered__ring(U_2696) ),
inference(clausify,[status(thm)],[f_870_3]) ).
cnf(f_870_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),c_Groups_Ominus__class_Ominus(U_2696,U_2697,U_2700)),U_2698),U_2699),U_2701)
| ~ c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2697),U_2698),U_2699),c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2700),U_2698),U_2701))
| ~ sP271(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701) ),
inference(clausify,[status(thm)],[f_870_3]) ).
cnf(f_870_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2697),U_2698),U_2699),c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),U_2700),U_2698),U_2701))
| ~ c_Orderings_Oord__class_Oless__eq(U_2696,c_Groups_Oplus__class_Oplus(U_2696,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2696),c_Groups_Ominus__class_Ominus(U_2696,U_2697,U_2700)),U_2698),U_2699),U_2701)
| ~ sP271(U_2696,U_2697,U_2698,U_2699,U_2700,U_2701) ),
inference(clausify,[status(thm)],[f_870_3]) ).
fof(f_871_1,plain,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_871_2,plain,
! [U_2707,U_2706,U_2705,U_2704,U_2703,U_2702] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2702,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2703),U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2706),U_2704),U_2707))
| ~ c_Orderings_Oord__class_Oless__eq(U_2702,U_2705,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),c_Groups_Ominus__class_Ominus(U_2702,U_2706,U_2703)),U_2704),U_2707)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2702,U_2705,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),c_Groups_Ominus__class_Ominus(U_2702,U_2706,U_2703)),U_2704),U_2707))
| ~ c_Orderings_Oord__class_Oless__eq(U_2702,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2703),U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2706),U_2704),U_2707)) ) )
| ~ class_Rings_Oordered__ring(U_2702) ),
inference(variable_rename,[status(thm)],[f_871_1]) ).
fof(f_871_3,plain,
( ! [U_2704,U_2702,U_2705,U_2706,U_2703,U_2707] :
( c_Orderings_Oord__class_Oless__eq(U_2702,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2703),U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2706),U_2704),U_2707))
| ~ c_Orderings_Oord__class_Oless__eq(U_2702,U_2705,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),c_Groups_Ominus__class_Ominus(U_2702,U_2706,U_2703)),U_2704),U_2707))
| ~ sP272(U_2704,U_2702,U_2705,U_2706,U_2703,U_2707) )
& ! [U_2704,U_2702,U_2705,U_2706,U_2703,U_2707] :
( c_Orderings_Oord__class_Oless__eq(U_2702,U_2705,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),c_Groups_Ominus__class_Ominus(U_2702,U_2706,U_2703)),U_2704),U_2707))
| ~ c_Orderings_Oord__class_Oless__eq(U_2702,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2703),U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2706),U_2704),U_2707))
| ~ sP272(U_2704,U_2702,U_2705,U_2706,U_2703,U_2707) )
& ! [U_2704,U_2702,U_2705,U_2706,U_2703,U_2707] :
( sP272(U_2704,U_2702,U_2705,U_2706,U_2703,U_2707)
| ~ class_Rings_Oordered__ring(U_2702) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP272])],[f_871_2]) ).
cnf(f_871_4,plain,
( sP272(U_2704,U_2702,U_2705,U_2706,U_2703,U_2707)
| ~ class_Rings_Oordered__ring(U_2702) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2702,U_2705,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),c_Groups_Ominus__class_Ominus(U_2702,U_2706,U_2703)),U_2704),U_2707))
| ~ c_Orderings_Oord__class_Oless__eq(U_2702,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2703),U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2706),U_2704),U_2707))
| ~ sP272(U_2704,U_2702,U_2705,U_2706,U_2703,U_2707) ),
inference(clausify,[status(thm)],[f_871_3]) ).
cnf(f_871_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2702,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2703),U_2704),U_2705),c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),U_2706),U_2704),U_2707))
| ~ c_Orderings_Oord__class_Oless__eq(U_2702,U_2705,c_Groups_Oplus__class_Oplus(U_2702,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2702),c_Groups_Ominus__class_Ominus(U_2702,U_2706,U_2703)),U_2704),U_2707))
| ~ sP272(U_2704,U_2702,U_2705,U_2706,U_2703,U_2707) ),
inference(clausify,[status(thm)],[f_871_3]) ).
fof(f_872_1,plain,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_872_2,plain,
! [U_2713,U_2712,U_2711,U_2710,U_2709,U_2708] :
( ( ( c_Orderings_Oord__class_Oless(U_2708,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2709),U_2710),U_2711),c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2712),U_2710),U_2713))
| ~ c_Orderings_Oord__class_Oless(U_2708,U_2711,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),c_Groups_Ominus__class_Ominus(U_2708,U_2712,U_2709)),U_2710),U_2713)) )
& ( c_Orderings_Oord__class_Oless(U_2708,U_2711,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),c_Groups_Ominus__class_Ominus(U_2708,U_2712,U_2709)),U_2710),U_2713))
| ~ c_Orderings_Oord__class_Oless(U_2708,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2709),U_2710),U_2711),c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2712),U_2710),U_2713)) ) )
| ~ class_Rings_Oordered__ring(U_2708) ),
inference(variable_rename,[status(thm)],[f_872_1]) ).
fof(f_872_3,plain,
( ! [U_2708,U_2710,U_2711,U_2709,U_2712,U_2713] :
( c_Orderings_Oord__class_Oless(U_2708,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2709),U_2710),U_2711),c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2712),U_2710),U_2713))
| ~ c_Orderings_Oord__class_Oless(U_2708,U_2711,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),c_Groups_Ominus__class_Ominus(U_2708,U_2712,U_2709)),U_2710),U_2713))
| ~ sP273(U_2708,U_2710,U_2711,U_2709,U_2712,U_2713) )
& ! [U_2708,U_2710,U_2711,U_2709,U_2712,U_2713] :
( c_Orderings_Oord__class_Oless(U_2708,U_2711,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),c_Groups_Ominus__class_Ominus(U_2708,U_2712,U_2709)),U_2710),U_2713))
| ~ c_Orderings_Oord__class_Oless(U_2708,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2709),U_2710),U_2711),c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2712),U_2710),U_2713))
| ~ sP273(U_2708,U_2710,U_2711,U_2709,U_2712,U_2713) )
& ! [U_2708,U_2710,U_2711,U_2709,U_2712,U_2713] :
( sP273(U_2708,U_2710,U_2711,U_2709,U_2712,U_2713)
| ~ class_Rings_Oordered__ring(U_2708) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP273])],[f_872_2]) ).
cnf(f_872_4,plain,
( sP273(U_2708,U_2710,U_2711,U_2709,U_2712,U_2713)
| ~ class_Rings_Oordered__ring(U_2708) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_5,plain,
( c_Orderings_Oord__class_Oless(U_2708,U_2711,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),c_Groups_Ominus__class_Ominus(U_2708,U_2712,U_2709)),U_2710),U_2713))
| ~ c_Orderings_Oord__class_Oless(U_2708,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2709),U_2710),U_2711),c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2712),U_2710),U_2713))
| ~ sP273(U_2708,U_2710,U_2711,U_2709,U_2712,U_2713) ),
inference(clausify,[status(thm)],[f_872_3]) ).
cnf(f_872_6,plain,
( c_Orderings_Oord__class_Oless(U_2708,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2709),U_2710),U_2711),c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),U_2712),U_2710),U_2713))
| ~ c_Orderings_Oord__class_Oless(U_2708,U_2711,c_Groups_Oplus__class_Oplus(U_2708,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2708),c_Groups_Ominus__class_Ominus(U_2708,U_2712,U_2709)),U_2710),U_2713))
| ~ sP273(U_2708,U_2710,U_2711,U_2709,U_2712,U_2713) ),
inference(clausify,[status(thm)],[f_872_3]) ).
fof(f_873_1,plain,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_873_2,plain,
! [U_2719,U_2718,U_2717,U_2716,U_2715,U_2714] :
( ( ( c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2716),U_2717),c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2718),U_2716),U_2719))
| ~ c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),c_Groups_Ominus__class_Ominus(U_2714,U_2715,U_2718)),U_2716),U_2717),U_2719) )
& ( c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),c_Groups_Ominus__class_Ominus(U_2714,U_2715,U_2718)),U_2716),U_2717),U_2719)
| ~ c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2716),U_2717),c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2718),U_2716),U_2719)) ) )
| ~ class_Rings_Oordered__ring(U_2714) ),
inference(variable_rename,[status(thm)],[f_873_1]) ).
fof(f_873_3,plain,
( ! [U_2715,U_2714,U_2716,U_2717,U_2718,U_2719] :
( c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2716),U_2717),c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2718),U_2716),U_2719))
| ~ c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),c_Groups_Ominus__class_Ominus(U_2714,U_2715,U_2718)),U_2716),U_2717),U_2719)
| ~ sP274(U_2715,U_2714,U_2716,U_2717,U_2718,U_2719) )
& ! [U_2715,U_2714,U_2716,U_2717,U_2718,U_2719] :
( c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),c_Groups_Ominus__class_Ominus(U_2714,U_2715,U_2718)),U_2716),U_2717),U_2719)
| ~ c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2716),U_2717),c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2718),U_2716),U_2719))
| ~ sP274(U_2715,U_2714,U_2716,U_2717,U_2718,U_2719) )
& ! [U_2715,U_2714,U_2716,U_2717,U_2718,U_2719] :
( sP274(U_2715,U_2714,U_2716,U_2717,U_2718,U_2719)
| ~ class_Rings_Oordered__ring(U_2714) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP274])],[f_873_2]) ).
cnf(f_873_4,plain,
( sP274(U_2715,U_2714,U_2716,U_2717,U_2718,U_2719)
| ~ class_Rings_Oordered__ring(U_2714) ),
inference(clausify,[status(thm)],[f_873_3]) ).
cnf(f_873_5,plain,
( c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),c_Groups_Ominus__class_Ominus(U_2714,U_2715,U_2718)),U_2716),U_2717),U_2719)
| ~ c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2716),U_2717),c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2718),U_2716),U_2719))
| ~ sP274(U_2715,U_2714,U_2716,U_2717,U_2718,U_2719) ),
inference(clausify,[status(thm)],[f_873_3]) ).
cnf(f_873_6,plain,
( c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2715),U_2716),U_2717),c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),U_2718),U_2716),U_2719))
| ~ c_Orderings_Oord__class_Oless(U_2714,c_Groups_Oplus__class_Oplus(U_2714,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2714),c_Groups_Ominus__class_Ominus(U_2714,U_2715,U_2718)),U_2716),U_2717),U_2719)
| ~ sP274(U_2715,U_2714,U_2716,U_2717,U_2718,U_2719) ),
inference(clausify,[status(thm)],[f_873_3]) ).
fof(f_874_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_874_2,plain,
! [U_2721,U_2720] :
( c_Groups_Ominus__class_Ominus(U_2720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2720),U_2721),U_2721),c_Groups_Oone__class_Oone(U_2720)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2720),c_Groups_Oplus__class_Oplus(U_2720,U_2721,c_Groups_Oone__class_Oone(U_2720))),c_Groups_Ominus__class_Ominus(U_2720,U_2721,c_Groups_Oone__class_Oone(U_2720)))
| ~ class_Rings_Oring__1(U_2720) ),
inference(variable_rename,[status(thm)],[f_874_1]) ).
fof(f_874_3,plain,
! [U_2721,U_2720] :
( c_Groups_Ominus__class_Ominus(U_2720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2720),U_2721),U_2721),c_Groups_Oone__class_Oone(U_2720)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2720),c_Groups_Oplus__class_Oplus(U_2720,U_2721,c_Groups_Oone__class_Oone(U_2720))),c_Groups_Ominus__class_Ominus(U_2720,U_2721,c_Groups_Oone__class_Oone(U_2720)))
| ~ class_Rings_Oring__1(U_2720) ),
inference(definitional_conversion,[status(esa)],[f_874_2]) ).
cnf(f_874_4,plain,
( c_Groups_Ominus__class_Ominus(U_2720,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2720),U_2721),U_2721),c_Groups_Oone__class_Oone(U_2720)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2720),c_Groups_Oplus__class_Oplus(U_2720,U_2721,c_Groups_Oone__class_Oone(U_2720))),c_Groups_Ominus__class_Ominus(U_2720,U_2721,c_Groups_Oone__class_Oone(U_2720)))
| ~ class_Rings_Oring__1(U_2720) ),
inference(clausify,[status(thm)],[f_874_3]) ).
fof(f_875_1,plain,
! [V_t_2,V_D_2,V_d_2,T_a] :
( ! [B_x,B_k] :
( ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) )
& ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)) ) )
| ~ c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
| ~ class_Rings_Odvd(T_a)
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__period_I3_J]) ).
fof(f_875_2,plain,
! [U_2727,U_2726,U_2725,U_2724] :
( ! [U_2723,U_2722] :
( ( c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,U_2723,U_2727))
| ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,c_Groups_Ominus__class_Ominus(U_2724,U_2723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2724),U_2722),U_2726)),U_2727)) )
& ( c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,c_Groups_Ominus__class_Ominus(U_2724,U_2723,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2724),U_2722),U_2726)),U_2727))
| ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,U_2723,U_2727)) ) )
| ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,U_2726)
| ~ class_Rings_Odvd(U_2724)
| ~ class_Rings_Ocomm__ring(U_2724) ),
inference(variable_rename,[status(thm)],[f_875_1]) ).
fof(f_875_3,plain,
! [U_2727,U_2726,U_2725,U_2724] :
( ( ! [U_2731] :
( ! [U_2729] : ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,c_Groups_Ominus__class_Ominus(U_2724,U_2731,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2724),U_2729),U_2726)),U_2727))
| c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,U_2731,U_2727)) )
& ! [U_2730] :
( ! [U_2728] : c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,c_Groups_Ominus__class_Ominus(U_2724,U_2730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2724),U_2728),U_2726)),U_2727))
| ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,U_2730,U_2727)) ) )
| ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,U_2726)
| ~ class_Rings_Odvd(U_2724)
| ~ class_Rings_Ocomm__ring(U_2724) ),
inference(miniscope,[status(thm)],[f_875_2]) ).
fof(f_875_4,plain,
( ! [U_2724,U_2725,U_2726,U_2727,U_2728,U_2731,U_2729,U_2730] :
( ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,c_Groups_Ominus__class_Ominus(U_2724,U_2731,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2724),U_2729),U_2726)),U_2727))
| c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,U_2731,U_2727))
| ~ sP275(U_2724,U_2725,U_2726,U_2727,U_2728,U_2731,U_2729,U_2730) )
& ! [U_2724,U_2725,U_2726,U_2727,U_2728,U_2731,U_2729,U_2730] :
( c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,c_Groups_Ominus__class_Ominus(U_2724,U_2730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2724),U_2728),U_2726)),U_2727))
| ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,U_2730,U_2727))
| ~ sP275(U_2724,U_2725,U_2726,U_2727,U_2728,U_2731,U_2729,U_2730) )
& ! [U_2724,U_2725,U_2726,U_2727,U_2728,U_2731,U_2729,U_2730] :
( sP275(U_2724,U_2725,U_2726,U_2727,U_2728,U_2731,U_2729,U_2730)
| ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,U_2726)
| ~ class_Rings_Odvd(U_2724)
| ~ class_Rings_Ocomm__ring(U_2724) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP275])],[f_875_3]) ).
cnf(f_875_5,plain,
( sP275(U_2724,U_2725,U_2726,U_2727,U_2728,U_2731,U_2729,U_2730)
| ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,U_2726)
| ~ class_Rings_Odvd(U_2724)
| ~ class_Rings_Ocomm__ring(U_2724) ),
inference(clausify,[status(thm)],[f_875_4]) ).
cnf(f_875_6,plain,
( c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,c_Groups_Ominus__class_Ominus(U_2724,U_2730,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2724),U_2728),U_2726)),U_2727))
| ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,U_2730,U_2727))
| ~ sP275(U_2724,U_2725,U_2726,U_2727,U_2728,U_2731,U_2729,U_2730) ),
inference(clausify,[status(thm)],[f_875_4]) ).
cnf(f_875_7,plain,
( ~ c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,c_Groups_Ominus__class_Ominus(U_2724,U_2731,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2724),U_2729),U_2726)),U_2727))
| c_Rings_Odvd__class_Odvd(U_2724,U_2725,c_Groups_Oplus__class_Oplus(U_2724,U_2731,U_2727))
| ~ sP275(U_2724,U_2725,U_2726,U_2727,U_2728,U_2731,U_2729,U_2730) ),
inference(clausify,[status(thm)],[f_875_4]) ).
fof(f_876_1,plain,
! [V_t_2,V_D_2,V_d_2,T_a] :
( ! [B_x,B_k] :
( ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2)) )
& ( c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,c_Groups_Ominus__class_Ominus(T_a,B_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),B_k),V_D_2)),V_t_2))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_d_2,c_Groups_Oplus__class_Oplus(T_a,B_x,V_t_2)) ) )
| ~ c_Rings_Odvd__class_Odvd(T_a,V_d_2,V_D_2)
| ~ class_Rings_Odvd(T_a)
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_inf__period_I4_J]) ).
fof(f_876_2,plain,
! [U_2737,U_2736,U_2735,U_2734] :
( ! [U_2733,U_2732] :
( ( c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,U_2733,U_2737))
| ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,c_Groups_Ominus__class_Ominus(U_2734,U_2733,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2734),U_2732),U_2736)),U_2737)) )
& ( c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,c_Groups_Ominus__class_Ominus(U_2734,U_2733,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2734),U_2732),U_2736)),U_2737))
| ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,U_2733,U_2737)) ) )
| ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,U_2736)
| ~ class_Rings_Odvd(U_2734)
| ~ class_Rings_Ocomm__ring(U_2734) ),
inference(variable_rename,[status(thm)],[f_876_1]) ).
fof(f_876_3,plain,
! [U_2737,U_2736,U_2735,U_2734] :
( ( ! [U_2741] :
( ! [U_2739] : ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,c_Groups_Ominus__class_Ominus(U_2734,U_2741,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2734),U_2739),U_2736)),U_2737))
| c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,U_2741,U_2737)) )
& ! [U_2740] :
( ! [U_2738] : c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,c_Groups_Ominus__class_Ominus(U_2734,U_2740,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2734),U_2738),U_2736)),U_2737))
| ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,U_2740,U_2737)) ) )
| ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,U_2736)
| ~ class_Rings_Odvd(U_2734)
| ~ class_Rings_Ocomm__ring(U_2734) ),
inference(miniscope,[status(thm)],[f_876_2]) ).
fof(f_876_4,plain,
( ! [U_2734,U_2735,U_2736,U_2737,U_2738,U_2739,U_2740,U_2741] :
( ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,c_Groups_Ominus__class_Ominus(U_2734,U_2741,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2734),U_2739),U_2736)),U_2737))
| c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,U_2741,U_2737))
| ~ sP276(U_2734,U_2735,U_2736,U_2737,U_2738,U_2739,U_2740,U_2741) )
& ! [U_2734,U_2735,U_2736,U_2737,U_2738,U_2739,U_2740,U_2741] :
( c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,c_Groups_Ominus__class_Ominus(U_2734,U_2740,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2734),U_2738),U_2736)),U_2737))
| ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,U_2740,U_2737))
| ~ sP276(U_2734,U_2735,U_2736,U_2737,U_2738,U_2739,U_2740,U_2741) )
& ! [U_2734,U_2735,U_2736,U_2737,U_2738,U_2739,U_2740,U_2741] :
( sP276(U_2734,U_2735,U_2736,U_2737,U_2738,U_2739,U_2740,U_2741)
| ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,U_2736)
| ~ class_Rings_Odvd(U_2734)
| ~ class_Rings_Ocomm__ring(U_2734) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP276])],[f_876_3]) ).
cnf(f_876_5,plain,
( sP276(U_2734,U_2735,U_2736,U_2737,U_2738,U_2739,U_2740,U_2741)
| ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,U_2736)
| ~ class_Rings_Odvd(U_2734)
| ~ class_Rings_Ocomm__ring(U_2734) ),
inference(clausify,[status(thm)],[f_876_4]) ).
cnf(f_876_6,plain,
( c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,c_Groups_Ominus__class_Ominus(U_2734,U_2740,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2734),U_2738),U_2736)),U_2737))
| ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,U_2740,U_2737))
| ~ sP276(U_2734,U_2735,U_2736,U_2737,U_2738,U_2739,U_2740,U_2741) ),
inference(clausify,[status(thm)],[f_876_4]) ).
cnf(f_876_7,plain,
( ~ c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,c_Groups_Ominus__class_Ominus(U_2734,U_2741,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2734),U_2739),U_2736)),U_2737))
| c_Rings_Odvd__class_Odvd(U_2734,U_2735,c_Groups_Oplus__class_Oplus(U_2734,U_2741,U_2737))
| ~ sP276(U_2734,U_2735,U_2736,U_2737,U_2738,U_2739,U_2740,U_2741) ),
inference(clausify,[status(thm)],[f_876_4]) ).
fof(f_877_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_877_2,plain,
! [U_2746,U_2745,U_2744,U_2743,U_2742] :
( c_Orderings_Oord__class_Oless__eq(U_2742,c_Groups_Oabs__class_Oabs(U_2742,c_Groups_Ominus__class_Ominus(U_2742,c_Groups_Oplus__class_Oplus(U_2742,U_2743,U_2744),c_Groups_Oplus__class_Oplus(U_2742,U_2745,U_2746))),c_Groups_Oplus__class_Oplus(U_2742,c_Groups_Oabs__class_Oabs(U_2742,c_Groups_Ominus__class_Ominus(U_2742,U_2743,U_2745)),c_Groups_Oabs__class_Oabs(U_2742,c_Groups_Ominus__class_Ominus(U_2742,U_2744,U_2746))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2742) ),
inference(variable_rename,[status(thm)],[f_877_1]) ).
fof(f_877_3,plain,
! [U_2743,U_2745,U_2746,U_2744,U_2742] :
( c_Orderings_Oord__class_Oless__eq(U_2742,c_Groups_Oabs__class_Oabs(U_2742,c_Groups_Ominus__class_Ominus(U_2742,c_Groups_Oplus__class_Oplus(U_2742,U_2743,U_2744),c_Groups_Oplus__class_Oplus(U_2742,U_2745,U_2746))),c_Groups_Oplus__class_Oplus(U_2742,c_Groups_Oabs__class_Oabs(U_2742,c_Groups_Ominus__class_Ominus(U_2742,U_2743,U_2745)),c_Groups_Oabs__class_Oabs(U_2742,c_Groups_Ominus__class_Ominus(U_2742,U_2744,U_2746))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2742) ),
inference(definitional_conversion,[status(esa)],[f_877_2]) ).
cnf(f_877_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2742,c_Groups_Oabs__class_Oabs(U_2742,c_Groups_Ominus__class_Ominus(U_2742,c_Groups_Oplus__class_Oplus(U_2742,U_2743,U_2744),c_Groups_Oplus__class_Oplus(U_2742,U_2745,U_2746))),c_Groups_Oplus__class_Oplus(U_2742,c_Groups_Oabs__class_Oabs(U_2742,c_Groups_Ominus__class_Ominus(U_2742,U_2743,U_2745)),c_Groups_Oabs__class_Oabs(U_2742,c_Groups_Ominus__class_Ominus(U_2742,U_2744,U_2746))))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2742) ),
inference(clausify,[status(thm)],[f_877_3]) ).
fof(f_878_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_878_2,plain,
! [U_2749,U_2748,U_2747] :
( c_Orderings_Oord__class_Oless__eq(U_2747,c_Groups_Oabs__class_Oabs(U_2747,c_Groups_Ominus__class_Ominus(U_2747,U_2748,U_2749)),c_Groups_Oplus__class_Oplus(U_2747,c_Groups_Oabs__class_Oabs(U_2747,U_2748),c_Groups_Oabs__class_Oabs(U_2747,U_2749)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2747) ),
inference(variable_rename,[status(thm)],[f_878_1]) ).
fof(f_878_3,plain,
! [U_2749,U_2747,U_2748] :
( c_Orderings_Oord__class_Oless__eq(U_2747,c_Groups_Oabs__class_Oabs(U_2747,c_Groups_Ominus__class_Ominus(U_2747,U_2748,U_2749)),c_Groups_Oplus__class_Oplus(U_2747,c_Groups_Oabs__class_Oabs(U_2747,U_2748),c_Groups_Oabs__class_Oabs(U_2747,U_2749)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2747) ),
inference(definitional_conversion,[status(esa)],[f_878_2]) ).
cnf(f_878_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2747,c_Groups_Oabs__class_Oabs(U_2747,c_Groups_Ominus__class_Ominus(U_2747,U_2748,U_2749)),c_Groups_Oplus__class_Oplus(U_2747,c_Groups_Oabs__class_Oabs(U_2747,U_2748),c_Groups_Oabs__class_Oabs(U_2747,U_2749)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2747) ),
inference(clausify,[status(thm)],[f_878_3]) ).
fof(f_879_1,plain,
! [V_ra_2,V_a_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2)
| ~ c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) )
& ( ( c_Orderings_Oord__class_Oless(T_a,V_x_2,c_Groups_Oplus__class_Oplus(T_a,V_a_2,V_ra_2))
& c_Orderings_Oord__class_Oless(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a_2,V_ra_2),V_x_2) )
| ~ c_Orderings_Oord__class_Oless(T_a,c_Groups_Oabs__class_Oabs(T_a,c_Groups_Ominus__class_Ominus(T_a,V_x_2,V_a_2)),V_ra_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_abs__diff__less__iff]) ).
fof(f_879_2,plain,
! [U_2753,U_2752,U_2751,U_2750] :
( ( ( c_Orderings_Oord__class_Oless(U_2750,c_Groups_Oabs__class_Oabs(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2751,U_2752)),U_2753)
| ~ c_Orderings_Oord__class_Oless(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2752,U_2753))
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2752,U_2753),U_2751) )
& ( ( c_Orderings_Oord__class_Oless(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2752,U_2753))
& c_Orderings_Oord__class_Oless(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2752,U_2753),U_2751) )
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Oabs__class_Oabs(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2751,U_2752)),U_2753) ) )
| ~ class_Rings_Olinordered__idom(U_2750) ),
inference(variable_rename,[status(thm)],[f_879_1]) ).
fof(f_879_3,plain,
( ! [U_2750,U_2751,U_2752,U_2753] :
( c_Orderings_Oord__class_Oless(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2752,U_2753))
| ~ sP277(U_2750,U_2751,U_2752,U_2753) )
& ! [U_2750,U_2751,U_2752,U_2753] :
( c_Orderings_Oord__class_Oless(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2752,U_2753),U_2751)
| ~ sP277(U_2750,U_2751,U_2752,U_2753) )
& ! [U_2750,U_2751,U_2752,U_2753] :
( c_Orderings_Oord__class_Oless(U_2750,c_Groups_Oabs__class_Oabs(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2751,U_2752)),U_2753)
| ~ c_Orderings_Oord__class_Oless(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2752,U_2753))
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2752,U_2753),U_2751)
| ~ sP278(U_2750,U_2751,U_2752,U_2753) )
& ! [U_2750,U_2751,U_2752,U_2753] :
( sP277(U_2750,U_2751,U_2752,U_2753)
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Oabs__class_Oabs(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2751,U_2752)),U_2753)
| ~ sP278(U_2750,U_2751,U_2752,U_2753) )
& ! [U_2750,U_2751,U_2752,U_2753] :
( sP278(U_2750,U_2751,U_2752,U_2753)
| ~ class_Rings_Olinordered__idom(U_2750) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP277,sP278])],[f_879_2]) ).
cnf(f_879_4,plain,
( sP278(U_2750,U_2751,U_2752,U_2753)
| ~ class_Rings_Olinordered__idom(U_2750) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_5,plain,
( sP277(U_2750,U_2751,U_2752,U_2753)
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Oabs__class_Oabs(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2751,U_2752)),U_2753)
| ~ sP278(U_2750,U_2751,U_2752,U_2753) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_6,plain,
( c_Orderings_Oord__class_Oless(U_2750,c_Groups_Oabs__class_Oabs(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2751,U_2752)),U_2753)
| ~ c_Orderings_Oord__class_Oless(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2752,U_2753))
| ~ c_Orderings_Oord__class_Oless(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2752,U_2753),U_2751)
| ~ sP278(U_2750,U_2751,U_2752,U_2753) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_7,plain,
( c_Orderings_Oord__class_Oless(U_2750,c_Groups_Ominus__class_Ominus(U_2750,U_2752,U_2753),U_2751)
| ~ sP277(U_2750,U_2751,U_2752,U_2753) ),
inference(clausify,[status(thm)],[f_879_3]) ).
cnf(f_879_8,plain,
( c_Orderings_Oord__class_Oless(U_2750,U_2751,c_Groups_Oplus__class_Oplus(U_2750,U_2752,U_2753))
| ~ sP277(U_2750,U_2751,U_2752,U_2753) ),
inference(clausify,[status(thm)],[f_879_3]) ).
fof(f_880_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_880_2,plain,
! [U_2756,U_2755,U_2754] :
( 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_2754,U_2755),c_RealVector_Onorm__class_Onorm(U_2754,U_2756))),c_RealVector_Onorm__class_Onorm(U_2754,c_Groups_Ominus__class_Ominus(U_2754,U_2755,U_2756)))
| ~ class_RealVector_Oreal__normed__vector(U_2754) ),
inference(variable_rename,[status(thm)],[f_880_1]) ).
fof(f_880_3,plain,
! [U_2756,U_2755,U_2754] :
( 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_2754,U_2755),c_RealVector_Onorm__class_Onorm(U_2754,U_2756))),c_RealVector_Onorm__class_Onorm(U_2754,c_Groups_Ominus__class_Ominus(U_2754,U_2755,U_2756)))
| ~ class_RealVector_Oreal__normed__vector(U_2754) ),
inference(definitional_conversion,[status(esa)],[f_880_2]) ).
cnf(f_880_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_2754,U_2755),c_RealVector_Onorm__class_Onorm(U_2754,U_2756))),c_RealVector_Onorm__class_Onorm(U_2754,c_Groups_Ominus__class_Ominus(U_2754,U_2755,U_2756)))
| ~ class_RealVector_Oreal__normed__vector(U_2754) ),
inference(clausify,[status(thm)],[f_880_3]) ).
fof(f_881_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_881_2,plain,
! [U_2759,U_2758,U_2757] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2757,U_2758,U_2759)
| ~ c_Orderings_Oord__class_Oless__eq(U_2757,c_Groups_Ominus__class_Ominus(U_2757,U_2758,U_2759),c_Groups_Ozero__class_Ozero(U_2757)) )
& ( c_Orderings_Oord__class_Oless__eq(U_2757,c_Groups_Ominus__class_Ominus(U_2757,U_2758,U_2759),c_Groups_Ozero__class_Ozero(U_2757))
| ~ c_Orderings_Oord__class_Oless__eq(U_2757,U_2758,U_2759) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2757) ),
inference(variable_rename,[status(thm)],[f_881_1]) ).
fof(f_881_3,plain,
( ! [U_2757,U_2758,U_2759] :
( c_Orderings_Oord__class_Oless__eq(U_2757,U_2758,U_2759)
| ~ c_Orderings_Oord__class_Oless__eq(U_2757,c_Groups_Ominus__class_Ominus(U_2757,U_2758,U_2759),c_Groups_Ozero__class_Ozero(U_2757))
| ~ sP279(U_2757,U_2758,U_2759) )
& ! [U_2757,U_2758,U_2759] :
( c_Orderings_Oord__class_Oless__eq(U_2757,c_Groups_Ominus__class_Ominus(U_2757,U_2758,U_2759),c_Groups_Ozero__class_Ozero(U_2757))
| ~ c_Orderings_Oord__class_Oless__eq(U_2757,U_2758,U_2759)
| ~ sP279(U_2757,U_2758,U_2759) )
& ! [U_2757,U_2758,U_2759] :
( sP279(U_2757,U_2758,U_2759)
| ~ class_Groups_Oordered__ab__group__add(U_2757) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279])],[f_881_2]) ).
cnf(f_881_4,plain,
( sP279(U_2757,U_2758,U_2759)
| ~ class_Groups_Oordered__ab__group__add(U_2757) ),
inference(clausify,[status(thm)],[f_881_3]) ).
cnf(f_881_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2757,c_Groups_Ominus__class_Ominus(U_2757,U_2758,U_2759),c_Groups_Ozero__class_Ozero(U_2757))
| ~ c_Orderings_Oord__class_Oless__eq(U_2757,U_2758,U_2759)
| ~ sP279(U_2757,U_2758,U_2759) ),
inference(clausify,[status(thm)],[f_881_3]) ).
cnf(f_881_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2757,U_2758,U_2759)
| ~ c_Orderings_Oord__class_Oless__eq(U_2757,c_Groups_Ominus__class_Ominus(U_2757,U_2758,U_2759),c_Groups_Ozero__class_Ozero(U_2757))
| ~ sP279(U_2757,U_2758,U_2759) ),
inference(clausify,[status(thm)],[f_881_3]) ).
fof(f_882_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_882_2,plain,
! [U_2764,U_2763,U_2762,U_2761,U_2760] :
( c_Groups_Ominus__class_Ominus(U_2760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),U_2762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2763),U_2764)) = c_Groups_Oplus__class_Oplus(U_2760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),c_Groups_Ominus__class_Ominus(U_2760,U_2762,U_2764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),c_Groups_Ominus__class_Ominus(U_2760,U_2761,U_2763)),U_2764))
| ~ class_Rings_Oring(U_2760) ),
inference(variable_rename,[status(thm)],[f_882_1]) ).
fof(f_882_3,plain,
! [U_2760,U_2761,U_2762,U_2763,U_2764] :
( c_Groups_Ominus__class_Ominus(U_2760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),U_2762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2763),U_2764)) = c_Groups_Oplus__class_Oplus(U_2760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),c_Groups_Ominus__class_Ominus(U_2760,U_2762,U_2764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),c_Groups_Ominus__class_Ominus(U_2760,U_2761,U_2763)),U_2764))
| ~ class_Rings_Oring(U_2760) ),
inference(definitional_conversion,[status(esa)],[f_882_2]) ).
cnf(f_882_4,plain,
( c_Groups_Ominus__class_Ominus(U_2760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),U_2762),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2763),U_2764)) = c_Groups_Oplus__class_Oplus(U_2760,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),U_2761),c_Groups_Ominus__class_Ominus(U_2760,U_2762,U_2764)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2760),c_Groups_Ominus__class_Ominus(U_2760,U_2761,U_2763)),U_2764))
| ~ class_Rings_Oring(U_2760) ),
inference(clausify,[status(thm)],[f_882_3]) ).
fof(f_883_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_883_2,plain,
! [U_2769,U_2768,U_2767,U_2766,U_2765] :
( c_Groups_Ominus__class_Ominus(U_2765,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2766),U_2767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2768),U_2769)) = c_Groups_Oplus__class_Oplus(U_2765,c_Groups_Oplus__class_Oplus(U_2765,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),c_Groups_Ominus__class_Ominus(U_2765,U_2766,U_2768)),c_Groups_Ominus__class_Ominus(U_2765,U_2767,U_2769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),c_Groups_Ominus__class_Ominus(U_2765,U_2766,U_2768)),U_2769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2768),c_Groups_Ominus__class_Ominus(U_2765,U_2767,U_2769)))
| ~ class_RealVector_Oreal__normed__algebra(U_2765) ),
inference(variable_rename,[status(thm)],[f_883_1]) ).
fof(f_883_3,plain,
! [U_2765,U_2766,U_2767,U_2768,U_2769] :
( c_Groups_Ominus__class_Ominus(U_2765,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2766),U_2767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2768),U_2769)) = c_Groups_Oplus__class_Oplus(U_2765,c_Groups_Oplus__class_Oplus(U_2765,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),c_Groups_Ominus__class_Ominus(U_2765,U_2766,U_2768)),c_Groups_Ominus__class_Ominus(U_2765,U_2767,U_2769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),c_Groups_Ominus__class_Ominus(U_2765,U_2766,U_2768)),U_2769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2768),c_Groups_Ominus__class_Ominus(U_2765,U_2767,U_2769)))
| ~ class_RealVector_Oreal__normed__algebra(U_2765) ),
inference(definitional_conversion,[status(esa)],[f_883_2]) ).
cnf(f_883_4,plain,
( c_Groups_Ominus__class_Ominus(U_2765,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2766),U_2767),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2768),U_2769)) = c_Groups_Oplus__class_Oplus(U_2765,c_Groups_Oplus__class_Oplus(U_2765,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),c_Groups_Ominus__class_Ominus(U_2765,U_2766,U_2768)),c_Groups_Ominus__class_Ominus(U_2765,U_2767,U_2769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),c_Groups_Ominus__class_Ominus(U_2765,U_2766,U_2768)),U_2769)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2765),U_2768),c_Groups_Ominus__class_Ominus(U_2765,U_2767,U_2769)))
| ~ class_RealVector_Oreal__normed__algebra(U_2765) ),
inference(clausify,[status(thm)],[f_883_3]) ).
fof(f_884_1,plain,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_884_2,plain,
! [U_2775,U_2774,U_2773,U_2772,U_2771,U_2770] :
( ( ( c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2771),U_2772),U_2773) = c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2774),U_2772),U_2775)
| c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),c_Groups_Ominus__class_Ominus(U_2770,U_2771,U_2774)),U_2772),U_2773) != U_2775 )
& ( c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),c_Groups_Ominus__class_Ominus(U_2770,U_2771,U_2774)),U_2772),U_2773) = U_2775
| c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2771),U_2772),U_2773) != c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2774),U_2772),U_2775) ) )
| ~ class_Rings_Oring(U_2770) ),
inference(variable_rename,[status(thm)],[f_884_1]) ).
fof(f_884_3,plain,
( ! [U_2772,U_2773,U_2774,U_2775,U_2770,U_2771] :
( c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2771),U_2772),U_2773) = c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2774),U_2772),U_2775)
| c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),c_Groups_Ominus__class_Ominus(U_2770,U_2771,U_2774)),U_2772),U_2773) != U_2775
| ~ sP280(U_2772,U_2773,U_2774,U_2775,U_2770,U_2771) )
& ! [U_2772,U_2773,U_2774,U_2775,U_2770,U_2771] :
( c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),c_Groups_Ominus__class_Ominus(U_2770,U_2771,U_2774)),U_2772),U_2773) = U_2775
| c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2771),U_2772),U_2773) != c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2774),U_2772),U_2775)
| ~ sP280(U_2772,U_2773,U_2774,U_2775,U_2770,U_2771) )
& ! [U_2772,U_2773,U_2774,U_2775,U_2770,U_2771] :
( sP280(U_2772,U_2773,U_2774,U_2775,U_2770,U_2771)
| ~ class_Rings_Oring(U_2770) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP280])],[f_884_2]) ).
cnf(f_884_4,plain,
( sP280(U_2772,U_2773,U_2774,U_2775,U_2770,U_2771)
| ~ class_Rings_Oring(U_2770) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_5,plain,
( c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),c_Groups_Ominus__class_Ominus(U_2770,U_2771,U_2774)),U_2772),U_2773) = U_2775
| c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2771),U_2772),U_2773) != c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2774),U_2772),U_2775)
| ~ sP280(U_2772,U_2773,U_2774,U_2775,U_2770,U_2771) ),
inference(clausify,[status(thm)],[f_884_3]) ).
cnf(f_884_6,plain,
( c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2771),U_2772),U_2773) = c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),U_2774),U_2772),U_2775)
| c_Groups_Oplus__class_Oplus(U_2770,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2770),c_Groups_Ominus__class_Ominus(U_2770,U_2771,U_2774)),U_2772),U_2773) != U_2775
| ~ sP280(U_2772,U_2773,U_2774,U_2775,U_2770,U_2771) ),
inference(clausify,[status(thm)],[f_884_3]) ).
fof(f_885_1,plain,
! [V_d_2,V_b_2,V_ca_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_ca_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_ca_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_ca_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_ca_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_885_2,plain,
! [U_2781,U_2780,U_2779,U_2778,U_2777,U_2776] :
( ( ( c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2777),U_2778),U_2779) = c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2780),U_2778),U_2781)
| U_2779 != c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),c_Groups_Ominus__class_Ominus(U_2776,U_2780,U_2777)),U_2778),U_2781) )
& ( U_2779 = c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),c_Groups_Ominus__class_Ominus(U_2776,U_2780,U_2777)),U_2778),U_2781)
| c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2777),U_2778),U_2779) != c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2780),U_2778),U_2781) ) )
| ~ class_Rings_Oring(U_2776) ),
inference(variable_rename,[status(thm)],[f_885_1]) ).
fof(f_885_3,plain,
( ! [U_2779,U_2776,U_2777,U_2780,U_2781,U_2778] :
( c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2777),U_2778),U_2779) = c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2780),U_2778),U_2781)
| U_2779 != c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),c_Groups_Ominus__class_Ominus(U_2776,U_2780,U_2777)),U_2778),U_2781)
| ~ sP281(U_2779,U_2776,U_2777,U_2780,U_2781,U_2778) )
& ! [U_2779,U_2776,U_2777,U_2780,U_2781,U_2778] :
( U_2779 = c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),c_Groups_Ominus__class_Ominus(U_2776,U_2780,U_2777)),U_2778),U_2781)
| c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2777),U_2778),U_2779) != c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2780),U_2778),U_2781)
| ~ sP281(U_2779,U_2776,U_2777,U_2780,U_2781,U_2778) )
& ! [U_2779,U_2776,U_2777,U_2780,U_2781,U_2778] :
( sP281(U_2779,U_2776,U_2777,U_2780,U_2781,U_2778)
| ~ class_Rings_Oring(U_2776) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281])],[f_885_2]) ).
cnf(f_885_4,plain,
( sP281(U_2779,U_2776,U_2777,U_2780,U_2781,U_2778)
| ~ class_Rings_Oring(U_2776) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_5,plain,
( U_2779 = c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),c_Groups_Ominus__class_Ominus(U_2776,U_2780,U_2777)),U_2778),U_2781)
| c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2777),U_2778),U_2779) != c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2780),U_2778),U_2781)
| ~ sP281(U_2779,U_2776,U_2777,U_2780,U_2781,U_2778) ),
inference(clausify,[status(thm)],[f_885_3]) ).
cnf(f_885_6,plain,
( c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2777),U_2778),U_2779) = c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),U_2780),U_2778),U_2781)
| U_2779 != c_Groups_Oplus__class_Oplus(U_2776,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2776),c_Groups_Ominus__class_Ominus(U_2776,U_2780,U_2777)),U_2778),U_2781)
| ~ sP281(U_2779,U_2776,U_2777,U_2780,U_2781,U_2778) ),
inference(clausify,[status(thm)],[f_885_3]) ).
fof(f_886_1,plain,
! [V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ouminus__class_Ouminus(T_a,V_a)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__0]) ).
fof(f_886_2,plain,
! [U_2783,U_2782] :
( c_Groups_Ominus__class_Ominus(U_2782,c_Groups_Ozero__class_Ozero(U_2782),U_2783) = c_Groups_Ouminus__class_Ouminus(U_2782,U_2783)
| ~ class_Groups_Ogroup__add(U_2782) ),
inference(variable_rename,[status(thm)],[f_886_1]) ).
fof(f_886_3,plain,
! [U_2782,U_2783] :
( c_Groups_Ominus__class_Ominus(U_2782,c_Groups_Ozero__class_Ozero(U_2782),U_2783) = c_Groups_Ouminus__class_Ouminus(U_2782,U_2783)
| ~ class_Groups_Ogroup__add(U_2782) ),
inference(definitional_conversion,[status(esa)],[f_886_2]) ).
cnf(f_886_4,plain,
( c_Groups_Ominus__class_Ominus(U_2782,c_Groups_Ozero__class_Ozero(U_2782),U_2783) = c_Groups_Ouminus__class_Ouminus(U_2782,U_2783)
| ~ class_Groups_Ogroup__add(U_2782) ),
inference(clausify,[status(thm)],[f_886_3]) ).
fof(f_887_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b)) = c_Groups_Oplus__class_Oplus(T_a,V_a,V_b)
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__minus__eq__add]) ).
fof(f_887_2,plain,
! [U_2786,U_2785,U_2784] :
( c_Groups_Ominus__class_Ominus(U_2784,U_2785,c_Groups_Ouminus__class_Ouminus(U_2784,U_2786)) = c_Groups_Oplus__class_Oplus(U_2784,U_2785,U_2786)
| ~ class_Groups_Ogroup__add(U_2784) ),
inference(variable_rename,[status(thm)],[f_887_1]) ).
fof(f_887_3,plain,
! [U_2786,U_2785,U_2784] :
( c_Groups_Ominus__class_Ominus(U_2784,U_2785,c_Groups_Ouminus__class_Ouminus(U_2784,U_2786)) = c_Groups_Oplus__class_Oplus(U_2784,U_2785,U_2786)
| ~ class_Groups_Ogroup__add(U_2784) ),
inference(definitional_conversion,[status(esa)],[f_887_2]) ).
cnf(f_887_4,plain,
( c_Groups_Ominus__class_Ominus(U_2784,U_2785,c_Groups_Ouminus__class_Ouminus(U_2784,U_2786)) = c_Groups_Oplus__class_Oplus(U_2784,U_2785,U_2786)
| ~ class_Groups_Ogroup__add(U_2784) ),
inference(clausify,[status(thm)],[f_887_3]) ).
fof(f_888_1,plain,
! [V_y,V_x,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_x,V_y) = c_Groups_Oplus__class_Oplus(T_a,V_x,c_Groups_Ouminus__class_Ouminus(T_a,V_y))
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J]) ).
fof(f_888_2,plain,
! [U_2789,U_2788,U_2787] :
( c_Groups_Ominus__class_Ominus(U_2787,U_2788,U_2789) = c_Groups_Oplus__class_Oplus(U_2787,U_2788,c_Groups_Ouminus__class_Ouminus(U_2787,U_2789))
| ~ class_Rings_Ocomm__ring__1(U_2787) ),
inference(variable_rename,[status(thm)],[f_888_1]) ).
fof(f_888_3,plain,
! [U_2787,U_2788,U_2789] :
( c_Groups_Ominus__class_Ominus(U_2787,U_2788,U_2789) = c_Groups_Oplus__class_Oplus(U_2787,U_2788,c_Groups_Ouminus__class_Ouminus(U_2787,U_2789))
| ~ class_Rings_Ocomm__ring__1(U_2787) ),
inference(definitional_conversion,[status(esa)],[f_888_2]) ).
cnf(f_888_4,plain,
( c_Groups_Ominus__class_Ominus(U_2787,U_2788,U_2789) = c_Groups_Oplus__class_Oplus(U_2787,U_2788,c_Groups_Ouminus__class_Ouminus(U_2787,U_2789))
| ~ class_Rings_Ocomm__ring__1(U_2787) ),
inference(clausify,[status(thm)],[f_888_3]) ).
fof(f_889_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_ab__diff__minus]) ).
fof(f_889_2,plain,
! [U_2792,U_2791,U_2790] :
( c_Groups_Ominus__class_Ominus(U_2790,U_2791,U_2792) = c_Groups_Oplus__class_Oplus(U_2790,U_2791,c_Groups_Ouminus__class_Ouminus(U_2790,U_2792))
| ~ class_Groups_Oab__group__add(U_2790) ),
inference(variable_rename,[status(thm)],[f_889_1]) ).
fof(f_889_3,plain,
! [U_2790,U_2791,U_2792] :
( c_Groups_Ominus__class_Ominus(U_2790,U_2791,U_2792) = c_Groups_Oplus__class_Oplus(U_2790,U_2791,c_Groups_Ouminus__class_Ouminus(U_2790,U_2792))
| ~ class_Groups_Oab__group__add(U_2790) ),
inference(definitional_conversion,[status(esa)],[f_889_2]) ).
cnf(f_889_4,plain,
( c_Groups_Ominus__class_Ominus(U_2790,U_2791,U_2792) = c_Groups_Oplus__class_Oplus(U_2790,U_2791,c_Groups_Ouminus__class_Ouminus(U_2790,U_2792))
| ~ class_Groups_Oab__group__add(U_2790) ),
inference(clausify,[status(thm)],[f_889_3]) ).
fof(f_890_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(T_a,V_a,V_b) = c_Groups_Oplus__class_Oplus(T_a,V_a,c_Groups_Ouminus__class_Ouminus(T_a,V_b))
| ~ class_Groups_Ogroup__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__def]) ).
fof(f_890_2,plain,
! [U_2795,U_2794,U_2793] :
( c_Groups_Ominus__class_Ominus(U_2793,U_2794,U_2795) = c_Groups_Oplus__class_Oplus(U_2793,U_2794,c_Groups_Ouminus__class_Ouminus(U_2793,U_2795))
| ~ class_Groups_Ogroup__add(U_2793) ),
inference(variable_rename,[status(thm)],[f_890_1]) ).
fof(f_890_3,plain,
! [U_2793,U_2794,U_2795] :
( c_Groups_Ominus__class_Ominus(U_2793,U_2794,U_2795) = c_Groups_Oplus__class_Oplus(U_2793,U_2794,c_Groups_Ouminus__class_Ouminus(U_2793,U_2795))
| ~ class_Groups_Ogroup__add(U_2793) ),
inference(definitional_conversion,[status(esa)],[f_890_2]) ).
cnf(f_890_4,plain,
( c_Groups_Ominus__class_Ominus(U_2793,U_2794,U_2795) = c_Groups_Oplus__class_Oplus(U_2793,U_2794,c_Groups_Ouminus__class_Ouminus(U_2793,U_2795))
| ~ class_Groups_Ogroup__add(U_2793) ),
inference(clausify,[status(thm)],[f_890_3]) ).
fof(f_891_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_891_2,plain,
! [U_2798,U_2797,U_2796] :
( c_Orderings_Oord__class_Oless__eq(U_2796,c_Groups_Oabs__class_Oabs(U_2796,c_Groups_Ominus__class_Ominus(U_2796,c_Groups_Oabs__class_Oabs(U_2796,U_2797),c_Groups_Oabs__class_Oabs(U_2796,U_2798))),c_Groups_Oabs__class_Oabs(U_2796,c_Groups_Ominus__class_Ominus(U_2796,U_2797,U_2798)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2796) ),
inference(variable_rename,[status(thm)],[f_891_1]) ).
fof(f_891_3,plain,
! [U_2796,U_2797,U_2798] :
( c_Orderings_Oord__class_Oless__eq(U_2796,c_Groups_Oabs__class_Oabs(U_2796,c_Groups_Ominus__class_Ominus(U_2796,c_Groups_Oabs__class_Oabs(U_2796,U_2797),c_Groups_Oabs__class_Oabs(U_2796,U_2798))),c_Groups_Oabs__class_Oabs(U_2796,c_Groups_Ominus__class_Ominus(U_2796,U_2797,U_2798)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2796) ),
inference(definitional_conversion,[status(esa)],[f_891_2]) ).
cnf(f_891_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2796,c_Groups_Oabs__class_Oabs(U_2796,c_Groups_Ominus__class_Ominus(U_2796,c_Groups_Oabs__class_Oabs(U_2796,U_2797),c_Groups_Oabs__class_Oabs(U_2796,U_2798))),c_Groups_Oabs__class_Oabs(U_2796,c_Groups_Ominus__class_Ominus(U_2796,U_2797,U_2798)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2796) ),
inference(clausify,[status(thm)],[f_891_3]) ).
fof(f_892_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_892_2,plain,
! [U_2801,U_2800,U_2799] :
( c_Orderings_Oord__class_Oless__eq(U_2799,c_Groups_Ominus__class_Ominus(U_2799,c_Groups_Oabs__class_Oabs(U_2799,U_2800),c_Groups_Oabs__class_Oabs(U_2799,U_2801)),c_Groups_Oabs__class_Oabs(U_2799,c_Groups_Ominus__class_Ominus(U_2799,U_2800,U_2801)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2799) ),
inference(variable_rename,[status(thm)],[f_892_1]) ).
fof(f_892_3,plain,
! [U_2799,U_2800,U_2801] :
( c_Orderings_Oord__class_Oless__eq(U_2799,c_Groups_Ominus__class_Ominus(U_2799,c_Groups_Oabs__class_Oabs(U_2799,U_2800),c_Groups_Oabs__class_Oabs(U_2799,U_2801)),c_Groups_Oabs__class_Oabs(U_2799,c_Groups_Ominus__class_Ominus(U_2799,U_2800,U_2801)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2799) ),
inference(definitional_conversion,[status(esa)],[f_892_2]) ).
cnf(f_892_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2799,c_Groups_Ominus__class_Ominus(U_2799,c_Groups_Oabs__class_Oabs(U_2799,U_2800),c_Groups_Oabs__class_Oabs(U_2799,U_2801)),c_Groups_Oabs__class_Oabs(U_2799,c_Groups_Ominus__class_Ominus(U_2799,U_2800,U_2801)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2799) ),
inference(clausify,[status(thm)],[f_892_3]) ).
fof(f_893_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_893_2,plain,
! [U_2804,U_2803,U_2802] :
( c_Orderings_Oord__class_Oless__eq(U_2802,c_Groups_Ominus__class_Ominus(U_2802,c_Groups_Oabs__class_Oabs(U_2802,U_2803),c_Groups_Oabs__class_Oabs(U_2802,U_2804)),c_Groups_Oabs__class_Oabs(U_2802,c_Groups_Ominus__class_Ominus(U_2802,U_2804,U_2803)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2802) ),
inference(variable_rename,[status(thm)],[f_893_1]) ).
fof(f_893_3,plain,
! [U_2802,U_2803,U_2804] :
( c_Orderings_Oord__class_Oless__eq(U_2802,c_Groups_Ominus__class_Ominus(U_2802,c_Groups_Oabs__class_Oabs(U_2802,U_2803),c_Groups_Oabs__class_Oabs(U_2802,U_2804)),c_Groups_Oabs__class_Oabs(U_2802,c_Groups_Ominus__class_Ominus(U_2802,U_2804,U_2803)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2802) ),
inference(definitional_conversion,[status(esa)],[f_893_2]) ).
cnf(f_893_4,plain,
( c_Orderings_Oord__class_Oless__eq(U_2802,c_Groups_Ominus__class_Ominus(U_2802,c_Groups_Oabs__class_Oabs(U_2802,U_2803),c_Groups_Oabs__class_Oabs(U_2802,U_2804)),c_Groups_Oabs__class_Oabs(U_2802,c_Groups_Ominus__class_Ominus(U_2802,U_2804,U_2803)))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2802) ),
inference(clausify,[status(thm)],[f_893_3]) ).
fof(f_894_1,plain,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w),
inference(fof_nnf,[status(thm)],[fact_diff__int__def__symmetric]) ).
fof(f_894_2,plain,
! [U_2806,U_2805] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2805,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2806)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2805,U_2806),
inference(variable_rename,[status(thm)],[f_894_1]) ).
fof(f_894_3,plain,
! [U_2805,U_2806] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2805,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2806)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2805,U_2806),
inference(definitional_conversion,[status(esa)],[f_894_2]) ).
cnf(f_894_4,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2805,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2806)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2805,U_2806),
inference(clausify,[status(thm)],[f_894_3]) ).
fof(f_895_1,plain,
! [V_w,V_z] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,V_w)),
inference(fof_nnf,[status(thm)],[fact_diff__int__def]) ).
fof(f_895_2,plain,
! [U_2808,U_2807] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2807,U_2808) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2807,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2808)),
inference(variable_rename,[status(thm)],[f_895_1]) ).
fof(f_895_3,plain,
! [U_2807,U_2808] : c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2807,U_2808) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2807,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2808)),
inference(definitional_conversion,[status(esa)],[f_895_2]) ).
cnf(f_895_4,plain,
c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2807,U_2808) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,U_2807,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint,U_2808)),
inference(clausify,[status(thm)],[f_895_3]) ).
fof(f_896_1,plain,
! [V_b,V_a,T_a] :
( c_Groups_Ouminus__class_Ouminus(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b)) = c_Groups_Ominus__class_Ominus(T_a,V_b,V_a)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__diff__eq]) ).
fof(f_896_2,plain,
! [U_2811,U_2810,U_2809] :
( c_Groups_Ouminus__class_Ouminus(U_2809,c_Groups_Ominus__class_Ominus(U_2809,U_2810,U_2811)) = c_Groups_Ominus__class_Ominus(U_2809,U_2811,U_2810)
| ~ class_Groups_Oab__group__add(U_2809) ),
inference(variable_rename,[status(thm)],[f_896_1]) ).
fof(f_896_3,plain,
! [U_2809,U_2810,U_2811] :
( c_Groups_Ouminus__class_Ouminus(U_2809,c_Groups_Ominus__class_Ominus(U_2809,U_2810,U_2811)) = c_Groups_Ominus__class_Ominus(U_2809,U_2811,U_2810)
| ~ class_Groups_Oab__group__add(U_2809) ),
inference(definitional_conversion,[status(esa)],[f_896_2]) ).
cnf(f_896_4,plain,
( c_Groups_Ouminus__class_Ouminus(U_2809,c_Groups_Ominus__class_Ominus(U_2809,U_2810,U_2811)) = c_Groups_Ominus__class_Ominus(U_2809,U_2811,U_2810)
| ~ class_Groups_Oab__group__add(U_2809) ),
inference(clausify,[status(thm)],[f_896_3]) ).
fof(f_897_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_897_2,plain,
! [U_2814,U_2813,U_2812] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2812,U_2813),c_RealVector_Onorm__class_Onorm(U_2812,U_2814)),c_RealVector_Onorm__class_Onorm(U_2812,c_Groups_Ominus__class_Ominus(U_2812,U_2813,U_2814)))
| ~ class_RealVector_Oreal__normed__vector(U_2812) ),
inference(variable_rename,[status(thm)],[f_897_1]) ).
fof(f_897_3,plain,
! [U_2812,U_2813,U_2814] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2812,U_2813),c_RealVector_Onorm__class_Onorm(U_2812,U_2814)),c_RealVector_Onorm__class_Onorm(U_2812,c_Groups_Ominus__class_Ominus(U_2812,U_2813,U_2814)))
| ~ class_RealVector_Oreal__normed__vector(U_2812) ),
inference(definitional_conversion,[status(esa)],[f_897_2]) ).
cnf(f_897_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_2812,U_2813),c_RealVector_Onorm__class_Onorm(U_2812,U_2814)),c_RealVector_Onorm__class_Onorm(U_2812,c_Groups_Ominus__class_Ominus(U_2812,U_2813,U_2814)))
| ~ class_RealVector_Oreal__normed__vector(U_2812) ),
inference(clausify,[status(thm)],[f_897_3]) ).
fof(f_898_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_898_2,plain,
! [U_2817,U_2816,U_2815] :
( c_Groups_Ominus__class_Ominus(U_2815,c_Groups_Oplus__class_Oplus(U_2815,U_2816,U_2817),U_2817) = U_2816
| ~ class_Groups_Ogroup__add(U_2815) ),
inference(variable_rename,[status(thm)],[f_898_1]) ).
fof(f_898_3,plain,
! [U_2816,U_2815,U_2817] :
( c_Groups_Ominus__class_Ominus(U_2815,c_Groups_Oplus__class_Oplus(U_2815,U_2816,U_2817),U_2817) = U_2816
| ~ class_Groups_Ogroup__add(U_2815) ),
inference(definitional_conversion,[status(esa)],[f_898_2]) ).
cnf(f_898_4,plain,
( c_Groups_Ominus__class_Ominus(U_2815,c_Groups_Oplus__class_Oplus(U_2815,U_2816,U_2817),U_2817) = U_2816
| ~ class_Groups_Ogroup__add(U_2815) ),
inference(clausify,[status(thm)],[f_898_3]) ).
fof(f_899_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_899_2,plain,
! [U_2820,U_2819,U_2818] :
( c_Groups_Oplus__class_Oplus(U_2818,c_Groups_Ominus__class_Ominus(U_2818,U_2819,U_2820),U_2820) = U_2819
| ~ class_Groups_Ogroup__add(U_2818) ),
inference(variable_rename,[status(thm)],[f_899_1]) ).
fof(f_899_3,plain,
! [U_2819,U_2818,U_2820] :
( c_Groups_Oplus__class_Oplus(U_2818,c_Groups_Ominus__class_Ominus(U_2818,U_2819,U_2820),U_2820) = U_2819
| ~ class_Groups_Ogroup__add(U_2818) ),
inference(definitional_conversion,[status(esa)],[f_899_2]) ).
cnf(f_899_4,plain,
( c_Groups_Oplus__class_Oplus(U_2818,c_Groups_Ominus__class_Ominus(U_2818,U_2819,U_2820),U_2820) = U_2819
| ~ class_Groups_Ogroup__add(U_2818) ),
inference(clausify,[status(thm)],[f_899_3]) ).
fof(f_900_1,plain,
! [V_d_2,V_ca_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_ca_2,V_d_2) )
& ( c_Orderings_Oord__class_Oless__eq(T_a,V_ca_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_ca_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_900_2,plain,
! [U_2825,U_2824,U_2823,U_2822,U_2821] :
( ( ( c_Orderings_Oord__class_Oless__eq(U_2821,U_2822,U_2823)
| ~ c_Orderings_Oord__class_Oless__eq(U_2821,U_2824,U_2825) )
& ( c_Orderings_Oord__class_Oless__eq(U_2821,U_2824,U_2825)
| ~ c_Orderings_Oord__class_Oless__eq(U_2821,U_2822,U_2823) ) )
| c_Groups_Ominus__class_Ominus(U_2821,U_2822,U_2823) != c_Groups_Ominus__class_Ominus(U_2821,U_2824,U_2825)
| ~ class_Groups_Oordered__ab__group__add(U_2821) ),
inference(variable_rename,[status(thm)],[f_900_1]) ).
fof(f_900_3,plain,
( ! [U_2822,U_2821,U_2823,U_2824,U_2825] :
( c_Orderings_Oord__class_Oless__eq(U_2821,U_2822,U_2823)
| ~ c_Orderings_Oord__class_Oless__eq(U_2821,U_2824,U_2825)
| ~ sP282(U_2822,U_2821,U_2823,U_2824,U_2825) )
& ! [U_2822,U_2821,U_2823,U_2824,U_2825] :
( c_Orderings_Oord__class_Oless__eq(U_2821,U_2824,U_2825)
| ~ c_Orderings_Oord__class_Oless__eq(U_2821,U_2822,U_2823)
| ~ sP282(U_2822,U_2821,U_2823,U_2824,U_2825) )
& ! [U_2822,U_2821,U_2823,U_2824,U_2825] :
( sP282(U_2822,U_2821,U_2823,U_2824,U_2825)
| c_Groups_Ominus__class_Ominus(U_2821,U_2822,U_2823) != c_Groups_Ominus__class_Ominus(U_2821,U_2824,U_2825)
| ~ class_Groups_Oordered__ab__group__add(U_2821) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP282])],[f_900_2]) ).
cnf(f_900_4,plain,
( sP282(U_2822,U_2821,U_2823,U_2824,U_2825)
| c_Groups_Ominus__class_Ominus(U_2821,U_2822,U_2823) != c_Groups_Ominus__class_Ominus(U_2821,U_2824,U_2825)
| ~ class_Groups_Oordered__ab__group__add(U_2821) ),
inference(clausify,[status(thm)],[f_900_3]) ).
cnf(f_900_5,plain,
( c_Orderings_Oord__class_Oless__eq(U_2821,U_2824,U_2825)
| ~ c_Orderings_Oord__class_Oless__eq(U_2821,U_2822,U_2823)
| ~ sP282(U_2822,U_2821,U_2823,U_2824,U_2825) ),
inference(clausify,[status(thm)],[f_900_3]) ).
cnf(f_900_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2821,U_2822,U_2823)
| ~ c_Orderings_Oord__class_Oless__eq(U_2821,U_2824,U_2825)
| ~ sP282(U_2822,U_2821,U_2823,U_2824,U_2825) ),
inference(clausify,[status(thm)],[f_900_3]) ).
fof(f_901_1,plain,
! [V_z,V_y,V_x,T_a] :
( c_Rings_Odvd__class_Odvd(T_a,V_x,c_Groups_Ominus__class_Ominus(T_a,V_y,V_z))
| ~ c_Rings_Odvd__class_Odvd(T_a,V_x,V_z)
| ~ c_Rings_Odvd__class_Odvd(T_a,V_x,V_y)
| ~ class_Rings_Ocomm__ring__1(T_a) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diff]) ).
fof(f_901_2,plain,
! [U_2829,U_2828,U_2827,U_2826] :
( c_Rings_Odvd__class_Odvd(U_2826,U_2827,c_Groups_Ominus__class_Ominus(U_2826,U_2828,U_2829))
| ~ c_Rings_Odvd__class_Odvd(U_2826,U_2827,U_2829)
| ~ c_Rings_Odvd__class_Odvd(U_2826,U_2827,U_2828)
| ~ class_Rings_Ocomm__ring__1(U_2826) ),
inference(variable_rename,[status(thm)],[f_901_1]) ).
fof(f_901_3,plain,
! [U_2828,U_2829,U_2827,U_2826] :
( c_Rings_Odvd__class_Odvd(U_2826,U_2827,c_Groups_Ominus__class_Ominus(U_2826,U_2828,U_2829))
| ~ c_Rings_Odvd__class_Odvd(U_2826,U_2827,U_2829)
| ~ c_Rings_Odvd__class_Odvd(U_2826,U_2827,U_2828)
| ~ class_Rings_Ocomm__ring__1(U_2826) ),
inference(definitional_conversion,[status(esa)],[f_901_2]) ).
cnf(f_901_4,plain,
( c_Rings_Odvd__class_Odvd(U_2826,U_2827,c_Groups_Ominus__class_Ominus(U_2826,U_2828,U_2829))
| ~ c_Rings_Odvd__class_Odvd(U_2826,U_2827,U_2829)
| ~ c_Rings_Odvd__class_Odvd(U_2826,U_2827,U_2828)
| ~ class_Rings_Ocomm__ring__1(U_2826) ),
inference(clausify,[status(thm)],[f_901_3]) ).
fof(f_902_1,plain,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_m)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,V_n)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,V_k,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_m,V_n)) ),
inference(fof_nnf,[status(thm)],[fact_zdvd__zdiffD]) ).
fof(f_902_2,plain,
! [U_2832,U_2831,U_2830] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,U_2831)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,U_2832)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2831,U_2832)) ),
inference(variable_rename,[status(thm)],[f_902_1]) ).
fof(f_902_3,plain,
! [U_2832,U_2831,U_2830] :
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,U_2831)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,U_2832)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2831,U_2832)) ),
inference(definitional_conversion,[status(esa)],[f_902_2]) ).
cnf(f_902_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,U_2831)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,U_2832)
| ~ c_Rings_Odvd__class_Odvd(tc_Int_Oint,U_2830,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2831,U_2832)) ),
inference(clausify,[status(thm)],[f_902_3]) ).
fof(f_903_1,plain,
! [V_l_2,V_k_2] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_k_2,V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_k_2,V_l_2) ) ),
inference(fof_nnf,[status(thm)],[fact_less__bin__lemma]) ).
fof(f_903_2,plain,
! [U_2834,U_2833] :
( ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2833,U_2834)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2833,U_2834),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2833,U_2834),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2833,U_2834) ) ),
inference(variable_rename,[status(thm)],[f_903_1]) ).
fof(f_903_3,plain,
( ! [U_2838,U_2836] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2836,U_2838)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2836,U_2838),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2837,U_2835] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2835,U_2837),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2835,U_2837) ) ),
inference(miniscope,[status(thm)],[f_903_2]) ).
fof(f_903_4,plain,
( ! [U_2838,U_2836] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2836,U_2838)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2836,U_2838),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) )
& ! [U_2835,U_2837] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2835,U_2837),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2835,U_2837) ) ),
inference(definitional_conversion,[status(esa)],[f_903_3]) ).
cnf(f_903_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2835,U_2837),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2835,U_2837) ),
inference(clausify,[status(thm)],[f_903_4]) ).
cnf(f_903_6,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2836,U_2838)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2836,U_2838),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ),
inference(clausify,[status(thm)],[f_903_4]) ).
fof(f_904_1,plain,
! [V_x_2,V_B_2,V_A_2,T_b,T_a] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,T_a),V_A_2,V_B_2),V_x_2) = c_Groups_Ominus__class_Ominus(T_a,hAPP(V_A_2,V_x_2),hAPP(V_B_2,V_x_2))
| ~ class_Groups_Ominus(T_a) ),
inference(fof_nnf,[status(thm)],[fact_minus__apply]) ).
fof(f_904_2,plain,
! [U_2843,U_2842,U_2841,U_2840,U_2839] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,U_2839),U_2841,U_2842),U_2843) = c_Groups_Ominus__class_Ominus(U_2839,hAPP(U_2841,U_2843),hAPP(U_2842,U_2843))
| ~ class_Groups_Ominus(U_2839) ),
inference(variable_rename,[status(thm)],[f_904_1]) ).
fof(f_904_3,plain,
! [U_2840,U_2839,U_2841,U_2842,U_2843] :
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,U_2839),U_2841,U_2842),U_2843) = c_Groups_Ominus__class_Ominus(U_2839,hAPP(U_2841,U_2843),hAPP(U_2842,U_2843))
| ~ class_Groups_Ominus(U_2839) ),
inference(definitional_conversion,[status(esa)],[f_904_2]) ).
cnf(f_904_4,plain,
( hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_2840,U_2839),U_2841,U_2842),U_2843) = c_Groups_Ominus__class_Ominus(U_2839,hAPP(U_2841,U_2843),hAPP(U_2842,U_2843))
| ~ class_Groups_Ominus(U_2839) ),
inference(clausify,[status(thm)],[f_904_3]) ).
fof(f_905_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_905_2,plain,
! [U_2846,U_2845,U_2844] :
( c_RealVector_Onorm__class_Onorm(U_2844,c_Groups_Ominus__class_Ominus(U_2844,U_2845,U_2846)) = c_RealVector_Onorm__class_Onorm(U_2844,c_Groups_Ominus__class_Ominus(U_2844,U_2846,U_2845))
| ~ class_RealVector_Oreal__normed__vector(U_2844) ),
inference(variable_rename,[status(thm)],[f_905_1]) ).
fof(f_905_3,plain,
! [U_2844,U_2845,U_2846] :
( c_RealVector_Onorm__class_Onorm(U_2844,c_Groups_Ominus__class_Ominus(U_2844,U_2845,U_2846)) = c_RealVector_Onorm__class_Onorm(U_2844,c_Groups_Ominus__class_Ominus(U_2844,U_2846,U_2845))
| ~ class_RealVector_Oreal__normed__vector(U_2844) ),
inference(definitional_conversion,[status(esa)],[f_905_2]) ).
cnf(f_905_4,plain,
( c_RealVector_Onorm__class_Onorm(U_2844,c_Groups_Ominus__class_Ominus(U_2844,U_2845,U_2846)) = c_RealVector_Onorm__class_Onorm(U_2844,c_Groups_Ominus__class_Ominus(U_2844,U_2846,U_2845))
| ~ class_RealVector_Oreal__normed__vector(U_2844) ),
inference(clausify,[status(thm)],[f_905_3]) ).
fof(f_906_1,plain,
! [V_x,V_q,V_p,T_a] :
( hAPP(c_Polynomial_Opoly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q)),V_x) = c_Groups_Ominus__class_Ominus(T_a,hAPP(c_Polynomial_Opoly(T_a,V_p),V_x),hAPP(c_Polynomial_Opoly(T_a,V_q),V_x))
| ~ class_Rings_Ocomm__ring(T_a) ),
inference(fof_nnf,[status(thm)],[fact_poly__diff]) ).
fof(f_906_2,plain,
! [U_2850,U_2849,U_2848,U_2847] :
( hAPP(c_Polynomial_Opoly(U_2847,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2847),U_2848,U_2849)),U_2850) = c_Groups_Ominus__class_Ominus(U_2847,hAPP(c_Polynomial_Opoly(U_2847,U_2848),U_2850),hAPP(c_Polynomial_Opoly(U_2847,U_2849),U_2850))
| ~ class_Rings_Ocomm__ring(U_2847) ),
inference(variable_rename,[status(thm)],[f_906_1]) ).
fof(f_906_3,plain,
! [U_2847,U_2848,U_2849,U_2850] :
( hAPP(c_Polynomial_Opoly(U_2847,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2847),U_2848,U_2849)),U_2850) = c_Groups_Ominus__class_Ominus(U_2847,hAPP(c_Polynomial_Opoly(U_2847,U_2848),U_2850),hAPP(c_Polynomial_Opoly(U_2847,U_2849),U_2850))
| ~ class_Rings_Ocomm__ring(U_2847) ),
inference(definitional_conversion,[status(esa)],[f_906_2]) ).
cnf(f_906_4,plain,
( hAPP(c_Polynomial_Opoly(U_2847,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2847),U_2848,U_2849)),U_2850) = c_Groups_Ominus__class_Ominus(U_2847,hAPP(c_Polynomial_Opoly(U_2847,U_2848),U_2850),hAPP(c_Polynomial_Opoly(U_2847,U_2849),U_2850))
| ~ class_Rings_Ocomm__ring(U_2847) ),
inference(clausify,[status(thm)],[f_906_3]) ).
fof(f_907_1,plain,
! [V_q,V_b,V_p,V_a,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Polynomial_OpCons(T_a,V_a,V_p),c_Polynomial_OpCons(T_a,V_b,V_q)) = c_Polynomial_OpCons(T_a,c_Groups_Ominus__class_Ominus(T_a,V_a,V_b),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,V_q))
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__pCons]) ).
fof(f_907_2,plain,
! [U_2855,U_2854,U_2853,U_2852,U_2851] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2851),c_Polynomial_OpCons(U_2851,U_2852,U_2853),c_Polynomial_OpCons(U_2851,U_2854,U_2855)) = c_Polynomial_OpCons(U_2851,c_Groups_Ominus__class_Ominus(U_2851,U_2852,U_2854),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2851),U_2853,U_2855))
| ~ class_Groups_Oab__group__add(U_2851) ),
inference(variable_rename,[status(thm)],[f_907_1]) ).
fof(f_907_3,plain,
! [U_2852,U_2851,U_2853,U_2854,U_2855] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2851),c_Polynomial_OpCons(U_2851,U_2852,U_2853),c_Polynomial_OpCons(U_2851,U_2854,U_2855)) = c_Polynomial_OpCons(U_2851,c_Groups_Ominus__class_Ominus(U_2851,U_2852,U_2854),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2851),U_2853,U_2855))
| ~ class_Groups_Oab__group__add(U_2851) ),
inference(definitional_conversion,[status(esa)],[f_907_2]) ).
cnf(f_907_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2851),c_Polynomial_OpCons(U_2851,U_2852,U_2853),c_Polynomial_OpCons(U_2851,U_2854,U_2855)) = c_Polynomial_OpCons(U_2851,c_Groups_Ominus__class_Ominus(U_2851,U_2852,U_2854),c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2851),U_2853,U_2855))
| ~ class_Groups_Oab__group__add(U_2851) ),
inference(clausify,[status(thm)],[f_907_3]) ).
fof(f_908_1,plain,
! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] :
( ( ( V_a_2 = V_b_2
| V_ca_2 != V_d_2 )
& ( V_ca_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_ca_2,V_d_2)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__eq]) ).
fof(f_908_2,plain,
! [U_2860,U_2859,U_2858,U_2857,U_2856] :
( ( ( U_2857 = U_2858
| U_2859 != U_2860 )
& ( U_2859 = U_2860
| U_2857 != U_2858 ) )
| c_Groups_Ominus__class_Ominus(U_2856,U_2857,U_2858) != c_Groups_Ominus__class_Ominus(U_2856,U_2859,U_2860)
| ~ class_Groups_Oab__group__add(U_2856) ),
inference(variable_rename,[status(thm)],[f_908_1]) ).
fof(f_908_3,plain,
( ! [U_2857,U_2859,U_2858,U_2860] :
( U_2857 = U_2858
| U_2859 != U_2860
| ~ sP283(U_2857,U_2859,U_2858,U_2860) )
& ! [U_2857,U_2859,U_2858,U_2860] :
( U_2859 = U_2860
| U_2857 != U_2858
| ~ sP283(U_2857,U_2859,U_2858,U_2860) )
& ! [U_2857,U_2859,U_2856,U_2858,U_2860] :
( sP283(U_2857,U_2859,U_2858,U_2860)
| c_Groups_Ominus__class_Ominus(U_2856,U_2857,U_2858) != c_Groups_Ominus__class_Ominus(U_2856,U_2859,U_2860)
| ~ class_Groups_Oab__group__add(U_2856) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP283])],[f_908_2]) ).
cnf(f_908_4,plain,
( sP283(U_2857,U_2859,U_2858,U_2860)
| c_Groups_Ominus__class_Ominus(U_2856,U_2857,U_2858) != c_Groups_Ominus__class_Ominus(U_2856,U_2859,U_2860)
| ~ class_Groups_Oab__group__add(U_2856) ),
inference(clausify,[status(thm)],[f_908_3]) ).
cnf(f_908_5,plain,
( U_2859 = U_2860
| U_2857 != U_2858
| ~ sP283(U_2857,U_2859,U_2858,U_2860) ),
inference(clausify,[status(thm)],[f_908_3]) ).
cnf(f_908_6,plain,
( U_2857 = U_2858
| U_2859 != U_2860
| ~ sP283(U_2857,U_2859,U_2858,U_2860) ),
inference(clausify,[status(thm)],[f_908_3]) ).
fof(f_909_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_909_2,plain,
! [U_2863,U_2862,U_2861] :
( ( ( c_Orderings_Oord__class_Oless(U_2861,U_2862,U_2863)
| ~ c_Orderings_Oord__class_Oless(U_2861,c_Groups_Ominus__class_Ominus(U_2861,U_2862,U_2863),c_Groups_Ozero__class_Ozero(U_2861)) )
& ( c_Orderings_Oord__class_Oless(U_2861,c_Groups_Ominus__class_Ominus(U_2861,U_2862,U_2863),c_Groups_Ozero__class_Ozero(U_2861))
| ~ c_Orderings_Oord__class_Oless(U_2861,U_2862,U_2863) ) )
| ~ class_Groups_Oordered__ab__group__add(U_2861) ),
inference(variable_rename,[status(thm)],[f_909_1]) ).
fof(f_909_3,plain,
( ! [U_2862,U_2861,U_2863] :
( c_Orderings_Oord__class_Oless(U_2861,U_2862,U_2863)
| ~ c_Orderings_Oord__class_Oless(U_2861,c_Groups_Ominus__class_Ominus(U_2861,U_2862,U_2863),c_Groups_Ozero__class_Ozero(U_2861))
| ~ sP284(U_2862,U_2861,U_2863) )
& ! [U_2862,U_2861,U_2863] :
( c_Orderings_Oord__class_Oless(U_2861,c_Groups_Ominus__class_Ominus(U_2861,U_2862,U_2863),c_Groups_Ozero__class_Ozero(U_2861))
| ~ c_Orderings_Oord__class_Oless(U_2861,U_2862,U_2863)
| ~ sP284(U_2862,U_2861,U_2863) )
& ! [U_2862,U_2861,U_2863] :
( sP284(U_2862,U_2861,U_2863)
| ~ class_Groups_Oordered__ab__group__add(U_2861) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284])],[f_909_2]) ).
cnf(f_909_4,plain,
( sP284(U_2862,U_2861,U_2863)
| ~ class_Groups_Oordered__ab__group__add(U_2861) ),
inference(clausify,[status(thm)],[f_909_3]) ).
cnf(f_909_5,plain,
( c_Orderings_Oord__class_Oless(U_2861,c_Groups_Ominus__class_Ominus(U_2861,U_2862,U_2863),c_Groups_Ozero__class_Ozero(U_2861))
| ~ c_Orderings_Oord__class_Oless(U_2861,U_2862,U_2863)
| ~ sP284(U_2862,U_2861,U_2863) ),
inference(clausify,[status(thm)],[f_909_3]) ).
cnf(f_909_6,plain,
( c_Orderings_Oord__class_Oless(U_2861,U_2862,U_2863)
| ~ c_Orderings_Oord__class_Oless(U_2861,c_Groups_Ominus__class_Ominus(U_2861,U_2862,U_2863),c_Groups_Ozero__class_Ozero(U_2861))
| ~ sP284(U_2862,U_2861,U_2863) ),
inference(clausify,[status(thm)],[f_909_3]) ).
fof(f_910_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_910_2,plain,
! [U_2866,U_2865,U_2864] :
( c_Groups_Oabs__class_Oabs(U_2864,c_Groups_Ominus__class_Ominus(U_2864,U_2865,U_2866)) = c_Groups_Oabs__class_Oabs(U_2864,c_Groups_Ominus__class_Ominus(U_2864,U_2866,U_2865))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2864) ),
inference(variable_rename,[status(thm)],[f_910_1]) ).
fof(f_910_3,plain,
! [U_2866,U_2865,U_2864] :
( c_Groups_Oabs__class_Oabs(U_2864,c_Groups_Ominus__class_Ominus(U_2864,U_2865,U_2866)) = c_Groups_Oabs__class_Oabs(U_2864,c_Groups_Ominus__class_Ominus(U_2864,U_2866,U_2865))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2864) ),
inference(definitional_conversion,[status(esa)],[f_910_2]) ).
cnf(f_910_4,plain,
( c_Groups_Oabs__class_Oabs(U_2864,c_Groups_Ominus__class_Ominus(U_2864,U_2865,U_2866)) = c_Groups_Oabs__class_Oabs(U_2864,c_Groups_Ominus__class_Ominus(U_2864,U_2866,U_2865))
| ~ class_Groups_Oordered__ab__group__add__abs(U_2864) ),
inference(clausify,[status(thm)],[f_910_3]) ).
fof(f_911_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_911_2,plain,
! [U_2870,U_2869,U_2868,U_2867] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2867),U_2868),c_Groups_Ominus__class_Ominus(U_2867,U_2869,U_2870)) = c_Groups_Ominus__class_Ominus(U_2867,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2867),U_2868),U_2869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2867),U_2868),U_2870))
| ~ class_RealVector_Oreal__normed__algebra(U_2867) ),
inference(variable_rename,[status(thm)],[f_911_1]) ).
fof(f_911_3,plain,
! [U_2867,U_2868,U_2869,U_2870] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2867),U_2868),c_Groups_Ominus__class_Ominus(U_2867,U_2869,U_2870)) = c_Groups_Ominus__class_Ominus(U_2867,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2867),U_2868),U_2869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2867),U_2868),U_2870))
| ~ class_RealVector_Oreal__normed__algebra(U_2867) ),
inference(definitional_conversion,[status(esa)],[f_911_2]) ).
cnf(f_911_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2867),U_2868),c_Groups_Ominus__class_Ominus(U_2867,U_2869,U_2870)) = c_Groups_Ominus__class_Ominus(U_2867,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2867),U_2868),U_2869),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2867),U_2868),U_2870))
| ~ class_RealVector_Oreal__normed__algebra(U_2867) ),
inference(clausify,[status(thm)],[f_911_3]) ).
fof(f_912_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_912_2,plain,
! [U_2874,U_2873,U_2872,U_2871] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2871),U_2872),c_Groups_Ominus__class_Ominus(U_2871,U_2873,U_2874)) = c_Groups_Ominus__class_Ominus(U_2871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2871),U_2872),U_2873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2871),U_2872),U_2874))
| ~ class_RealVector_Oreal__normed__algebra(U_2871) ),
inference(variable_rename,[status(thm)],[f_912_1]) ).
fof(f_912_3,plain,
! [U_2871,U_2872,U_2873,U_2874] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2871),U_2872),c_Groups_Ominus__class_Ominus(U_2871,U_2873,U_2874)) = c_Groups_Ominus__class_Ominus(U_2871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2871),U_2872),U_2873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2871),U_2872),U_2874))
| ~ class_RealVector_Oreal__normed__algebra(U_2871) ),
inference(definitional_conversion,[status(esa)],[f_912_2]) ).
cnf(f_912_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2871),U_2872),c_Groups_Ominus__class_Ominus(U_2871,U_2873,U_2874)) = c_Groups_Ominus__class_Ominus(U_2871,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2871),U_2872),U_2873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2871),U_2872),U_2874))
| ~ class_RealVector_Oreal__normed__algebra(U_2871) ),
inference(clausify,[status(thm)],[f_912_3]) ).
fof(f_913_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_913_2,plain,
! [U_2878,U_2877,U_2876,U_2875] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2875),c_Groups_Ominus__class_Ominus(U_2875,U_2876,U_2877)),U_2878) = c_Groups_Ominus__class_Ominus(U_2875,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2875),U_2876),U_2878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2875),U_2877),U_2878))
| ~ class_RealVector_Oreal__normed__algebra(U_2875) ),
inference(variable_rename,[status(thm)],[f_913_1]) ).
fof(f_913_3,plain,
! [U_2875,U_2876,U_2877,U_2878] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2875),c_Groups_Ominus__class_Ominus(U_2875,U_2876,U_2877)),U_2878) = c_Groups_Ominus__class_Ominus(U_2875,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2875),U_2876),U_2878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2875),U_2877),U_2878))
| ~ class_RealVector_Oreal__normed__algebra(U_2875) ),
inference(definitional_conversion,[status(esa)],[f_913_2]) ).
cnf(f_913_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2875),c_Groups_Ominus__class_Ominus(U_2875,U_2876,U_2877)),U_2878) = c_Groups_Ominus__class_Ominus(U_2875,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2875),U_2876),U_2878),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2875),U_2877),U_2878))
| ~ class_RealVector_Oreal__normed__algebra(U_2875) ),
inference(clausify,[status(thm)],[f_913_3]) ).
fof(f_914_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_914_2,plain,
! [U_2882,U_2881,U_2880,U_2879] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2879),c_Groups_Ominus__class_Ominus(U_2879,U_2880,U_2881)),U_2882) = c_Groups_Ominus__class_Ominus(U_2879,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2879),U_2880),U_2882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2879),U_2881),U_2882))
| ~ class_RealVector_Oreal__normed__algebra(U_2879) ),
inference(variable_rename,[status(thm)],[f_914_1]) ).
fof(f_914_3,plain,
! [U_2879,U_2880,U_2881,U_2882] :
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2879),c_Groups_Ominus__class_Ominus(U_2879,U_2880,U_2881)),U_2882) = c_Groups_Ominus__class_Ominus(U_2879,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2879),U_2880),U_2882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2879),U_2881),U_2882))
| ~ class_RealVector_Oreal__normed__algebra(U_2879) ),
inference(definitional_conversion,[status(esa)],[f_914_2]) ).
cnf(f_914_4,plain,
( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2879),c_Groups_Ominus__class_Ominus(U_2879,U_2880,U_2881)),U_2882) = c_Groups_Ominus__class_Ominus(U_2879,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2879),U_2880),U_2882),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2879),U_2881),U_2882))
| ~ class_RealVector_Oreal__normed__algebra(U_2879) ),
inference(clausify,[status(thm)],[f_914_3]) ).
fof(f_915_1,plain,
! [V_d_2,V_ca_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_ca_2,V_d_2) )
& ( c_Orderings_Oord__class_Oless(T_a,V_ca_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_ca_2,V_d_2)
| ~ class_Groups_Oordered__ab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__eq__diff__less]) ).
fof(f_915_2,plain,
! [U_2887,U_2886,U_2885,U_2884,U_2883] :
( ( ( c_Orderings_Oord__class_Oless(U_2883,U_2884,U_2885)
| ~ c_Orderings_Oord__class_Oless(U_2883,U_2886,U_2887) )
& ( c_Orderings_Oord__class_Oless(U_2883,U_2886,U_2887)
| ~ c_Orderings_Oord__class_Oless(U_2883,U_2884,U_2885) ) )
| c_Groups_Ominus__class_Ominus(U_2883,U_2884,U_2885) != c_Groups_Ominus__class_Ominus(U_2883,U_2886,U_2887)
| ~ class_Groups_Oordered__ab__group__add(U_2883) ),
inference(variable_rename,[status(thm)],[f_915_1]) ).
fof(f_915_3,plain,
( ! [U_2885,U_2884,U_2883,U_2886,U_2887] :
( c_Orderings_Oord__class_Oless(U_2883,U_2884,U_2885)
| ~ c_Orderings_Oord__class_Oless(U_2883,U_2886,U_2887)
| ~ sP285(U_2885,U_2884,U_2883,U_2886,U_2887) )
& ! [U_2885,U_2884,U_2883,U_2886,U_2887] :
( c_Orderings_Oord__class_Oless(U_2883,U_2886,U_2887)
| ~ c_Orderings_Oord__class_Oless(U_2883,U_2884,U_2885)
| ~ sP285(U_2885,U_2884,U_2883,U_2886,U_2887) )
& ! [U_2885,U_2884,U_2883,U_2886,U_2887] :
( sP285(U_2885,U_2884,U_2883,U_2886,U_2887)
| c_Groups_Ominus__class_Ominus(U_2883,U_2884,U_2885) != c_Groups_Ominus__class_Ominus(U_2883,U_2886,U_2887)
| ~ class_Groups_Oordered__ab__group__add(U_2883) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP285])],[f_915_2]) ).
cnf(f_915_4,plain,
( sP285(U_2885,U_2884,U_2883,U_2886,U_2887)
| c_Groups_Ominus__class_Ominus(U_2883,U_2884,U_2885) != c_Groups_Ominus__class_Ominus(U_2883,U_2886,U_2887)
| ~ class_Groups_Oordered__ab__group__add(U_2883) ),
inference(clausify,[status(thm)],[f_915_3]) ).
cnf(f_915_5,plain,
( c_Orderings_Oord__class_Oless(U_2883,U_2886,U_2887)
| ~ c_Orderings_Oord__class_Oless(U_2883,U_2884,U_2885)
| ~ sP285(U_2885,U_2884,U_2883,U_2886,U_2887) ),
inference(clausify,[status(thm)],[f_915_3]) ).
cnf(f_915_6,plain,
( c_Orderings_Oord__class_Oless(U_2883,U_2884,U_2885)
| ~ c_Orderings_Oord__class_Oless(U_2883,U_2886,U_2887)
| ~ sP285(U_2885,U_2884,U_2883,U_2886,U_2887) ),
inference(clausify,[status(thm)],[f_915_3]) ).
fof(f_916_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_916_2,plain,
! [U_2889,U_2888] :
( c_Groups_Ominus__class_Ominus(U_2888,U_2889,c_Groups_Ozero__class_Ozero(U_2888)) = U_2889
| ~ class_Groups_Ogroup__add(U_2888) ),
inference(variable_rename,[status(thm)],[f_916_1]) ).
fof(f_916_3,plain,
! [U_2888,U_2889] :
( c_Groups_Ominus__class_Ominus(U_2888,U_2889,c_Groups_Ozero__class_Ozero(U_2888)) = U_2889
| ~ class_Groups_Ogroup__add(U_2888) ),
inference(definitional_conversion,[status(esa)],[f_916_2]) ).
cnf(f_916_4,plain,
( c_Groups_Ominus__class_Ominus(U_2888,U_2889,c_Groups_Ozero__class_Ozero(U_2888)) = U_2889
| ~ class_Groups_Ogroup__add(U_2888) ),
inference(clausify,[status(thm)],[f_916_3]) ).
fof(f_917_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_917_2,plain,
! [U_2891,U_2890] :
( c_Groups_Ominus__class_Ominus(U_2890,U_2891,U_2891) = c_Groups_Ozero__class_Ozero(U_2890)
| ~ class_Groups_Ogroup__add(U_2890) ),
inference(variable_rename,[status(thm)],[f_917_1]) ).
fof(f_917_3,plain,
! [U_2890,U_2891] :
( c_Groups_Ominus__class_Ominus(U_2890,U_2891,U_2891) = c_Groups_Ozero__class_Ozero(U_2890)
| ~ class_Groups_Ogroup__add(U_2890) ),
inference(definitional_conversion,[status(esa)],[f_917_2]) ).
cnf(f_917_4,plain,
( c_Groups_Ominus__class_Ominus(U_2890,U_2891,U_2891) = c_Groups_Ozero__class_Ozero(U_2890)
| ~ class_Groups_Ogroup__add(U_2890) ),
inference(clausify,[status(thm)],[f_917_3]) ).
fof(f_918_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_918_2,plain,
! [U_2894,U_2893,U_2892] :
( ( ( U_2893 = U_2894
| c_Groups_Ominus__class_Ominus(U_2892,U_2893,U_2894) != c_Groups_Ozero__class_Ozero(U_2892) )
& ( c_Groups_Ominus__class_Ominus(U_2892,U_2893,U_2894) = c_Groups_Ozero__class_Ozero(U_2892)
| U_2893 != U_2894 ) )
| ~ class_Groups_Oab__group__add(U_2892) ),
inference(variable_rename,[status(thm)],[f_918_1]) ).
fof(f_918_3,plain,
( ! [U_2894,U_2892,U_2893] :
( U_2893 = U_2894
| c_Groups_Ominus__class_Ominus(U_2892,U_2893,U_2894) != c_Groups_Ozero__class_Ozero(U_2892)
| ~ sP286(U_2894,U_2892,U_2893) )
& ! [U_2894,U_2892,U_2893] :
( c_Groups_Ominus__class_Ominus(U_2892,U_2893,U_2894) = c_Groups_Ozero__class_Ozero(U_2892)
| U_2893 != U_2894
| ~ sP286(U_2894,U_2892,U_2893) )
& ! [U_2894,U_2892,U_2893] :
( sP286(U_2894,U_2892,U_2893)
| ~ class_Groups_Oab__group__add(U_2892) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286])],[f_918_2]) ).
cnf(f_918_4,plain,
( sP286(U_2894,U_2892,U_2893)
| ~ class_Groups_Oab__group__add(U_2892) ),
inference(clausify,[status(thm)],[f_918_3]) ).
cnf(f_918_5,plain,
( c_Groups_Ominus__class_Ominus(U_2892,U_2893,U_2894) = c_Groups_Ozero__class_Ozero(U_2892)
| U_2893 != U_2894
| ~ sP286(U_2894,U_2892,U_2893) ),
inference(clausify,[status(thm)],[f_918_3]) ).
cnf(f_918_6,plain,
( U_2893 = U_2894
| c_Groups_Ominus__class_Ominus(U_2892,U_2893,U_2894) != c_Groups_Ozero__class_Ozero(U_2892)
| ~ sP286(U_2894,U_2892,U_2893) ),
inference(clausify,[status(thm)],[f_918_3]) ).
fof(f_919_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_919_2,plain,
! [U_2897,U_2896,U_2895] :
( ( ( c_Groups_Ominus__class_Ominus(U_2895,U_2896,U_2897) = c_Groups_Ozero__class_Ozero(U_2895)
| U_2896 != U_2897 )
& ( U_2896 = U_2897
| c_Groups_Ominus__class_Ominus(U_2895,U_2896,U_2897) != c_Groups_Ozero__class_Ozero(U_2895) ) )
| ~ class_Groups_Ogroup__add(U_2895) ),
inference(variable_rename,[status(thm)],[f_919_1]) ).
fof(f_919_3,plain,
( ! [U_2896,U_2897,U_2895] :
( c_Groups_Ominus__class_Ominus(U_2895,U_2896,U_2897) = c_Groups_Ozero__class_Ozero(U_2895)
| U_2896 != U_2897
| ~ sP287(U_2896,U_2897,U_2895) )
& ! [U_2896,U_2897,U_2895] :
( U_2896 = U_2897
| c_Groups_Ominus__class_Ominus(U_2895,U_2896,U_2897) != c_Groups_Ozero__class_Ozero(U_2895)
| ~ sP287(U_2896,U_2897,U_2895) )
& ! [U_2896,U_2897,U_2895] :
( sP287(U_2896,U_2897,U_2895)
| ~ class_Groups_Ogroup__add(U_2895) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP287])],[f_919_2]) ).
cnf(f_919_4,plain,
( sP287(U_2896,U_2897,U_2895)
| ~ class_Groups_Ogroup__add(U_2895) ),
inference(clausify,[status(thm)],[f_919_3]) ).
cnf(f_919_5,plain,
( U_2896 = U_2897
| c_Groups_Ominus__class_Ominus(U_2895,U_2896,U_2897) != c_Groups_Ozero__class_Ozero(U_2895)
| ~ sP287(U_2896,U_2897,U_2895) ),
inference(clausify,[status(thm)],[f_919_3]) ).
cnf(f_919_6,plain,
( c_Groups_Ominus__class_Ominus(U_2895,U_2896,U_2897) = c_Groups_Ozero__class_Ozero(U_2895)
| U_2896 != U_2897
| ~ sP287(U_2896,U_2897,U_2895) ),
inference(clausify,[status(thm)],[f_919_3]) ).
fof(f_920_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_920_2,plain,
! [U_2900,U_2899,U_2898] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2898),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2899,U_2900)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2898),U_2899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2898),U_2900)),
inference(variable_rename,[status(thm)],[f_920_1]) ).
fof(f_920_3,plain,
! [U_2900,U_2899,U_2898] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2898),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2899,U_2900)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2898),U_2899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2898),U_2900)),
inference(definitional_conversion,[status(esa)],[f_920_2]) ).
cnf(f_920_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2898),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2899,U_2900)) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2898),U_2899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2898),U_2900)),
inference(clausify,[status(thm)],[f_920_3]) ).
fof(f_921_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_921_2,plain,
! [U_2903,U_2902,U_2901] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2901,U_2902)),U_2903) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2901),U_2903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2902),U_2903)),
inference(variable_rename,[status(thm)],[f_921_1]) ).
fof(f_921_3,plain,
! [U_2901,U_2902,U_2903] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2901,U_2902)),U_2903) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2901),U_2903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2902),U_2903)),
inference(definitional_conversion,[status(esa)],[f_921_2]) ).
cnf(f_921_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2901,U_2902)),U_2903) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2901),U_2903),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2902),U_2903)),
inference(clausify,[status(thm)],[f_921_3]) ).
fof(f_922_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_922_2,plain,
! [U_2906,U_2905,U_2904] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2904,c_Groups_Ominus__class_Ominus(U_2904,U_2905,U_2906)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2904,U_2905),c_RealVector_Onorm__class_Onorm(U_2904,U_2906)))
| ~ class_RealVector_Oreal__normed__vector(U_2904) ),
inference(variable_rename,[status(thm)],[f_922_1]) ).
fof(f_922_3,plain,
! [U_2904,U_2905,U_2906] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2904,c_Groups_Ominus__class_Ominus(U_2904,U_2905,U_2906)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2904,U_2905),c_RealVector_Onorm__class_Onorm(U_2904,U_2906)))
| ~ class_RealVector_Oreal__normed__vector(U_2904) ),
inference(definitional_conversion,[status(esa)],[f_922_2]) ).
cnf(f_922_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2904,c_Groups_Ominus__class_Ominus(U_2904,U_2905,U_2906)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2904,U_2905),c_RealVector_Onorm__class_Onorm(U_2904,U_2906)))
| ~ class_RealVector_Oreal__normed__vector(U_2904) ),
inference(clausify,[status(thm)],[f_922_3]) ).
fof(f_923_1,plain,
! [V_z_2,V_w_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,V_w_2,V_z_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_w_2,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_z_2,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(fof_nnf,[status(thm)],[fact_zle__diff1__eq]) ).
fof(f_923_2,plain,
! [U_2908,U_2907] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2907,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2908,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2907,U_2908) )
& ( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2907,U_2908)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2907,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2908,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(variable_rename,[status(thm)],[f_923_1]) ).
fof(f_923_3,plain,
( ! [U_2912,U_2910] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2910,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2912,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2910,U_2912) )
& ! [U_2911,U_2909] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2909,U_2911)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2909,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2911,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(miniscope,[status(thm)],[f_923_2]) ).
fof(f_923_4,plain,
( ! [U_2912,U_2910] :
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2910,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2912,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2910,U_2912) )
& ! [U_2909,U_2911] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2909,U_2911)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2909,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2911,c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
inference(definitional_conversion,[status(esa)],[f_923_3]) ).
cnf(f_923_5,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2909,U_2911)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2909,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2911,c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
inference(clausify,[status(thm)],[f_923_4]) ).
cnf(f_923_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2910,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2912,c_Groups_Oone__class_Oone(tc_Int_Oint)))
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,U_2910,U_2912) ),
inference(clausify,[status(thm)],[f_923_4]) ).
fof(f_924_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_924_2,plain,
! [U_2917,U_2916,U_2915,U_2914,U_2913] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2913,c_Groups_Ominus__class_Ominus(U_2913,c_Groups_Oplus__class_Oplus(U_2913,U_2914,U_2915),c_Groups_Oplus__class_Oplus(U_2913,U_2916,U_2917))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2913,c_Groups_Ominus__class_Ominus(U_2913,U_2914,U_2916)),c_RealVector_Onorm__class_Onorm(U_2913,c_Groups_Ominus__class_Ominus(U_2913,U_2915,U_2917))))
| ~ class_RealVector_Oreal__normed__vector(U_2913) ),
inference(variable_rename,[status(thm)],[f_924_1]) ).
fof(f_924_3,plain,
! [U_2915,U_2913,U_2914,U_2916,U_2917] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2913,c_Groups_Ominus__class_Ominus(U_2913,c_Groups_Oplus__class_Oplus(U_2913,U_2914,U_2915),c_Groups_Oplus__class_Oplus(U_2913,U_2916,U_2917))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2913,c_Groups_Ominus__class_Ominus(U_2913,U_2914,U_2916)),c_RealVector_Onorm__class_Onorm(U_2913,c_Groups_Ominus__class_Ominus(U_2913,U_2915,U_2917))))
| ~ class_RealVector_Oreal__normed__vector(U_2913) ),
inference(definitional_conversion,[status(esa)],[f_924_2]) ).
cnf(f_924_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2913,c_Groups_Ominus__class_Ominus(U_2913,c_Groups_Oplus__class_Oplus(U_2913,U_2914,U_2915),c_Groups_Oplus__class_Oplus(U_2913,U_2916,U_2917))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2913,c_Groups_Ominus__class_Ominus(U_2913,U_2914,U_2916)),c_RealVector_Onorm__class_Onorm(U_2913,c_Groups_Ominus__class_Ominus(U_2913,U_2915,U_2917))))
| ~ class_RealVector_Oreal__normed__vector(U_2913) ),
inference(clausify,[status(thm)],[f_924_3]) ).
fof(f_925_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_925_2,plain,
! [U_2920,U_2919,U_2918] :
( c_Groups_Ominus__class_Ominus(U_2918,hAPP(hAPP(c_Power_Opower__class_Opower(U_2918),U_2919),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2918),U_2920),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2918),c_Groups_Ominus__class_Ominus(U_2918,U_2919,U_2920)),c_Groups_Oplus__class_Oplus(U_2918,U_2919,U_2920))
| ~ class_Rings_Ocomm__ring__1(U_2918) ),
inference(variable_rename,[status(thm)],[f_925_1]) ).
fof(f_925_3,plain,
! [U_2918,U_2919,U_2920] :
( c_Groups_Ominus__class_Ominus(U_2918,hAPP(hAPP(c_Power_Opower__class_Opower(U_2918),U_2919),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2918),U_2920),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2918),c_Groups_Ominus__class_Ominus(U_2918,U_2919,U_2920)),c_Groups_Oplus__class_Oplus(U_2918,U_2919,U_2920))
| ~ class_Rings_Ocomm__ring__1(U_2918) ),
inference(definitional_conversion,[status(esa)],[f_925_2]) ).
cnf(f_925_4,plain,
( c_Groups_Ominus__class_Ominus(U_2918,hAPP(hAPP(c_Power_Opower__class_Opower(U_2918),U_2919),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(hAPP(c_Power_Opower__class_Opower(U_2918),U_2920),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2918),c_Groups_Ominus__class_Ominus(U_2918,U_2919,U_2920)),c_Groups_Oplus__class_Oplus(U_2918,U_2919,U_2920))
| ~ class_Rings_Ocomm__ring__1(U_2918) ),
inference(clausify,[status(thm)],[f_925_3]) ).
fof(f_926_1,plain,
! [V_z,V_x,V_d] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_z)),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_d)),V_z)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_d) ),
inference(fof_nnf,[status(thm)],[fact_decr__lemma]) ).
fof(f_926_2,plain,
! [U_2923,U_2922,U_2921] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2922,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2922,U_2923)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2921)),U_2923)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2921) ),
inference(variable_rename,[status(thm)],[f_926_1]) ).
fof(f_926_3,plain,
! [U_2921,U_2922,U_2923] :
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2922,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2922,U_2923)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2921)),U_2923)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2921) ),
inference(definitional_conversion,[status(esa)],[f_926_2]) ).
cnf(f_926_4,plain,
( c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2922,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oabs__class_Oabs(tc_Int_Oint,c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2922,U_2923)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2921)),U_2923)
| ~ c_Orderings_Oord__class_Oless(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2921) ),
inference(clausify,[status(thm)],[f_926_3]) ).
fof(f_927_1,plain,
! [V_X_2,V_M_2,T_a,T_b] :
( ! [B_n] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,B_n)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(T_b,hAPP(V_X_2,V_M_2))))
| ~ c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) )
| ? [B_n] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(T_b,c_Groups_Ominus__class_Ominus(T_b,hAPP(V_X_2,V_M_2),hAPP(V_X_2,B_n))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless__eq(T_a,V_M_2,B_n) )
| ~ class_Orderings_Oord(T_a)
| ~ class_RealVector_Oreal__normed__vector(T_b) ),
inference(fof_nnf,[status(thm)],[fact_lemmaCauchy]) ).
fof(f_927_2,plain,
! [U_2929,U_2928,U_2927,U_2926] :
( ! [U_2925] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2926,hAPP(U_2929,U_2925)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2926,hAPP(U_2929,U_2928))))
| ~ c_Orderings_Oord__class_Oless__eq(U_2927,U_2928,U_2925) )
| ? [U_2924] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2926,c_Groups_Ominus__class_Ominus(U_2926,hAPP(U_2929,U_2928),hAPP(U_2929,U_2924))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless__eq(U_2927,U_2928,U_2924) )
| ~ class_Orderings_Oord(U_2927)
| ~ class_RealVector_Oreal__normed__vector(U_2926) ),
inference(variable_rename,[status(thm)],[f_927_1]) ).
fof(f_927_3,plain,
! [U_2929,U_2928,U_2927,U_2926] :
( ! [U_2925] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2926,hAPP(U_2929,U_2925)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2926,hAPP(U_2929,U_2928))))
| ~ c_Orderings_Oord__class_Oless__eq(U_2927,U_2928,U_2925) )
| ( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2926,c_Groups_Ominus__class_Ominus(U_2926,hAPP(U_2929,U_2928),hAPP(U_2929,sK49(U_2929,U_2928,U_2927,U_2926)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
& c_Orderings_Oord__class_Oless__eq(U_2927,U_2928,sK49(U_2929,U_2928,U_2927,U_2926)) )
| ~ class_Orderings_Oord(U_2927)
| ~ class_RealVector_Oreal__normed__vector(U_2926) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_2924,sK49(U_2929,U_2928,U_2927,U_2926))],[f_927_2]) ).
fof(f_927_4,plain,
( ! [U_2926,U_2927,U_2928,U_2929] :
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2926,c_Groups_Ominus__class_Ominus(U_2926,hAPP(U_2929,U_2928),hAPP(U_2929,sK49(U_2929,U_2928,U_2927,U_2926)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ sP288(U_2926,U_2927,U_2928,U_2929) )
& ! [U_2926,U_2927,U_2928,U_2929] :
( c_Orderings_Oord__class_Oless__eq(U_2927,U_2928,sK49(U_2929,U_2928,U_2927,U_2926))
| ~ sP288(U_2926,U_2927,U_2928,U_2929) )
& ! [U_2925,U_2926,U_2927,U_2928,U_2929] :
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2926,hAPP(U_2929,U_2925)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2926,hAPP(U_2929,U_2928))))
| ~ c_Orderings_Oord__class_Oless__eq(U_2927,U_2928,U_2925)
| sP288(U_2926,U_2927,U_2928,U_2929)
| ~ class_Orderings_Oord(U_2927)
| ~ class_RealVector_Oreal__normed__vector(U_2926) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP288])],[f_927_3]) ).
cnf(f_927_5,plain,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2926,hAPP(U_2929,U_2925)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(U_2926,hAPP(U_2929,U_2928))))
| ~ c_Orderings_Oord__class_Oless__eq(U_2927,U_2928,U_2925)
| sP288(U_2926,U_2927,U_2928,U_2929)
| ~ class_Orderings_Oord(U_2927)
| ~ class_RealVector_Oreal__normed__vector(U_2926) ),
inference(clausify,[status(thm)],[f_927_4]) ).
cnf(f_927_6,plain,
( c_Orderings_Oord__class_Oless__eq(U_2927,U_2928,sK49(U_2929,U_2928,U_2927,U_2926))
| ~ sP288(U_2926,U_2927,U_2928,U_2929) ),
inference(clausify,[status(thm)],[f_927_4]) ).
cnf(f_927_7,plain,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_2926,c_Groups_Ominus__class_Ominus(U_2926,hAPP(U_2929,U_2928),hAPP(U_2929,sK49(U_2929,U_2928,U_2927,U_2926)))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal))
| ~ sP288(U_2926,U_2927,U_2928,U_2929) ),
inference(clausify,[status(thm)],[f_927_4]) ).
fof(f_928_1,plain,
! [V_x,V_y] :
( ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) )
& ( c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,V_x,V_y)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,V_y,V_x) ) ),
inference(fof_nnf,[status(thm)],[fact_tsub__def]) ).
fof(f_928_2,plain,
! [U_2931,U_2930] :
( ( c_Nat__Transfer_Otsub(U_2931,U_2930) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2930,U_2931) )
& ( c_Nat__Transfer_Otsub(U_2931,U_2930) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2931,U_2930)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2930,U_2931) ) ),
inference(variable_rename,[status(thm)],[f_928_1]) ).
fof(f_928_3,plain,
( ! [U_2935,U_2933] :
( c_Nat__Transfer_Otsub(U_2935,U_2933) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2933,U_2935) )
& ! [U_2934,U_2932] :
( c_Nat__Transfer_Otsub(U_2934,U_2932) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2934,U_2932)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2932,U_2934) ) ),
inference(miniscope,[status(thm)],[f_928_2]) ).
fof(f_928_4,plain,
( ! [U_2935,U_2933] :
( c_Nat__Transfer_Otsub(U_2935,U_2933) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2933,U_2935) )
& ! [U_2934,U_2932] :
( c_Nat__Transfer_Otsub(U_2934,U_2932) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2934,U_2932)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2932,U_2934) ) ),
inference(definitional_conversion,[status(esa)],[f_928_3]) ).
cnf(f_928_5,plain,
( c_Nat__Transfer_Otsub(U_2934,U_2932) = c_Groups_Ominus__class_Ominus(tc_Int_Oint,U_2934,U_2932)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2932,U_2934) ),
inference(clausify,[status(thm)],[f_928_4]) ).
cnf(f_928_6,plain,
( c_Nat__Transfer_Otsub(U_2935,U_2933) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
| c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,U_2933,U_2935) ),
inference(clausify,[status(thm)],[f_928_4]) ).
fof(f_929_1,plain,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,V_x,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,V_y)),
inference(fof_nnf,[status(thm)],[fact_complex__diff__def]) ).
fof(f_929_2,plain,
! [U_2937,U_2936] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2936,U_2937) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2936,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2937)),
inference(variable_rename,[status(thm)],[f_929_1]) ).
fof(f_929_3,plain,
! [U_2936,U_2937] : c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2936,U_2937) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2936,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2937)),
inference(definitional_conversion,[status(esa)],[f_929_2]) ).
cnf(f_929_4,plain,
c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,U_2936,U_2937) = c_Groups_Oplus__class_Oplus(tc_Complex_Ocomplex,U_2936,c_Groups_Ouminus__class_Ouminus(tc_Complex_Ocomplex,U_2937)),
inference(clausify,[status(thm)],[f_929_3]) ).
fof(f_930_1,plain,
! [V_y_2,V_x_2,T_a] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2)
| ( ~ c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
& V_x_2 != V_y_2 ) )
& ( c_Polynomial_Opos__poly(T_a,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_y_2,V_x_2))
| V_x_2 = V_y_2
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(T_a),V_x_2,V_y_2) ) )
| ~ class_Rings_Olinordered__idom(T_a) ),
inference(fof_nnf,[status(thm)],[fact_less__eq__poly__def]) ).
fof(f_930_2,plain,
! [U_2940,U_2939,U_2938] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2938),U_2939,U_2940)
| ( ~ c_Polynomial_Opos__poly(U_2938,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2938),U_2940,U_2939))
& U_2939 != U_2940 ) )
& ( c_Polynomial_Opos__poly(U_2938,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2938),U_2940,U_2939))
| U_2939 = U_2940
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2938),U_2939,U_2940) ) )
| ~ class_Rings_Olinordered__idom(U_2938) ),
inference(variable_rename,[status(thm)],[f_930_1]) ).
fof(f_930_3,plain,
( ! [U_2938,U_2939,U_2940] :
( ~ c_Polynomial_Opos__poly(U_2938,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2938),U_2940,U_2939))
| ~ sP289(U_2938,U_2939,U_2940) )
& ! [U_2938,U_2939,U_2940] :
( U_2939 != U_2940
| ~ sP289(U_2938,U_2939,U_2940) )
& ! [U_2938,U_2939,U_2940] :
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2938),U_2939,U_2940)
| sP289(U_2938,U_2939,U_2940)
| ~ sP290(U_2938,U_2939,U_2940) )
& ! [U_2938,U_2939,U_2940] :
( c_Polynomial_Opos__poly(U_2938,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2938),U_2940,U_2939))
| U_2939 = U_2940
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2938),U_2939,U_2940)
| ~ sP290(U_2938,U_2939,U_2940) )
& ! [U_2938,U_2939,U_2940] :
( sP290(U_2938,U_2939,U_2940)
| ~ class_Rings_Olinordered__idom(U_2938) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP289,sP290])],[f_930_2]) ).
cnf(f_930_4,plain,
( sP290(U_2938,U_2939,U_2940)
| ~ class_Rings_Olinordered__idom(U_2938) ),
inference(clausify,[status(thm)],[f_930_3]) ).
cnf(f_930_5,plain,
( c_Polynomial_Opos__poly(U_2938,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2938),U_2940,U_2939))
| U_2939 = U_2940
| ~ c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2938),U_2939,U_2940)
| ~ sP290(U_2938,U_2939,U_2940) ),
inference(clausify,[status(thm)],[f_930_3]) ).
cnf(f_930_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Polynomial_Opoly(U_2938),U_2939,U_2940)
| sP289(U_2938,U_2939,U_2940)
| ~ sP290(U_2938,U_2939,U_2940) ),
inference(clausify,[status(thm)],[f_930_3]) ).
cnf(f_930_7,plain,
( U_2939 != U_2940
| ~ sP289(U_2938,U_2939,U_2940) ),
inference(clausify,[status(thm)],[f_930_3]) ).
cnf(f_930_8,plain,
( ~ c_Polynomial_Opos__poly(U_2938,c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_2938),U_2940,U_2939))
| ~ sP289(U_2938,U_2939,U_2940) ),
inference(clausify,[status(thm)],[f_930_3]) ).
fof(f_931_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_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_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_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_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_le__diff__iff]) ).
fof(f_931_2,plain,
! [U_2943,U_2942,U_2941] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2942,U_2941),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2943,U_2941))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2942,U_2943) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2942,U_2943)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2942,U_2941),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2943,U_2941)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2941,U_2943)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2941,U_2942) ),
inference(variable_rename,[status(thm)],[f_931_1]) ).
fof(f_931_3,plain,
( ! [U_2941,U_2942,U_2943] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2942,U_2941),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2943,U_2941))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2942,U_2943)
| ~ sP291(U_2941,U_2942,U_2943) )
& ! [U_2941,U_2942,U_2943] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2942,U_2943)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2942,U_2941),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2943,U_2941))
| ~ sP291(U_2941,U_2942,U_2943) )
& ! [U_2941,U_2942,U_2943] :
( sP291(U_2941,U_2942,U_2943)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2941,U_2943)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2941,U_2942) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP291])],[f_931_2]) ).
cnf(f_931_4,plain,
( sP291(U_2941,U_2942,U_2943)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2941,U_2943)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2941,U_2942) ),
inference(clausify,[status(thm)],[f_931_3]) ).
cnf(f_931_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2942,U_2943)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2942,U_2941),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2943,U_2941))
| ~ sP291(U_2941,U_2942,U_2943) ),
inference(clausify,[status(thm)],[f_931_3]) ).
cnf(f_931_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2942,U_2941),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2943,U_2941))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2942,U_2943)
| ~ sP291(U_2941,U_2942,U_2943) ),
inference(clausify,[status(thm)],[f_931_3]) ).
fof(f_932_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_932_2,plain,
! [U_2946,U_2945,U_2944] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2945,U_2944),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2946,U_2944)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2945,U_2946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2944,U_2946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2944,U_2945) ),
inference(variable_rename,[status(thm)],[f_932_1]) ).
fof(f_932_3,plain,
! [U_2946,U_2944,U_2945] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2945,U_2944),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2946,U_2944)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2945,U_2946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2944,U_2946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2944,U_2945) ),
inference(definitional_conversion,[status(esa)],[f_932_2]) ).
cnf(f_932_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2945,U_2944),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2946,U_2944)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2945,U_2946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2944,U_2946)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2944,U_2945) ),
inference(clausify,[status(thm)],[f_932_3]) ).
fof(f_933_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2)
| V_ma_2 != V_n_2 )
& ( V_ma_2 = V_n_2
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_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_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_eq__diff__iff]) ).
fof(f_933_2,plain,
! [U_2949,U_2948,U_2947] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2948,U_2947) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2949,U_2947)
| U_2948 != U_2949 )
& ( U_2948 = U_2949
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2948,U_2947) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2949,U_2947) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2947,U_2949)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2947,U_2948) ),
inference(variable_rename,[status(thm)],[f_933_1]) ).
fof(f_933_3,plain,
( ! [U_2949,U_2948,U_2947] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2948,U_2947) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2949,U_2947)
| U_2948 != U_2949
| ~ sP292(U_2949,U_2948,U_2947) )
& ! [U_2949,U_2948,U_2947] :
( U_2948 = U_2949
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2948,U_2947) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2949,U_2947)
| ~ sP292(U_2949,U_2948,U_2947) )
& ! [U_2949,U_2948,U_2947] :
( sP292(U_2949,U_2948,U_2947)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2947,U_2949)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2947,U_2948) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP292])],[f_933_2]) ).
cnf(f_933_4,plain,
( sP292(U_2949,U_2948,U_2947)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2947,U_2949)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2947,U_2948) ),
inference(clausify,[status(thm)],[f_933_3]) ).
cnf(f_933_5,plain,
( U_2948 = U_2949
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2948,U_2947) != c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2949,U_2947)
| ~ sP292(U_2949,U_2948,U_2947) ),
inference(clausify,[status(thm)],[f_933_3]) ).
cnf(f_933_6,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2948,U_2947) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2949,U_2947)
| U_2948 != U_2949
| ~ sP292(U_2949,U_2948,U_2947) ),
inference(clausify,[status(thm)],[f_933_3]) ).
fof(f_934_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_934_2,plain,
! [U_2951,U_2950] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2951,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2951,U_2950)) = U_2950
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2950,U_2951) ),
inference(variable_rename,[status(thm)],[f_934_1]) ).
fof(f_934_3,plain,
! [U_2951,U_2950] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2951,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2951,U_2950)) = U_2950
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2950,U_2951) ),
inference(definitional_conversion,[status(esa)],[f_934_2]) ).
cnf(f_934_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2951,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2951,U_2950)) = U_2950
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2950,U_2951) ),
inference(clausify,[status(thm)],[f_934_3]) ).
fof(f_935_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_935_2,plain,
! [U_2954,U_2953,U_2952] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2952,U_2954),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2953,U_2954))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2952,U_2953) ),
inference(variable_rename,[status(thm)],[f_935_1]) ).
fof(f_935_3,plain,
! [U_2952,U_2954,U_2953] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2952,U_2954),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2953,U_2954))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2952,U_2953) ),
inference(definitional_conversion,[status(esa)],[f_935_2]) ).
cnf(f_935_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2952,U_2954),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2953,U_2954))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2952,U_2953) ),
inference(clausify,[status(thm)],[f_935_3]) ).
fof(f_936_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_936_2,plain,
! [U_2957,U_2956,U_2955] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2957,U_2956),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2957,U_2955))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2955,U_2956) ),
inference(variable_rename,[status(thm)],[f_936_1]) ).
fof(f_936_3,plain,
! [U_2955,U_2956,U_2957] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2957,U_2956),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2957,U_2955))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2955,U_2956) ),
inference(definitional_conversion,[status(esa)],[f_936_2]) ).
cnf(f_936_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2957,U_2956),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2957,U_2955))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2955,U_2956) ),
inference(clausify,[status(thm)],[f_936_3]) ).
fof(f_937_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_937_2,plain,
! [U_2959,U_2958] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2958,U_2959),U_2958),
inference(variable_rename,[status(thm)],[f_937_1]) ).
fof(f_937_3,plain,
! [U_2959,U_2958] : c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2958,U_2959),U_2958),
inference(definitional_conversion,[status(esa)],[f_937_2]) ).
cnf(f_937_4,plain,
c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2958,U_2959),U_2958),
inference(clausify,[status(thm)],[f_937_3]) ).
fof(f_938_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_938_2,plain,
! [U_2961,U_2960] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2960,U_2961),U_2961) = U_2960,
inference(variable_rename,[status(thm)],[f_938_1]) ).
fof(f_938_3,plain,
! [U_2960,U_2961] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2960,U_2961),U_2961) = U_2960,
inference(definitional_conversion,[status(esa)],[f_938_2]) ).
cnf(f_938_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2960,U_2961),U_2961) = U_2960,
inference(clausify,[status(thm)],[f_938_3]) ).
fof(f_939_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_939_2,plain,
! [U_2963,U_2962] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2962,U_2963),U_2962) = U_2963,
inference(variable_rename,[status(thm)],[f_939_1]) ).
fof(f_939_3,plain,
! [U_2963,U_2962] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2962,U_2963),U_2962) = U_2963,
inference(definitional_conversion,[status(esa)],[f_939_2]) ).
cnf(f_939_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2962,U_2963),U_2962) = U_2963,
inference(clausify,[status(thm)],[f_939_3]) ).
fof(f_940_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_940_2,plain,
! [U_2966,U_2965,U_2964] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2964,U_2965),U_2966) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2964,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2965,U_2966)),
inference(variable_rename,[status(thm)],[f_940_1]) ).
fof(f_940_3,plain,
! [U_2965,U_2964,U_2966] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2964,U_2965),U_2966) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2964,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2965,U_2966)),
inference(definitional_conversion,[status(esa)],[f_940_2]) ).
cnf(f_940_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2964,U_2965),U_2966) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2964,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2965,U_2966)),
inference(clausify,[status(thm)],[f_940_3]) ).
fof(f_941_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_941_2,plain,
! [U_2969,U_2968,U_2967] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2967,U_2968),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2967,U_2969)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2968,U_2969),
inference(variable_rename,[status(thm)],[f_941_1]) ).
fof(f_941_3,plain,
! [U_2968,U_2967,U_2969] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2967,U_2968),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2967,U_2969)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2968,U_2969),
inference(definitional_conversion,[status(esa)],[f_941_2]) ).
cnf(f_941_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2967,U_2968),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2967,U_2969)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2968,U_2969),
inference(clausify,[status(thm)],[f_941_3]) ).
fof(f_942_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_942_2,plain,
! [U_2972,U_2971,U_2970] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2970,U_2971),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2972,U_2971)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2970,U_2972),
inference(variable_rename,[status(thm)],[f_942_1]) ).
fof(f_942_3,plain,
! [U_2971,U_2970,U_2972] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2970,U_2971),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2972,U_2971)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2970,U_2972),
inference(definitional_conversion,[status(esa)],[f_942_2]) ).
cnf(f_942_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2970,U_2971),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2972,U_2971)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2970,U_2972),
inference(clausify,[status(thm)],[f_942_3]) ).
fof(f_943_1,plain,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diff__nat]) ).
fof(f_943_2,plain,
! [U_2975,U_2974,U_2973] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2973,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2974,U_2975))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2973,U_2975)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2973,U_2974) ),
inference(variable_rename,[status(thm)],[f_943_1]) ).
fof(f_943_3,plain,
! [U_2974,U_2973,U_2975] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2973,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2974,U_2975))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2973,U_2975)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2973,U_2974) ),
inference(definitional_conversion,[status(esa)],[f_943_2]) ).
cnf(f_943_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2973,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2974,U_2975))
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2973,U_2975)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_2973,U_2974) ),
inference(clausify,[status(thm)],[f_943_3]) ).
fof(f_944_1,plain,
! [V_y_2,V_x_2] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x_2,V_y_2),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,V_x_2,V_y_2) ) ),
inference(fof_nnf,[status(thm)],[fact_real__le__eq__diff]) ).
fof(f_944_2,plain,
! [U_2977,U_2976] :
( ( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2976,U_2977)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2976,U_2977),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_2976,U_2977),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2976,U_2977) ) ),
inference(variable_rename,[status(thm)],[f_944_1]) ).
fof(f_944_3,plain,
( ! [U_2981,U_2979] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2979,U_2981)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2979,U_2981),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_2980,U_2978] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2978,U_2980),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2978,U_2980) ) ),
inference(miniscope,[status(thm)],[f_944_2]) ).
fof(f_944_4,plain,
( ! [U_2979,U_2981] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2979,U_2981)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2979,U_2981),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) )
& ! [U_2978,U_2980] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2978,U_2980),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2978,U_2980) ) ),
inference(definitional_conversion,[status(esa)],[f_944_3]) ).
cnf(f_944_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2978,U_2980),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2978,U_2980) ),
inference(clausify,[status(thm)],[f_944_4]) ).
cnf(f_944_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,U_2979,U_2981)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_2979,U_2981),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(clausify,[status(thm)],[f_944_4]) ).
fof(f_945_1,plain,
! [V_ma_2,V_n_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_ma_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_zero__less__diff]) ).
fof(f_945_2,plain,
! [U_2983,U_2982] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2982,U_2983))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2983,U_2982) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2983,U_2982)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2982,U_2983)) ) ),
inference(variable_rename,[status(thm)],[f_945_1]) ).
fof(f_945_3,plain,
( ! [U_2987,U_2985] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2985,U_2987))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2987,U_2985) )
& ! [U_2986,U_2984] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2986,U_2984)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2984,U_2986)) ) ),
inference(miniscope,[status(thm)],[f_945_2]) ).
fof(f_945_4,plain,
( ! [U_2985,U_2987] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2985,U_2987))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2987,U_2985) )
& ! [U_2984,U_2986] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2986,U_2984)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2984,U_2986)) ) ),
inference(definitional_conversion,[status(esa)],[f_945_3]) ).
cnf(f_945_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2986,U_2984)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2984,U_2986)) ),
inference(clausify,[status(thm)],[f_945_4]) ).
cnf(f_945_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2985,U_2987))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_2987,U_2985) ),
inference(clausify,[status(thm)],[f_945_4]) ).
fof(f_946_1,plain,
! [V_m,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_m)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__less]) ).
fof(f_946_2,plain,
! [U_2989,U_2988] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2989,U_2988),U_2989)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2989)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2988) ),
inference(variable_rename,[status(thm)],[f_946_1]) ).
fof(f_946_3,plain,
! [U_2989,U_2988] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2989,U_2988),U_2989)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2989)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2988) ),
inference(definitional_conversion,[status(esa)],[f_946_2]) ).
cnf(f_946_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2989,U_2988),U_2989)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2989)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_2988) ),
inference(clausify,[status(thm)],[f_946_3]) ).
fof(f_947_1,plain,
! [V_n,V_m] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n),c_Nat_OSuc(V_m)),
inference(fof_nnf,[status(thm)],[fact_diff__less__Suc]) ).
fof(f_947_2,plain,
! [U_2991,U_2990] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2990,U_2991),c_Nat_OSuc(U_2990)),
inference(variable_rename,[status(thm)],[f_947_1]) ).
fof(f_947_3,plain,
! [U_2991,U_2990] : c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2990,U_2991),c_Nat_OSuc(U_2990)),
inference(definitional_conversion,[status(esa)],[f_947_2]) ).
cnf(f_947_4,plain,
c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2990,U_2991),c_Nat_OSuc(U_2990)),
inference(clausify,[status(thm)],[f_947_3]) ).
fof(f_948_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_948_2,plain,
! [U_2993,U_2992] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2992,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2992,U_2993)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_948_1]) ).
fof(f_948_3,plain,
! [U_2992,U_2993] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2992,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2992,U_2993)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_948_2]) ).
cnf(f_948_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2992,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_2992,U_2993)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_948_3]) ).
fof(f_949_1,plain,
! [V_n_2,V_ma_2] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_ma_2,V_n_2)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_n_2) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(fof_nnf,[status(thm)],[fact_diff__is__0__eq]) ).
fof(f_949_2,plain,
! [U_2995,U_2994] :
( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2994,U_2995) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2994,U_2995) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2994,U_2995)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2994,U_2995) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(variable_rename,[status(thm)],[f_949_1]) ).
fof(f_949_3,plain,
( ! [U_2999,U_2997] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2997,U_2999) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2997,U_2999) )
& ! [U_2998,U_2996] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2996,U_2998)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2996,U_2998) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(miniscope,[status(thm)],[f_949_2]) ).
fof(f_949_4,plain,
( ! [U_2999,U_2997] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2997,U_2999) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2997,U_2999) )
& ! [U_2996,U_2998] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2996,U_2998)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2996,U_2998) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
inference(definitional_conversion,[status(esa)],[f_949_3]) ).
cnf(f_949_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2996,U_2998)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2996,U_2998) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_949_4]) ).
cnf(f_949_6,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_2997,U_2999) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_2997,U_2999) ),
inference(clausify,[status(thm)],[f_949_4]) ).
fof(f_950_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_950_2,plain,
! [U_3001,U_3000] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3000,U_3001) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3000,U_3001) ),
inference(variable_rename,[status(thm)],[f_950_1]) ).
fof(f_950_3,plain,
! [U_3001,U_3000] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3000,U_3001) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3000,U_3001) ),
inference(definitional_conversion,[status(esa)],[f_950_2]) ).
cnf(f_950_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3000,U_3001) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3000,U_3001) ),
inference(clausify,[status(thm)],[f_950_3]) ).
fof(f_951_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_951_2,plain,
! [U_3003,U_3002] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3003),U_3002) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3003,U_3002))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3002,U_3003) ),
inference(variable_rename,[status(thm)],[f_951_1]) ).
fof(f_951_3,plain,
! [U_3002,U_3003] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3003),U_3002) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3003,U_3002))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3002,U_3003) ),
inference(definitional_conversion,[status(esa)],[f_951_2]) ).
cnf(f_951_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3003),U_3002) = c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3003,U_3002))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3002,U_3003) ),
inference(clausify,[status(thm)],[f_951_3]) ).
fof(f_952_1,plain,
! [V_k_2,V_j_2,V_i_2] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_i_2,V_k_2),V_j_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_i_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_j_2,V_k_2)) ) ),
inference(fof_nnf,[status(thm)],[fact_less__diff__conv]) ).
fof(f_952_2,plain,
! [U_3006,U_3005,U_3004] :
( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3004,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3005,U_3006))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3004,U_3006),U_3005) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3004,U_3006),U_3005)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3004,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3005,U_3006)) ) ),
inference(variable_rename,[status(thm)],[f_952_1]) ).
fof(f_952_3,plain,
( ! [U_3012,U_3010,U_3008] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3008,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3010,U_3012))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3008,U_3012),U_3010) )
& ! [U_3011,U_3009,U_3007] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3007,U_3011),U_3009)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3007,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3009,U_3011)) ) ),
inference(miniscope,[status(thm)],[f_952_2]) ).
fof(f_952_4,plain,
( ! [U_3010,U_3008,U_3012] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3008,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3010,U_3012))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3008,U_3012),U_3010) )
& ! [U_3007,U_3009,U_3011] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3007,U_3011),U_3009)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3007,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3009,U_3011)) ) ),
inference(definitional_conversion,[status(esa)],[f_952_3]) ).
cnf(f_952_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3007,U_3011),U_3009)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3007,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3009,U_3011)) ),
inference(clausify,[status(thm)],[f_952_4]) ).
cnf(f_952_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3008,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3010,U_3012))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3008,U_3012),U_3010) ),
inference(clausify,[status(thm)],[f_952_4]) ).
fof(f_953_1,plain,
! [V_n,V_m] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_n,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = V_m
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_m,V_n) ),
inference(fof_nnf,[status(thm)],[fact_add__diff__inverse]) ).
fof(f_953_2,plain,
! [U_3014,U_3013] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3014,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3013,U_3014)) = U_3013
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3013,U_3014) ),
inference(variable_rename,[status(thm)],[f_953_1]) ).
fof(f_953_3,plain,
! [U_3014,U_3013] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3014,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3013,U_3014)) = U_3013
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3013,U_3014) ),
inference(definitional_conversion,[status(esa)],[f_953_2]) ).
cnf(f_953_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3014,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3013,U_3014)) = U_3013
| c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3013,U_3014) ),
inference(clausify,[status(thm)],[f_953_3]) ).
fof(f_954_1,plain,
! [V_n_2,V_ma_2,V_k_2] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_2,V_k_2),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n_2,V_k_2))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_ma_2,V_n_2)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_ma_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_ma_2) ),
inference(fof_nnf,[status(thm)],[fact_less__diff__iff]) ).
fof(f_954_2,plain,
! [U_3017,U_3016,U_3015] :
( ( ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3016,U_3015),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3017,U_3015))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3016,U_3017) )
& ( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3016,U_3017)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3016,U_3015),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3017,U_3015)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3015,U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3015,U_3016) ),
inference(variable_rename,[status(thm)],[f_954_1]) ).
fof(f_954_3,plain,
( ! [U_3016,U_3015,U_3017] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3016,U_3015),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3017,U_3015))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3016,U_3017)
| ~ sP293(U_3016,U_3015,U_3017) )
& ! [U_3016,U_3015,U_3017] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3016,U_3017)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3016,U_3015),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3017,U_3015))
| ~ sP293(U_3016,U_3015,U_3017) )
& ! [U_3016,U_3015,U_3017] :
( sP293(U_3016,U_3015,U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3015,U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3015,U_3016) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293])],[f_954_2]) ).
cnf(f_954_4,plain,
( sP293(U_3016,U_3015,U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3015,U_3017)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3015,U_3016) ),
inference(clausify,[status(thm)],[f_954_3]) ).
cnf(f_954_5,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3016,U_3017)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3016,U_3015),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3017,U_3015))
| ~ sP293(U_3016,U_3015,U_3017) ),
inference(clausify,[status(thm)],[f_954_3]) ).
cnf(f_954_6,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3016,U_3015),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3017,U_3015))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3016,U_3017)
| ~ sP293(U_3016,U_3015,U_3017) ),
inference(clausify,[status(thm)],[f_954_3]) ).
fof(f_955_1,plain,
! [V_c,V_b,V_a] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a,V_c),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_b,V_c))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_c,V_a)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a,V_b) ),
inference(fof_nnf,[status(thm)],[fact_diff__less__mono]) ).
fof(f_955_2,plain,
! [U_3020,U_3019,U_3018] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3018,U_3020),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3019,U_3020))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3020,U_3018)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3018,U_3019) ),
inference(variable_rename,[status(thm)],[f_955_1]) ).
fof(f_955_3,plain,
! [U_3020,U_3018,U_3019] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3018,U_3020),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3019,U_3020))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3020,U_3018)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3018,U_3019) ),
inference(definitional_conversion,[status(esa)],[f_955_2]) ).
cnf(f_955_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3018,U_3020),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3019,U_3020))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3020,U_3018)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3018,U_3019) ),
inference(clausify,[status(thm)],[f_955_3]) ).
fof(f_956_1,plain,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diffD]) ).
fof(f_956_2,plain,
! [U_3023,U_3022,U_3021] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3021,U_3022)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3023,U_3022)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3021,U_3023)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3021,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3022,U_3023)) ),
inference(variable_rename,[status(thm)],[f_956_1]) ).
fof(f_956_3,plain,
! [U_3022,U_3021,U_3023] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3021,U_3022)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3023,U_3022)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3021,U_3023)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3021,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3022,U_3023)) ),
inference(definitional_conversion,[status(esa)],[f_956_2]) ).
cnf(f_956_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3021,U_3022)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3023,U_3022)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3021,U_3023)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3021,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3022,U_3023)) ),
inference(clausify,[status(thm)],[f_956_3]) ).
fof(f_957_1,plain,
! [V_n,V_m,V_k] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_n)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,V_m)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,V_k,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) ),
inference(fof_nnf,[status(thm)],[fact_dvd__diffD1]) ).
fof(f_957_2,plain,
! [U_3026,U_3025,U_3024] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3024,U_3026)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3026,U_3025)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3024,U_3025)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3024,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3025,U_3026)) ),
inference(variable_rename,[status(thm)],[f_957_1]) ).
fof(f_957_3,plain,
! [U_3024,U_3025,U_3026] :
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3024,U_3026)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3026,U_3025)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3024,U_3025)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3024,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3025,U_3026)) ),
inference(definitional_conversion,[status(esa)],[f_957_2]) ).
cnf(f_957_4,plain,
( c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3024,U_3026)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3026,U_3025)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3024,U_3025)
| ~ c_Rings_Odvd__class_Odvd(tc_Nat_Onat,U_3024,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3025,U_3026)) ),
inference(clausify,[status(thm)],[f_957_3]) ).
fof(f_958_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_958_2,plain,
! [U_3029,U_3028,U_3027] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3028,U_3029),U_3027) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3028,U_3027),U_3029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3027,U_3028) ),
inference(variable_rename,[status(thm)],[f_958_1]) ).
fof(f_958_3,plain,
! [U_3028,U_3029,U_3027] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3028,U_3029),U_3027) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3028,U_3027),U_3029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3027,U_3028) ),
inference(definitional_conversion,[status(esa)],[f_958_2]) ).
cnf(f_958_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3028,U_3029),U_3027) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3028,U_3027),U_3029)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3027,U_3028) ),
inference(clausify,[status(thm)],[f_958_3]) ).
fof(f_959_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_959_2,plain,
! [U_3032,U_3031,U_3030] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3031,U_3030),U_3032) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3031,U_3032),U_3030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3030,U_3031) ),
inference(variable_rename,[status(thm)],[f_959_1]) ).
fof(f_959_3,plain,
! [U_3031,U_3030,U_3032] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3031,U_3030),U_3032) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3031,U_3032),U_3030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3030,U_3031) ),
inference(definitional_conversion,[status(esa)],[f_959_2]) ).
cnf(f_959_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3031,U_3030),U_3032) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3031,U_3032),U_3030)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3030,U_3031) ),
inference(clausify,[status(thm)],[f_959_3]) ).
fof(f_960_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_960_2,plain,
! [U_3035,U_3034,U_3033] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3035,U_3034),U_3033) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3035,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3034,U_3033))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3033,U_3034) ),
inference(variable_rename,[status(thm)],[f_960_1]) ).
fof(f_960_3,plain,
! [U_3034,U_3033,U_3035] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3035,U_3034),U_3033) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3035,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3034,U_3033))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3033,U_3034) ),
inference(definitional_conversion,[status(esa)],[f_960_2]) ).
cnf(f_960_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3035,U_3034),U_3033) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3035,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3034,U_3033))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3033,U_3034) ),
inference(clausify,[status(thm)],[f_960_3]) ).
fof(f_961_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_961_2,plain,
! [U_3038,U_3037,U_3036] :
( ( ( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3037,U_3036) = U_3038
| U_3037 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3038,U_3036) )
& ( U_3037 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3038,U_3036)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3037,U_3036) != U_3038 ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3036,U_3037) ),
inference(variable_rename,[status(thm)],[f_961_1]) ).
fof(f_961_3,plain,
( ! [U_3036,U_3037,U_3038] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3037,U_3036) = U_3038
| U_3037 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3038,U_3036)
| ~ sP294(U_3036,U_3037,U_3038) )
& ! [U_3036,U_3037,U_3038] :
( U_3037 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3038,U_3036)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3037,U_3036) != U_3038
| ~ sP294(U_3036,U_3037,U_3038) )
& ! [U_3036,U_3037,U_3038] :
( sP294(U_3036,U_3037,U_3038)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3036,U_3037) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP294])],[f_961_2]) ).
cnf(f_961_4,plain,
( sP294(U_3036,U_3037,U_3038)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3036,U_3037) ),
inference(clausify,[status(thm)],[f_961_3]) ).
cnf(f_961_5,plain,
( U_3037 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3038,U_3036)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3037,U_3036) != U_3038
| ~ sP294(U_3036,U_3037,U_3038) ),
inference(clausify,[status(thm)],[f_961_3]) ).
cnf(f_961_6,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3037,U_3036) = U_3038
| U_3037 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3038,U_3036)
| ~ sP294(U_3036,U_3037,U_3038) ),
inference(clausify,[status(thm)],[f_961_3]) ).
fof(f_962_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_962_2,plain,
! [U_3040,U_3039] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3040,U_3039),U_3039) = U_3040
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3039,U_3040) ),
inference(variable_rename,[status(thm)],[f_962_1]) ).
fof(f_962_3,plain,
! [U_3040,U_3039] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3040,U_3039),U_3039) = U_3040
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3039,U_3040) ),
inference(definitional_conversion,[status(esa)],[f_962_2]) ).
cnf(f_962_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3040,U_3039),U_3039) = U_3040
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3039,U_3040) ),
inference(clausify,[status(thm)],[f_962_3]) ).
fof(f_963_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_963_2,plain,
! [U_3043,U_3042,U_3041] :
( ( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3043,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3042,U_3041))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3043,U_3041),U_3042) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3043,U_3041),U_3042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3043,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3042,U_3041)) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3041,U_3042) ),
inference(variable_rename,[status(thm)],[f_963_1]) ).
fof(f_963_3,plain,
( ! [U_3043,U_3041,U_3042] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3043,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3042,U_3041))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3043,U_3041),U_3042)
| ~ sP295(U_3043,U_3041,U_3042) )
& ! [U_3043,U_3041,U_3042] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3043,U_3041),U_3042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3043,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3042,U_3041))
| ~ sP295(U_3043,U_3041,U_3042) )
& ! [U_3043,U_3041,U_3042] :
( sP295(U_3043,U_3041,U_3042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3041,U_3042) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295])],[f_963_2]) ).
cnf(f_963_4,plain,
( sP295(U_3043,U_3041,U_3042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3041,U_3042) ),
inference(clausify,[status(thm)],[f_963_3]) ).
cnf(f_963_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3043,U_3041),U_3042)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3043,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3042,U_3041))
| ~ sP295(U_3043,U_3041,U_3042) ),
inference(clausify,[status(thm)],[f_963_3]) ).
cnf(f_963_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3043,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3042,U_3041))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3043,U_3041),U_3042)
| ~ sP295(U_3043,U_3041,U_3042) ),
inference(clausify,[status(thm)],[f_963_3]) ).
fof(f_964_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_964_2,plain,
! [U_3046,U_3045,U_3044] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3046,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3045,U_3044)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3046,U_3045),U_3044)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3044,U_3045) ),
inference(variable_rename,[status(thm)],[f_964_1]) ).
fof(f_964_3,plain,
! [U_3045,U_3046,U_3044] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3046,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3045,U_3044)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3046,U_3045),U_3044)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3044,U_3045) ),
inference(definitional_conversion,[status(esa)],[f_964_2]) ).
cnf(f_964_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3046,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3045,U_3044)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3046,U_3045),U_3044)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3044,U_3045) ),
inference(clausify,[status(thm)],[f_964_3]) ).
fof(f_965_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_965_2,plain,
! [U_3048,U_3047] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3047,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3048,U_3047)) = U_3048
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3047,U_3048) ),
inference(variable_rename,[status(thm)],[f_965_1]) ).
fof(f_965_3,plain,
! [U_3047,U_3048] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3047,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3048,U_3047)) = U_3048
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3047,U_3048) ),
inference(definitional_conversion,[status(esa)],[f_965_2]) ).
cnf(f_965_4,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3047,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3048,U_3047)) = U_3048
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3047,U_3048) ),
inference(clausify,[status(thm)],[f_965_3]) ).
fof(f_966_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_966_2,plain,
! [U_3051,U_3050,U_3049] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3051,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3050,U_3051),U_3049))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3049,U_3050) ),
inference(variable_rename,[status(thm)],[f_966_1]) ).
fof(f_966_3,plain,
! [U_3050,U_3049,U_3051] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3051,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3050,U_3051),U_3049))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3049,U_3050) ),
inference(definitional_conversion,[status(esa)],[f_966_2]) ).
cnf(f_966_4,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3051,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3050,U_3051),U_3049))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3049,U_3050) ),
inference(clausify,[status(thm)],[f_966_3]) ).
fof(f_967_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_967_2,plain,
! [U_3054,U_3053,U_3052] :
( ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3052,U_3053),U_3054)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3052,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3054,U_3053)) )
& ( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3052,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3054,U_3053))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3052,U_3053),U_3054) ) ),
inference(variable_rename,[status(thm)],[f_967_1]) ).
fof(f_967_3,plain,
( ! [U_3060,U_3058,U_3056] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3056,U_3058),U_3060)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3056,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3060,U_3058)) )
& ! [U_3059,U_3057,U_3055] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3055,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3059,U_3057))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3055,U_3057),U_3059) ) ),
inference(miniscope,[status(thm)],[f_967_2]) ).
fof(f_967_4,plain,
( ! [U_3060,U_3058,U_3056] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3056,U_3058),U_3060)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3056,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3060,U_3058)) )
& ! [U_3055,U_3057,U_3059] :
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3055,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3059,U_3057))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3055,U_3057),U_3059) ) ),
inference(definitional_conversion,[status(esa)],[f_967_3]) ).
cnf(f_967_5,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3055,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3059,U_3057))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3055,U_3057),U_3059) ),
inference(clausify,[status(thm)],[f_967_4]) ).
cnf(f_967_6,plain,
( c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3056,U_3058),U_3060)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3056,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3060,U_3058)) ),
inference(clausify,[status(thm)],[f_967_4]) ).
fof(f_968_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_968_2,plain,
! [U_3063,U_3062,U_3061] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3063,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3062,U_3061)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3063,U_3061),U_3062)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3061,U_3062) ),
inference(variable_rename,[status(thm)],[f_968_1]) ).
fof(f_968_3,plain,
! [U_3063,U_3062,U_3061] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3063,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3062,U_3061)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3063,U_3061),U_3062)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3061,U_3062) ),
inference(definitional_conversion,[status(esa)],[f_968_2]) ).
cnf(f_968_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3063,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3062,U_3061)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3063,U_3061),U_3062)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3061,U_3062) ),
inference(clausify,[status(thm)],[f_968_3]) ).
fof(f_969_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_969_2,plain,
! [U_3065,U_3064] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3064,c_Nat_OSuc(U_3065)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3064,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3065),
inference(variable_rename,[status(thm)],[f_969_1]) ).
fof(f_969_3,plain,
! [U_3065,U_3064] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3064,c_Nat_OSuc(U_3065)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3064,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3065),
inference(definitional_conversion,[status(esa)],[f_969_2]) ).
cnf(f_969_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3064,c_Nat_OSuc(U_3065)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3064,c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3065),
inference(clausify,[status(thm)],[f_969_3]) ).
fof(f_970_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_970_2,plain,
! [U_3066] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3066),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3066,
inference(variable_rename,[status(thm)],[f_970_1]) ).
fof(f_970_3,plain,
! [U_3066] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3066),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3066,
inference(definitional_conversion,[status(esa)],[f_970_2]) ).
cnf(f_970_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3066),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3066,
inference(clausify,[status(thm)],[f_970_3]) ).
fof(f_971_1,plain,
! [V_y,V_x] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,V_y) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_x,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_y)),
inference(fof_nnf,[status(thm)],[fact_minus__real__def]) ).
fof(f_971_2,plain,
! [U_3068,U_3067] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3067,U_3068) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3067,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_3068)),
inference(variable_rename,[status(thm)],[f_971_1]) ).
fof(f_971_3,plain,
! [U_3067,U_3068] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3067,U_3068) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3067,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_3068)),
inference(definitional_conversion,[status(esa)],[f_971_2]) ).
cnf(f_971_4,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3067,U_3068) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3067,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_3068)),
inference(clausify,[status(thm)],[f_971_3]) ).
fof(f_972_1,plain,
! [V_s,V_r] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_r,V_s) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,V_r,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,V_s)),
inference(fof_nnf,[status(thm)],[fact_real__diff__def]) ).
fof(f_972_2,plain,
! [U_3070,U_3069] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3069,U_3070) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3069,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_3070)),
inference(variable_rename,[status(thm)],[f_972_1]) ).
fof(f_972_3,plain,
! [U_3070,U_3069] : c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3069,U_3070) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3069,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_3070)),
inference(definitional_conversion,[status(esa)],[f_972_2]) ).
cnf(f_972_4,plain,
c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3069,U_3070) = c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,U_3069,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,U_3070)),
inference(clausify,[status(thm)],[f_972_3]) ).
fof(f_973_1,plain,
! [V_q,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a)),V_q) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(T_a),V_q)
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I1_J]) ).
fof(f_973_2,plain,
! [U_3072,U_3071] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_3071),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3071)),U_3072) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3071),U_3072)
| ~ class_Groups_Oab__group__add(U_3071) ),
inference(variable_rename,[status(thm)],[f_973_1]) ).
fof(f_973_3,plain,
! [U_3071,U_3072] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_3071),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3071)),U_3072) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3071),U_3072)
| ~ class_Groups_Oab__group__add(U_3071) ),
inference(definitional_conversion,[status(esa)],[f_973_2]) ).
cnf(f_973_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_3071),c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3071)),U_3072) = c_Groups_Ouminus__class_Ouminus(tc_Polynomial_Opoly(U_3071),U_3072)
| ~ class_Groups_Oab__group__add(U_3071) ),
inference(clausify,[status(thm)],[f_973_3]) ).
fof(f_974_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_974_2,plain,
! [U_3075,U_3074,U_3073] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3073),U_3074),c_Nat_OSuc(U_3075)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3073,U_3074),U_3075),
inference(variable_rename,[status(thm)],[f_974_1]) ).
fof(f_974_3,plain,
! [U_3073,U_3074,U_3075] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3073),U_3074),c_Nat_OSuc(U_3075)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3073,U_3074),U_3075),
inference(definitional_conversion,[status(esa)],[f_974_2]) ).
cnf(f_974_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3073),U_3074),c_Nat_OSuc(U_3075)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3073,U_3074),U_3075),
inference(clausify,[status(thm)],[f_974_3]) ).
fof(f_975_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_975_2,plain,
! [U_3077,U_3076] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3076),c_Nat_OSuc(U_3077)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3076,U_3077),
inference(variable_rename,[status(thm)],[f_975_1]) ).
fof(f_975_3,plain,
! [U_3076,U_3077] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3076),c_Nat_OSuc(U_3077)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3076,U_3077),
inference(definitional_conversion,[status(esa)],[f_975_2]) ).
cnf(f_975_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3076),c_Nat_OSuc(U_3077)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3076,U_3077),
inference(clausify,[status(thm)],[f_975_3]) ).
fof(f_976_1,plain,
! [V_p,T_a] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(T_a),V_p,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(T_a))) = V_p
| ~ class_Groups_Oab__group__add(T_a) ),
inference(fof_nnf,[status(thm)],[fact_diff__poly__code_I2_J]) ).
fof(f_976_2,plain,
! [U_3079,U_3078] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_3078),U_3079,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3078))) = U_3079
| ~ class_Groups_Oab__group__add(U_3078) ),
inference(variable_rename,[status(thm)],[f_976_1]) ).
fof(f_976_3,plain,
! [U_3078,U_3079] :
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_3078),U_3079,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3078))) = U_3079
| ~ class_Groups_Oab__group__add(U_3078) ),
inference(definitional_conversion,[status(esa)],[f_976_2]) ).
cnf(f_976_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Polynomial_Opoly(U_3078),U_3079,c_Groups_Ozero__class_Ozero(tc_Polynomial_Opoly(U_3078))) = U_3079
| ~ class_Groups_Oab__group__add(U_3078) ),
inference(clausify,[status(thm)],[f_976_3]) ).
fof(f_977_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_977_2,plain,
! [U_3082,U_3081,U_3080] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3082,U_3081),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3082,U_3080))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3080,U_3082)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3080,U_3081) ),
inference(variable_rename,[status(thm)],[f_977_1]) ).
fof(f_977_3,plain,
! [U_3081,U_3080,U_3082] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3082,U_3081),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3082,U_3080))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3080,U_3082)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3080,U_3081) ),
inference(definitional_conversion,[status(esa)],[f_977_2]) ).
cnf(f_977_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3082,U_3081),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3082,U_3080))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3080,U_3082)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3080,U_3081) ),
inference(clausify,[status(thm)],[f_977_3]) ).
fof(f_978_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_978_2,plain,
! [U_3085,U_3084,U_3083] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3083,U_3085),U_3084)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3083,U_3084) ),
inference(variable_rename,[status(thm)],[f_978_1]) ).
fof(f_978_3,plain,
! [U_3085,U_3083,U_3084] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3083,U_3085),U_3084)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3083,U_3084) ),
inference(definitional_conversion,[status(esa)],[f_978_2]) ).
cnf(f_978_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3083,U_3085),U_3084)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3083,U_3084) ),
inference(clausify,[status(thm)],[f_978_3]) ).
fof(f_979_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_979_2,plain,
! [U_3087,U_3086] :
( U_3086 = U_3087
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3087,U_3086) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3086,U_3087) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(variable_rename,[status(thm)],[f_979_1]) ).
fof(f_979_3,plain,
! [U_3087,U_3086] :
( U_3086 = U_3087
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3087,U_3086) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3086,U_3087) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(definitional_conversion,[status(esa)],[f_979_2]) ).
cnf(f_979_4,plain,
( U_3086 = U_3087
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3087,U_3086) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
| c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3086,U_3087) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
inference(clausify,[status(thm)],[f_979_3]) ).
fof(f_980_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_980_2,plain,
! [U_3088] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3088,U_3088) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_980_1]) ).
fof(f_980_3,plain,
! [U_3088] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3088,U_3088) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_980_2]) ).
cnf(f_980_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3088,U_3088) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_980_3]) ).
fof(f_981_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_981_2,plain,
! [U_3089] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3089,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3089,
inference(variable_rename,[status(thm)],[f_981_1]) ).
fof(f_981_3,plain,
! [U_3089] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3089,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3089,
inference(definitional_conversion,[status(esa)],[f_981_2]) ).
cnf(f_981_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3089,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3089,
inference(clausify,[status(thm)],[f_981_3]) ).
fof(f_982_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_982_2,plain,
! [U_3090] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(variable_rename,[status(thm)],[f_982_1]) ).
fof(f_982_3,plain,
! [U_3090] : c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_982_2]) ).
cnf(f_982_4,plain,
c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3090) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_982_3]) ).
fof(f_983_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_983_2,plain,
! [U_3093,U_3092,U_3091] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3092,U_3093)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),U_3092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),U_3093)),
inference(variable_rename,[status(thm)],[f_983_1]) ).
fof(f_983_3,plain,
! [U_3091,U_3092,U_3093] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3092,U_3093)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),U_3092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),U_3093)),
inference(definitional_conversion,[status(esa)],[f_983_2]) ).
cnf(f_983_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3092,U_3093)) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),U_3092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),U_3093)),
inference(clausify,[status(thm)],[f_983_3]) ).
fof(f_984_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_984_2,plain,
! [U_3096,U_3095,U_3094] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3094,U_3095)),U_3096) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3094),U_3096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3095),U_3096)),
inference(variable_rename,[status(thm)],[f_984_1]) ).
fof(f_984_3,plain,
! [U_3094,U_3095,U_3096] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3094,U_3095)),U_3096) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3094),U_3096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3095),U_3096)),
inference(definitional_conversion,[status(esa)],[f_984_2]) ).
cnf(f_984_4,plain,
hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3094,U_3095)),U_3096) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3094),U_3096),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3095),U_3096)),
inference(clausify,[status(thm)],[f_984_3]) ).
fof(f_985_1,plain,
! [V_m,V_n] :
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_m,V_n)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_m),c_RealDef_Oreal(tc_Nat_Onat,V_n))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n,V_m) ),
inference(fof_nnf,[status(thm)],[fact_real__of__nat__diff]) ).
fof(f_985_2,plain,
! [U_3098,U_3097] :
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3098,U_3097)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3098),c_RealDef_Oreal(tc_Nat_Onat,U_3097))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3097,U_3098) ),
inference(variable_rename,[status(thm)],[f_985_1]) ).
fof(f_985_3,plain,
! [U_3097,U_3098] :
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3098,U_3097)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3098),c_RealDef_Oreal(tc_Nat_Onat,U_3097))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3097,U_3098) ),
inference(definitional_conversion,[status(esa)],[f_985_2]) ).
cnf(f_985_4,plain,
( c_RealDef_Oreal(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3098,U_3097)) = c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3098),c_RealDef_Oreal(tc_Nat_Onat,U_3097))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3097,U_3098) ),
inference(clausify,[status(thm)],[f_985_3]) ).
fof(f_986_1,plain,
! [V_x,V_a] :
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(V_x),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natceiling__subtract]) ).
fof(f_986_2,plain,
! [U_3100,U_3099] :
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3100,c_RealDef_Oreal(tc_Nat_Onat,U_3099))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_3100),U_3099)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3099),U_3100) ),
inference(variable_rename,[status(thm)],[f_986_1]) ).
fof(f_986_3,plain,
! [U_3099,U_3100] :
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3100,c_RealDef_Oreal(tc_Nat_Onat,U_3099))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_3100),U_3099)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3099),U_3100) ),
inference(definitional_conversion,[status(esa)],[f_986_2]) ).
cnf(f_986_4,plain,
( c_RComplete_Onatceiling(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3100,c_RealDef_Oreal(tc_Nat_Onat,U_3099))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatceiling(U_3100),U_3099)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3099),U_3100) ),
inference(clausify,[status(thm)],[f_986_3]) ).
fof(f_987_1,plain,
! [V_x,V_a] :
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,V_x,c_RealDef_Oreal(tc_Nat_Onat,V_a))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(V_x),V_a)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,V_a),V_x) ),
inference(fof_nnf,[status(thm)],[fact_natfloor__subtract]) ).
fof(f_987_2,plain,
! [U_3102,U_3101] :
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3102,c_RealDef_Oreal(tc_Nat_Onat,U_3101))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3102),U_3101)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3101),U_3102) ),
inference(variable_rename,[status(thm)],[f_987_1]) ).
fof(f_987_3,plain,
! [U_3101,U_3102] :
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3102,c_RealDef_Oreal(tc_Nat_Onat,U_3101))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3102),U_3101)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3101),U_3102) ),
inference(definitional_conversion,[status(esa)],[f_987_2]) ).
cnf(f_987_4,plain,
( c_RComplete_Onatfloor(c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,U_3102,c_RealDef_Oreal(tc_Nat_Onat,U_3101))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_RComplete_Onatfloor(U_3102),U_3101)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealDef_Oreal(tc_Nat_Onat,U_3101),U_3102) ),
inference(clausify,[status(thm)],[f_987_3]) ).
fof(f_988_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_988_2,plain,
! [U_3105,U_3104,U_3103] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3103,U_3104),c_RealVector_Onorm__class_Onorm(U_3103,U_3105)),c_RealVector_Onorm__class_Onorm(U_3103,c_Groups_Oplus__class_Oplus(U_3103,U_3104,U_3105)))
| ~ class_RealVector_Oreal__normed__vector(U_3103) ),
inference(variable_rename,[status(thm)],[f_988_1]) ).
fof(f_988_3,plain,
! [U_3105,U_3103,U_3104] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(U_3103,U_3104),c_RealVector_Onorm__class_Onorm(U_3103,U_3105)),c_RealVector_Onorm__class_Onorm(U_3103,c_Groups_Oplus__class_Oplus(U_3103,U_3104,U_3105)))
| ~ class_RealVector_Oreal__normed__vector(U_3103) ),
inference(definitional_conversion,[status(esa)],[f_988_2]) ).
cnf(f_988_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_3103,U_3104),c_RealVector_Onorm__class_Onorm(U_3103,U_3105)),c_RealVector_Onorm__class_Onorm(U_3103,c_Groups_Oplus__class_Oplus(U_3103,U_3104,U_3105)))
| ~ class_RealVector_Oreal__normed__vector(U_3103) ),
inference(clausify,[status(thm)],[f_988_3]) ).
fof(f_989_1,plain,
! [V_i,V_n] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(V_i)),V_n)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_diff__Suc__less]) ).
fof(f_989_2,plain,
! [U_3107,U_3106] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3106,c_Nat_OSuc(U_3107)),U_3106)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3106) ),
inference(variable_rename,[status(thm)],[f_989_1]) ).
fof(f_989_3,plain,
! [U_3107,U_3106] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3106,c_Nat_OSuc(U_3107)),U_3106)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3106) ),
inference(definitional_conversion,[status(esa)],[f_989_2]) ).
cnf(f_989_4,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3106,c_Nat_OSuc(U_3107)),U_3106)
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3106) ),
inference(clausify,[status(thm)],[f_989_3]) ).
fof(f_990_1,plain,
! [V_n] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_n,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = V_n
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n) ),
inference(fof_nnf,[status(thm)],[fact_Suc__pred]) ).
fof(f_990_2,plain,
! [U_3108] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3108,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3108
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3108) ),
inference(variable_rename,[status(thm)],[f_990_1]) ).
fof(f_990_3,plain,
! [U_3108] :
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3108,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3108
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3108) ),
inference(definitional_conversion,[status(esa)],[f_990_2]) ).
cnf(f_990_4,plain,
( c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3108,c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3108
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_3108) ),
inference(clausify,[status(thm)],[f_990_3]) ).
fof(f_991_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_a_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
| ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split]) ).
fof(f_991_2,plain,
! [U_3113,U_3112,U_3111] :
( ( hBOOL(hAPP(U_3111,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3112,U_3113)))
| ? [U_3110] :
( ~ hBOOL(hAPP(U_3111,U_3110))
& U_3112 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3113,U_3110) )
| ( ~ hBOOL(hAPP(U_3111,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3112,U_3113) ) )
& ( ( ! [U_3109] :
( hBOOL(hAPP(U_3111,U_3109))
| U_3112 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3113,U_3109) )
& ( hBOOL(hAPP(U_3111,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3112,U_3113) ) )
| ~ hBOOL(hAPP(U_3111,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3112,U_3113))) ) ),
inference(variable_rename,[status(thm)],[f_991_1]) ).
fof(f_991_3,plain,
( ! [U_3119,U_3117,U_3115] :
( hBOOL(hAPP(U_3115,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3117,U_3119)))
| ? [U_3110] :
( ~ hBOOL(hAPP(U_3115,U_3110))
& U_3117 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3119,U_3110) )
| ( ~ hBOOL(hAPP(U_3115,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3117,U_3119) ) )
& ! [U_3118,U_3116,U_3114] :
( ( ! [U_3109] :
( hBOOL(hAPP(U_3114,U_3109))
| U_3116 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3118,U_3109) )
& ( hBOOL(hAPP(U_3114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3116,U_3118) ) )
| ~ hBOOL(hAPP(U_3114,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3116,U_3118))) ) ),
inference(miniscope,[status(thm)],[f_991_2]) ).
fof(f_991_4,plain,
( ! [U_3119,U_3117,U_3115] :
( hBOOL(hAPP(U_3115,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3117,U_3119)))
| ( ~ hBOOL(hAPP(U_3115,sK50(U_3119,U_3117,U_3115)))
& U_3117 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3119,sK50(U_3119,U_3117,U_3115)) )
| ( ~ hBOOL(hAPP(U_3115,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3117,U_3119) ) )
& ! [U_3118,U_3116,U_3114] :
( ( ! [U_3109] :
( hBOOL(hAPP(U_3114,U_3109))
| U_3116 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3118,U_3109) )
& ( hBOOL(hAPP(U_3114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3116,U_3118) ) )
| ~ hBOOL(hAPP(U_3114,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3116,U_3118))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_3110,sK50(U_3119,U_3117,U_3115))],[f_991_3]) ).
fof(f_991_5,plain,
( ! [U_3115,U_3117,U_3119] :
( ~ hBOOL(hAPP(U_3115,sK50(U_3119,U_3117,U_3115)))
| ~ sP298(U_3115,U_3117,U_3119) )
& ! [U_3115,U_3117,U_3119] :
( U_3117 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3119,sK50(U_3119,U_3117,U_3115))
| ~ sP298(U_3115,U_3117,U_3119) )
& ! [U_3115,U_3117,U_3119] :
( ~ hBOOL(hAPP(U_3115,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP297(U_3115,U_3117,U_3119) )
& ! [U_3115,U_3117,U_3119] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3117,U_3119)
| ~ sP297(U_3115,U_3117,U_3119) )
& ! [U_3109,U_3118,U_3114,U_3116] :
( hBOOL(hAPP(U_3114,U_3109))
| U_3116 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3118,U_3109)
| ~ sP296(U_3109,U_3118,U_3114,U_3116) )
& ! [U_3109,U_3118,U_3114,U_3116] :
( hBOOL(hAPP(U_3114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3116,U_3118)
| ~ sP296(U_3109,U_3118,U_3114,U_3116) )
& ! [U_3115,U_3117,U_3119] :
( hBOOL(hAPP(U_3115,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3117,U_3119)))
| sP298(U_3115,U_3117,U_3119)
| sP297(U_3115,U_3117,U_3119) )
& ! [U_3109,U_3118,U_3114,U_3116] :
( sP296(U_3109,U_3118,U_3114,U_3116)
| ~ hBOOL(hAPP(U_3114,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3116,U_3118))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP296,sP297,sP298])],[f_991_4]) ).
cnf(f_991_6,plain,
( sP296(U_3109,U_3118,U_3114,U_3116)
| ~ hBOOL(hAPP(U_3114,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3116,U_3118))) ),
inference(clausify,[status(thm)],[f_991_5]) ).
cnf(f_991_7,plain,
( hBOOL(hAPP(U_3115,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3117,U_3119)))
| sP298(U_3115,U_3117,U_3119)
| sP297(U_3115,U_3117,U_3119) ),
inference(clausify,[status(thm)],[f_991_5]) ).
cnf(f_991_8,plain,
( hBOOL(hAPP(U_3114,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3116,U_3118)
| ~ sP296(U_3109,U_3118,U_3114,U_3116) ),
inference(clausify,[status(thm)],[f_991_5]) ).
cnf(f_991_9,plain,
( hBOOL(hAPP(U_3114,U_3109))
| U_3116 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3118,U_3109)
| ~ sP296(U_3109,U_3118,U_3114,U_3116) ),
inference(clausify,[status(thm)],[f_991_5]) ).
cnf(f_991_10,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3117,U_3119)
| ~ sP297(U_3115,U_3117,U_3119) ),
inference(clausify,[status(thm)],[f_991_5]) ).
cnf(f_991_11,plain,
( ~ hBOOL(hAPP(U_3115,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP297(U_3115,U_3117,U_3119) ),
inference(clausify,[status(thm)],[f_991_5]) ).
cnf(f_991_12,plain,
( U_3117 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3119,sK50(U_3119,U_3117,U_3115))
| ~ sP298(U_3115,U_3117,U_3119) ),
inference(clausify,[status(thm)],[f_991_5]) ).
cnf(f_991_13,plain,
( ~ hBOOL(hAPP(U_3115,sK50(U_3119,U_3117,U_3115)))
| ~ sP298(U_3115,U_3117,U_3119) ),
inference(clausify,[status(thm)],[f_991_5]) ).
fof(f_992_1,plain,
! [V_b_2,V_a_2,V_P_2] :
( ( hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2)))
| ? [B_d] :
( ~ hBOOL(hAPP(V_P_2,B_d))
& V_a_2 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
| ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
& ( ( ! [B_d] :
( hBOOL(hAPP(V_P_2,B_d))
| V_a_2 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,V_b_2,B_d) )
& ( hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,V_a_2,V_b_2) ) )
| ~ hBOOL(hAPP(V_P_2,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,V_a_2,V_b_2))) ) ),
inference(fof_nnf,[status(thm)],[fact_nat__diff__split__asm]) ).
fof(f_992_2,plain,
! [U_3124,U_3123,U_3122] :
( ( hBOOL(hAPP(U_3122,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3123,U_3124)))
| ? [U_3121] :
( ~ hBOOL(hAPP(U_3122,U_3121))
& U_3123 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3124,U_3121) )
| ( ~ hBOOL(hAPP(U_3122,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3123,U_3124) ) )
& ( ( ! [U_3120] :
( hBOOL(hAPP(U_3122,U_3120))
| U_3123 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3124,U_3120) )
& ( hBOOL(hAPP(U_3122,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3123,U_3124) ) )
| ~ hBOOL(hAPP(U_3122,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3123,U_3124))) ) ),
inference(variable_rename,[status(thm)],[f_992_1]) ).
fof(f_992_3,plain,
( ! [U_3130,U_3128,U_3126] :
( hBOOL(hAPP(U_3126,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3128,U_3130)))
| ? [U_3121] :
( ~ hBOOL(hAPP(U_3126,U_3121))
& U_3128 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3130,U_3121) )
| ( ~ hBOOL(hAPP(U_3126,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3128,U_3130) ) )
& ! [U_3129,U_3127,U_3125] :
( ( ! [U_3120] :
( hBOOL(hAPP(U_3125,U_3120))
| U_3127 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3129,U_3120) )
& ( hBOOL(hAPP(U_3125,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3127,U_3129) ) )
| ~ hBOOL(hAPP(U_3125,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3127,U_3129))) ) ),
inference(miniscope,[status(thm)],[f_992_2]) ).
fof(f_992_4,plain,
( ! [U_3130,U_3128,U_3126] :
( hBOOL(hAPP(U_3126,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3128,U_3130)))
| ( ~ hBOOL(hAPP(U_3126,sK51(U_3130,U_3128,U_3126)))
& U_3128 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3130,sK51(U_3130,U_3128,U_3126)) )
| ( ~ hBOOL(hAPP(U_3126,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
& c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3128,U_3130) ) )
& ! [U_3129,U_3127,U_3125] :
( ( ! [U_3120] :
( hBOOL(hAPP(U_3125,U_3120))
| U_3127 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3129,U_3120) )
& ( hBOOL(hAPP(U_3125,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3127,U_3129) ) )
| ~ hBOOL(hAPP(U_3125,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3127,U_3129))) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_3121,sK51(U_3130,U_3128,U_3126))],[f_992_3]) ).
fof(f_992_5,plain,
( ! [U_3128,U_3126,U_3130] :
( ~ hBOOL(hAPP(U_3126,sK51(U_3130,U_3128,U_3126)))
| ~ sP301(U_3128,U_3126,U_3130) )
& ! [U_3128,U_3126,U_3130] :
( U_3128 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3130,sK51(U_3130,U_3128,U_3126))
| ~ sP301(U_3128,U_3126,U_3130) )
& ! [U_3128,U_3126,U_3130] :
( ~ hBOOL(hAPP(U_3126,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP300(U_3128,U_3126,U_3130) )
& ! [U_3128,U_3126,U_3130] :
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3128,U_3130)
| ~ sP300(U_3128,U_3126,U_3130) )
& ! [U_3120,U_3127,U_3129,U_3125] :
( hBOOL(hAPP(U_3125,U_3120))
| U_3127 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3129,U_3120)
| ~ sP299(U_3120,U_3127,U_3129,U_3125) )
& ! [U_3120,U_3127,U_3129,U_3125] :
( hBOOL(hAPP(U_3125,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3127,U_3129)
| ~ sP299(U_3120,U_3127,U_3129,U_3125) )
& ! [U_3128,U_3126,U_3130] :
( hBOOL(hAPP(U_3126,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3128,U_3130)))
| sP301(U_3128,U_3126,U_3130)
| sP300(U_3128,U_3126,U_3130) )
& ! [U_3120,U_3127,U_3129,U_3125] :
( sP299(U_3120,U_3127,U_3129,U_3125)
| ~ hBOOL(hAPP(U_3125,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3127,U_3129))) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP299,sP300,sP301])],[f_992_4]) ).
cnf(f_992_6,plain,
( sP299(U_3120,U_3127,U_3129,U_3125)
| ~ hBOOL(hAPP(U_3125,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3127,U_3129))) ),
inference(clausify,[status(thm)],[f_992_5]) ).
cnf(f_992_7,plain,
( hBOOL(hAPP(U_3126,c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3128,U_3130)))
| sP301(U_3128,U_3126,U_3130)
| sP300(U_3128,U_3126,U_3130) ),
inference(clausify,[status(thm)],[f_992_5]) ).
cnf(f_992_8,plain,
( hBOOL(hAPP(U_3125,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3127,U_3129)
| ~ sP299(U_3120,U_3127,U_3129,U_3125) ),
inference(clausify,[status(thm)],[f_992_5]) ).
cnf(f_992_9,plain,
( hBOOL(hAPP(U_3125,U_3120))
| U_3127 != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3129,U_3120)
| ~ sP299(U_3120,U_3127,U_3129,U_3125) ),
inference(clausify,[status(thm)],[f_992_5]) ).
cnf(f_992_10,plain,
( c_Orderings_Oord__class_Oless(tc_Nat_Onat,U_3128,U_3130)
| ~ sP300(U_3128,U_3126,U_3130) ),
inference(clausify,[status(thm)],[f_992_5]) ).
cnf(f_992_11,plain,
( ~ hBOOL(hAPP(U_3126,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
| ~ sP300(U_3128,U_3126,U_3130) ),
inference(clausify,[status(thm)],[f_992_5]) ).
cnf(f_992_12,plain,
( U_3128 = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3130,sK51(U_3130,U_3128,U_3126))
| ~ sP301(U_3128,U_3126,U_3130) ),
inference(clausify,[status(thm)],[f_992_5]) ).
cnf(f_992_13,plain,
( ~ hBOOL(hAPP(U_3126,sK51(U_3130,U_3128,U_3126)))
| ~ sP301(U_3128,U_3126,U_3130) ),
inference(clausify,[status(thm)],[f_992_5]) ).
fof(f_993_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_993_2,plain,
! [U_3133,U_3132,U_3131] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3132,U_3131)),U_3133) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3132),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3131,U_3133))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3131,U_3132) ),
inference(variable_rename,[status(thm)],[f_993_1]) ).
fof(f_993_3,plain,
! [U_3133,U_3132,U_3131] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3132,U_3131)),U_3133) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3132),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3131,U_3133))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3131,U_3132) ),
inference(definitional_conversion,[status(esa)],[f_993_2]) ).
cnf(f_993_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3132,U_3131)),U_3133) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Nat_OSuc(U_3132),c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3131,U_3133))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3131,U_3132) ),
inference(clausify,[status(thm)],[f_993_3]) ).
fof(f_994_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_994_2,plain,
! [U_3136,U_3135,U_3134] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3136,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3135,U_3134))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3136,U_3134),c_Nat_OSuc(U_3135))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3134,U_3135) ),
inference(variable_rename,[status(thm)],[f_994_1]) ).
fof(f_994_3,plain,
! [U_3134,U_3135,U_3136] :
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3136,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3135,U_3134))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3136,U_3134),c_Nat_OSuc(U_3135))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3134,U_3135) ),
inference(definitional_conversion,[status(esa)],[f_994_2]) ).
cnf(f_994_4,plain,
( c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3136,c_Nat_OSuc(c_Groups_Ominus__class_Ominus(tc_Nat_Onat,U_3135,U_3134))) = c_Groups_Ominus__class_Ominus(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,U_3136,U_3134),c_Nat_OSuc(U_3135))
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3134,U_3135) ),
inference(clausify,[status(thm)],[f_994_3]) ).
fof(f_995_1,plain,
! [V_n_2,V_ma_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_ma_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_ma_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_ma_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_ma_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_995_2,plain,
! [U_3141,U_3140,U_3139,U_3138,U_3137] :
( ( ( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3137),U_3139),U_3140) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3138),U_3139),U_3141)
| U_3140 != 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_3138,U_3137)),U_3139),U_3141) )
& ( U_3140 = 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_3138,U_3137)),U_3139),U_3141)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3137),U_3139),U_3140) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3138),U_3139),U_3141) ) )
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3137,U_3138) ),
inference(variable_rename,[status(thm)],[f_995_1]) ).
fof(f_995_3,plain,
( ! [U_3137,U_3138,U_3139,U_3140,U_3141] :
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3137),U_3139),U_3140) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3138),U_3139),U_3141)
| U_3140 != 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_3138,U_3137)),U_3139),U_3141)
| ~ sP302(U_3137,U_3138,U_3139,U_3140,U_3141) )
& ! [U_3137,U_3138,U_3139,U_3140,U_3141] :
( U_3140 = 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_3138,U_3137)),U_3139),U_3141)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3137),U_3139),U_3140) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3138),U_3139),U_3141)
| ~ sP302(U_3137,U_3138,U_3139,U_3140,U_3141) )
& ! [U_3137,U_3138,U_3139,U_3140,U_3141] :
( sP302(U_3137,U_3138,U_3139,U_3140,U_3141)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3137,U_3138) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP302])],[f_995_2]) ).
cnf(f_995_4,plain,
( sP302(U_3137,U_3138,U_3139,U_3140,U_3141)
| ~ c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,U_3137,U_3138) ),
inference(clausify,[status(thm)],[f_995_3]) ).
cnf(f_995_5,plain,
( U_3140 = 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_3138,U_3137)),U_3139),U_3141)
| c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3137),U_3139),U_3140) != c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3138),U_3139),U_3141)
| ~ sP302(U_3137,U_3138,U_3139,U_3140,U_3141) ),
inference(clausify,[status(thm)],[f_995_3]) ).
cnf(f_995_6,plain,
( c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3137),U_3139),U_3140) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3138),U_3139),U_3141)
| U_3140 != 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_3138,U_3137)),U_3139),U_3141)
| ~ sP302(U_3137,U_3138,U_3139,U_3140,U_3141) ),
inference(clausify,[status(thm)],[f_995_3]) ).
fof(f_996_1,plain,
! [T_1] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__comm__monoid__add]) ).
fof(f_996_2,plain,
! [U_3142] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3142))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3142) ),
inference(variable_rename,[status(thm)],[f_996_1]) ).
fof(f_996_3,plain,
! [U_3142] :
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3142))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3142) ),
inference(definitional_conversion,[status(esa)],[f_996_2]) ).
cnf(f_996_4,plain,
( class_Groups_Ocancel__comm__monoid__add(tc_Polynomial_Opoly(U_3142))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3142) ),
inference(clausify,[status(thm)],[f_996_3]) ).
fof(f_997_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add]) ).
fof(f_997_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_997_1]) ).
cnf(f_997_3,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_997_2]) ).
fof(f_998_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add]) ).
fof(f_998_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_998_1]) ).
cnf(f_998_3,plain,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_998_2]) ).
fof(f_999_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__comm__monoid__add]) ).
fof(f_999_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_999_1]) ).
cnf(f_999_3,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_999_2]) ).
fof(f_1000_1,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__comm__monoid__add]) ).
fof(f_1000_2,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1000_1]) ).
cnf(f_1000_3,plain,
class_Groups_Ocancel__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1000_2]) ).
fof(f_1001_1,plain,
! [T_2,T_1] :
( class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1))
| ~ class_Lattices_Oboolean__algebra(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Lattices_Oboolean__algebra]) ).
fof(f_1001_2,plain,
! [U_3144,U_3143] :
( class_Lattices_Oboolean__algebra(tc_fun(U_3144,U_3143))
| ~ class_Lattices_Oboolean__algebra(U_3143) ),
inference(variable_rename,[status(thm)],[f_1001_1]) ).
fof(f_1001_3,plain,
! [U_3143,U_3144] :
( class_Lattices_Oboolean__algebra(tc_fun(U_3144,U_3143))
| ~ class_Lattices_Oboolean__algebra(U_3143) ),
inference(definitional_conversion,[status(esa)],[f_1001_2]) ).
cnf(f_1001_4,plain,
( class_Lattices_Oboolean__algebra(tc_fun(U_3144,U_3143))
| ~ class_Lattices_Oboolean__algebra(U_3143) ),
inference(clausify,[status(thm)],[f_1001_3]) ).
fof(f_1002_1,plain,
! [T_2,T_1] :
( class_Orderings_Opreorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Opreorder(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Opreorder]) ).
fof(f_1002_2,plain,
! [U_3146,U_3145] :
( class_Orderings_Opreorder(tc_fun(U_3146,U_3145))
| ~ class_Orderings_Opreorder(U_3145) ),
inference(variable_rename,[status(thm)],[f_1002_1]) ).
fof(f_1002_3,plain,
! [U_3146,U_3145] :
( class_Orderings_Opreorder(tc_fun(U_3146,U_3145))
| ~ class_Orderings_Opreorder(U_3145) ),
inference(definitional_conversion,[status(esa)],[f_1002_2]) ).
cnf(f_1002_4,plain,
( class_Orderings_Opreorder(tc_fun(U_3146,U_3145))
| ~ class_Orderings_Opreorder(U_3145) ),
inference(clausify,[status(thm)],[f_1002_3]) ).
fof(f_1003_1,plain,
! [T_2,T_1] :
( class_Orderings_Oorder(tc_fun(T_2,T_1))
| ~ class_Orderings_Oorder(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oorder]) ).
fof(f_1003_2,plain,
! [U_3148,U_3147] :
( class_Orderings_Oorder(tc_fun(U_3148,U_3147))
| ~ class_Orderings_Oorder(U_3147) ),
inference(variable_rename,[status(thm)],[f_1003_1]) ).
fof(f_1003_3,plain,
! [U_3148,U_3147] :
( class_Orderings_Oorder(tc_fun(U_3148,U_3147))
| ~ class_Orderings_Oorder(U_3147) ),
inference(definitional_conversion,[status(esa)],[f_1003_2]) ).
cnf(f_1003_4,plain,
( class_Orderings_Oorder(tc_fun(U_3148,U_3147))
| ~ class_Orderings_Oorder(U_3147) ),
inference(clausify,[status(thm)],[f_1003_3]) ).
fof(f_1004_1,plain,
! [T_2,T_1] :
( class_Orderings_Oord(tc_fun(T_2,T_1))
| ~ class_Orderings_Oord(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Orderings_Oord]) ).
fof(f_1004_2,plain,
! [U_3150,U_3149] :
( class_Orderings_Oord(tc_fun(U_3150,U_3149))
| ~ class_Orderings_Oord(U_3149) ),
inference(variable_rename,[status(thm)],[f_1004_1]) ).
fof(f_1004_3,plain,
! [U_3149,U_3150] :
( class_Orderings_Oord(tc_fun(U_3150,U_3149))
| ~ class_Orderings_Oord(U_3149) ),
inference(definitional_conversion,[status(esa)],[f_1004_2]) ).
cnf(f_1004_4,plain,
( class_Orderings_Oord(tc_fun(U_3150,U_3149))
| ~ class_Orderings_Oord(U_3149) ),
inference(clausify,[status(thm)],[f_1004_3]) ).
fof(f_1005_1,plain,
! [T_2,T_1] :
( class_Groups_Ouminus(tc_fun(T_2,T_1))
| ~ class_Groups_Ouminus(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ouminus]) ).
fof(f_1005_2,plain,
! [U_3152,U_3151] :
( class_Groups_Ouminus(tc_fun(U_3152,U_3151))
| ~ class_Groups_Ouminus(U_3151) ),
inference(variable_rename,[status(thm)],[f_1005_1]) ).
fof(f_1005_3,plain,
! [U_3151,U_3152] :
( class_Groups_Ouminus(tc_fun(U_3152,U_3151))
| ~ class_Groups_Ouminus(U_3151) ),
inference(definitional_conversion,[status(esa)],[f_1005_2]) ).
cnf(f_1005_4,plain,
( class_Groups_Ouminus(tc_fun(U_3152,U_3151))
| ~ class_Groups_Ouminus(U_3151) ),
inference(clausify,[status(thm)],[f_1005_3]) ).
fof(f_1006_1,plain,
! [T_2,T_1] :
( class_Groups_Ominus(tc_fun(T_2,T_1))
| ~ class_Groups_Ominus(T_1) ),
inference(fof_nnf,[status(thm)],[arity_fun__Groups_Ominus]) ).
fof(f_1006_2,plain,
! [U_3154,U_3153] :
( class_Groups_Ominus(tc_fun(U_3154,U_3153))
| ~ class_Groups_Ominus(U_3153) ),
inference(variable_rename,[status(thm)],[f_1006_1]) ).
fof(f_1006_3,plain,
! [U_3153,U_3154] :
( class_Groups_Ominus(tc_fun(U_3154,U_3153))
| ~ class_Groups_Ominus(U_3153) ),
inference(definitional_conversion,[status(esa)],[f_1006_2]) ).
cnf(f_1006_4,plain,
( class_Groups_Ominus(tc_fun(U_3154,U_3153))
| ~ class_Groups_Ominus(U_3153) ),
inference(clausify,[status(thm)],[f_1006_3]) ).
fof(f_1007_1,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(f_1007_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1007_1]) ).
cnf(f_1007_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1007_2]) ).
fof(f_1008_1,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add]) ).
fof(f_1008_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1008_1]) ).
cnf(f_1008_3,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1008_2]) ).
fof(f_1009_1,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le]) ).
fof(f_1009_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1009_1]) ).
cnf(f_1009_3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1009_2]) ).
fof(f_1010_1,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1010_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1010_1]) ).
cnf(f_1010_3,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1010_2]) ).
fof(f_1011_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_1011_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1011_1]) ).
cnf(f_1011_3,plain,
class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1011_2]) ).
fof(f_1012_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__strict]) ).
fof(f_1012_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1012_1]) ).
cnf(f_1012_3,plain,
class_Rings_Olinordered__semiring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1012_2]) ).
fof(f_1013_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_1013_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1013_1]) ).
cnf(f_1013_3,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1013_2]) ).
fof(f_1014_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_1014_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1014_1]) ).
cnf(f_1014_3,plain,
class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1014_2]) ).
fof(f_1015_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_1015_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1015_1]) ).
cnf(f_1015_3,plain,
class_Groups_Oordered__comm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1015_2]) ).
fof(f_1016_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_1016_2,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1016_1]) ).
cnf(f_1016_3,plain,
class_Groups_Olinordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1016_2]) ).
fof(f_1017_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_1017_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1017_1]) ).
cnf(f_1017_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1017_2]) ).
fof(f_1018_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_1018_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1018_1]) ).
cnf(f_1018_3,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1018_2]) ).
fof(f_1019_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__cancel__semiring]) ).
fof(f_1019_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1019_1]) ).
cnf(f_1019_3,plain,
class_Rings_Oordered__cancel__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1019_2]) ).
fof(f_1020_1,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring__strict]) ).
fof(f_1020_2,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1020_1]) ).
cnf(f_1020_3,plain,
class_Rings_Olinordered__ring__strict(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1020_2]) ).
fof(f_1021_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_1021_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1021_1]) ).
cnf(f_1021_3,plain,
class_Rings_Oring__no__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1021_2]) ).
fof(f_1022_1,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__comm__semiring]) ).
fof(f_1022_2,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1022_1]) ).
cnf(f_1022_3,plain,
class_Rings_Oordered__comm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1022_2]) ).
fof(f_1023_1,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring__1]) ).
fof(f_1023_2,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1023_1]) ).
cnf(f_1023_3,plain,
class_Rings_Olinordered__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1023_2]) ).
fof(f_1024_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_1024_2,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1024_1]) ).
cnf(f_1024_3,plain,
class_Groups_Oordered__ab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1024_2]) ).
fof(f_1025_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocancel__semigroup__add]) ).
fof(f_1025_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1025_1]) ).
cnf(f_1025_3,plain,
class_Groups_Ocancel__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1025_2]) ).
fof(f_1026_1,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semiring]) ).
fof(f_1026_2,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1026_1]) ).
cnf(f_1026_3,plain,
class_Rings_Olinordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1026_2]) ).
fof(f_1027_1,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__semidom]) ).
fof(f_1027_2,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1027_1]) ).
cnf(f_1027_3,plain,
class_Rings_Olinordered__semidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1027_2]) ).
fof(f_1028_1,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__mult]) ).
fof(f_1028_2,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1028_1]) ).
cnf(f_1028_3,plain,
class_Groups_Oab__semigroup__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1028_2]) ).
fof(f_1029_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__mult]) ).
fof(f_1029_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1029_1]) ).
cnf(f_1029_3,plain,
class_Groups_Ocomm__monoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1029_2]) ).
fof(f_1030_1,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__semigroup__add]) ).
fof(f_1030_2,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1030_1]) ).
cnf(f_1030_3,plain,
class_Groups_Oab__semigroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1030_2]) ).
fof(f_1031_1,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__semiring]) ).
fof(f_1031_2,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1031_1]) ).
cnf(f_1031_3,plain,
class_Rings_Oordered__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1031_2]) ).
fof(f_1032_1,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring__abs]) ).
fof(f_1032_2,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1032_1]) ).
cnf(f_1032_3,plain,
class_Rings_Oordered__ring__abs(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1032_2]) ).
fof(f_1033_1,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ono__zero__divisors]) ).
fof(f_1033_2,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1033_1]) ).
cnf(f_1033_3,plain,
class_Rings_Ono__zero__divisors(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1033_2]) ).
fof(f_1034_1,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ocomm__monoid__add]) ).
fof(f_1034_2,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1034_1]) ).
cnf(f_1034_3,plain,
class_Groups_Ocomm__monoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1034_2]) ).
fof(f_1035_1,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__ring]) ).
fof(f_1035_2,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1035_1]) ).
cnf(f_1035_3,plain,
class_Rings_Olinordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1035_2]) ).
fof(f_1036_1,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Olinordered__idom]) ).
fof(f_1036_2,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1036_1]) ).
cnf(f_1036_3,plain,
class_Rings_Olinordered__idom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1036_2]) ).
fof(f_1037_1,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__1]) ).
fof(f_1037_2,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1037_1]) ).
cnf(f_1037_3,plain,
class_Rings_Ocomm__semiring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1037_2]) ).
fof(f_1038_1,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring__0]) ).
fof(f_1038_2,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1038_1]) ).
cnf(f_1038_3,plain,
class_Rings_Ocomm__semiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1038_2]) ).
fof(f_1039_1,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__semiring]) ).
fof(f_1039_2,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1039_1]) ).
cnf(f_1039_3,plain,
class_Rings_Ocomm__semiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1039_2]) ).
fof(f_1040_1,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oab__group__add]) ).
fof(f_1040_2,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1040_1]) ).
cnf(f_1040_3,plain,
class_Groups_Oab__group__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1040_2]) ).
fof(f_1041_1,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ozero__neq__one]) ).
fof(f_1041_2,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1041_1]) ).
cnf(f_1041_3,plain,
class_Rings_Ozero__neq__one(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1041_2]) ).
fof(f_1042_1,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oordered__ring]) ).
fof(f_1042_2,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1042_1]) ).
cnf(f_1042_3,plain,
class_Rings_Oordered__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1042_2]) ).
fof(f_1043_1,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Opreorder]) ).
fof(f_1043_2,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1043_1]) ).
cnf(f_1043_3,plain,
class_Orderings_Opreorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1043_2]) ).
fof(f_1044_1,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Olinorder]) ).
fof(f_1044_2,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1044_1]) ).
cnf(f_1044_3,plain,
class_Orderings_Olinorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1044_2]) ).
fof(f_1045_1,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__mult]) ).
fof(f_1045_2,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1045_1]) ).
cnf(f_1045_3,plain,
class_Groups_Omonoid__mult(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1045_2]) ).
fof(f_1046_1,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring__1]) ).
fof(f_1046_2,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1046_1]) ).
cnf(f_1046_3,plain,
class_Rings_Ocomm__ring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1046_2]) ).
fof(f_1047_1,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Omonoid__add]) ).
fof(f_1047_2,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1047_1]) ).
cnf(f_1047_3,plain,
class_Groups_Omonoid__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1047_2]) ).
fof(f_1048_1,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring__0]) ).
fof(f_1048_2,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1048_1]) ).
cnf(f_1048_3,plain,
class_Rings_Osemiring__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1048_2]) ).
fof(f_1049_1,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ogroup__add]) ).
fof(f_1049_2,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1049_1]) ).
cnf(f_1049_3,plain,
class_Groups_Ogroup__add(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1049_2]) ).
fof(f_1050_1,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Omult__zero]) ).
fof(f_1050_2,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1050_1]) ).
cnf(f_1050_3,plain,
class_Rings_Omult__zero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1050_2]) ).
fof(f_1051_1,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Ocomm__ring]) ).
fof(f_1051_2,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1051_1]) ).
cnf(f_1051_3,plain,
class_Rings_Ocomm__ring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1051_2]) ).
fof(f_1052_1,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oorder]) ).
fof(f_1052_2,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1052_1]) ).
cnf(f_1052_3,plain,
class_Orderings_Oorder(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1052_2]) ).
fof(f_1053_1,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Int_Oring__char__0]) ).
fof(f_1053_2,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1053_1]) ).
cnf(f_1053_3,plain,
class_Int_Oring__char__0(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1053_2]) ).
fof(f_1054_1,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Osemiring]) ).
fof(f_1054_2,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1054_1]) ).
cnf(f_1054_3,plain,
class_Rings_Osemiring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1054_2]) ).
fof(f_1055_1,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Orderings_Oord]) ).
fof(f_1055_2,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1055_1]) ).
cnf(f_1055_3,plain,
class_Orderings_Oord(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1055_2]) ).
fof(f_1056_1,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ouminus]) ).
fof(f_1056_2,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1056_1]) ).
cnf(f_1056_3,plain,
class_Groups_Ouminus(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1056_2]) ).
fof(f_1057_1,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Osgn__if]) ).
fof(f_1057_2,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1057_1]) ).
cnf(f_1057_3,plain,
class_Groups_Osgn__if(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1057_2]) ).
fof(f_1058_1,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oabs__if]) ).
fof(f_1058_2,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1058_1]) ).
cnf(f_1058_3,plain,
class_Groups_Oabs__if(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1058_2]) ).
fof(f_1059_1,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring__1]) ).
fof(f_1059_2,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1059_1]) ).
cnf(f_1059_3,plain,
class_Rings_Oring__1(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1059_2]) ).
fof(f_1060_1,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ominus]) ).
fof(f_1060_2,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1060_1]) ).
cnf(f_1060_3,plain,
class_Groups_Ominus(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1060_2]) ).
fof(f_1061_1,plain,
class_Power_Opower(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Power_Opower]) ).
fof(f_1061_2,plain,
class_Power_Opower(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1061_1]) ).
cnf(f_1061_3,plain,
class_Power_Opower(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1061_2]) ).
fof(f_1062_1,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Ozero]) ).
fof(f_1062_2,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1062_1]) ).
cnf(f_1062_3,plain,
class_Groups_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1062_2]) ).
fof(f_1063_1,plain,
class_Rings_Oring(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oring]) ).
fof(f_1063_2,plain,
class_Rings_Oring(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1063_1]) ).
cnf(f_1063_3,plain,
class_Rings_Oring(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1063_2]) ).
fof(f_1064_1,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Oidom]) ).
fof(f_1064_2,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1064_1]) ).
cnf(f_1064_3,plain,
class_Rings_Oidom(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1064_2]) ).
fof(f_1065_1,plain,
class_Groups_Oone(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Groups_Oone]) ).
fof(f_1065_2,plain,
class_Groups_Oone(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1065_1]) ).
cnf(f_1065_3,plain,
class_Groups_Oone(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1065_2]) ).
fof(f_1066_1,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(fof_nnf,[status(thm)],[arity_Int__Oint__Rings_Odvd]) ).
fof(f_1066_2,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(definitional_conversion,[status(esa)],[f_1066_1]) ).
cnf(f_1066_3,plain,
class_Rings_Odvd(tc_Int_Oint),
inference(clausify,[status(thm)],[f_1066_2]) ).
fof(f_1067_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_1067_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1067_1]) ).
cnf(f_1067_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1067_2]) ).
fof(f_1068_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_1068_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1068_1]) ).
cnf(f_1068_3,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1068_2]) ).
fof(f_1069_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_1069_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1069_1]) ).
cnf(f_1069_3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1069_2]) ).
fof(f_1070_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_1070_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1070_1]) ).
cnf(f_1070_3,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1070_2]) ).
fof(f_1071_1,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring__strict]) ).
fof(f_1071_2,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1071_1]) ).
cnf(f_1071_3,plain,
class_Rings_Olinordered__semiring__strict(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1071_2]) ).
fof(f_1072_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_1072_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1072_1]) ).
cnf(f_1072_3,plain,
class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1072_2]) ).
fof(f_1073_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_1073_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1073_1]) ).
cnf(f_1073_3,plain,
class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1073_2]) ).
fof(f_1074_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_1074_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1074_1]) ).
cnf(f_1074_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1074_2]) ).
fof(f_1075_1,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__cancel__semiring]) ).
fof(f_1075_2,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1075_1]) ).
cnf(f_1075_3,plain,
class_Rings_Oordered__cancel__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1075_2]) ).
fof(f_1076_1,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__comm__semiring]) ).
fof(f_1076_2,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1076_1]) ).
cnf(f_1076_3,plain,
class_Rings_Oordered__comm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1076_2]) ).
fof(f_1077_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocancel__semigroup__add]) ).
fof(f_1077_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1077_1]) ).
cnf(f_1077_3,plain,
class_Groups_Ocancel__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1077_2]) ).
fof(f_1078_1,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semiring]) ).
fof(f_1078_2,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1078_1]) ).
cnf(f_1078_3,plain,
class_Rings_Olinordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1078_2]) ).
fof(f_1079_1,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Olinordered__semidom]) ).
fof(f_1079_2,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1079_1]) ).
cnf(f_1079_3,plain,
class_Rings_Olinordered__semidom(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1079_2]) ).
fof(f_1080_1,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__mult]) ).
fof(f_1080_2,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1080_1]) ).
cnf(f_1080_3,plain,
class_Groups_Oab__semigroup__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1080_2]) ).
fof(f_1081_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__mult]) ).
fof(f_1081_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1081_1]) ).
cnf(f_1081_3,plain,
class_Groups_Ocomm__monoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1081_2]) ).
fof(f_1082_1,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oab__semigroup__add]) ).
fof(f_1082_2,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1082_1]) ).
cnf(f_1082_3,plain,
class_Groups_Oab__semigroup__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1082_2]) ).
fof(f_1083_1,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Oordered__semiring]) ).
fof(f_1083_2,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1083_1]) ).
cnf(f_1083_3,plain,
class_Rings_Oordered__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1083_2]) ).
fof(f_1084_1,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ono__zero__divisors]) ).
fof(f_1084_2,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1084_1]) ).
cnf(f_1084_3,plain,
class_Rings_Ono__zero__divisors(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1084_2]) ).
fof(f_1085_1,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ocomm__monoid__add]) ).
fof(f_1085_2,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1085_1]) ).
cnf(f_1085_3,plain,
class_Groups_Ocomm__monoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1085_2]) ).
fof(f_1086_1,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__1]) ).
fof(f_1086_2,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1086_1]) ).
cnf(f_1086_3,plain,
class_Rings_Ocomm__semiring__1(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1086_2]) ).
fof(f_1087_1,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring__0]) ).
fof(f_1087_2,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1087_1]) ).
cnf(f_1087_3,plain,
class_Rings_Ocomm__semiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1087_2]) ).
fof(f_1088_1,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ocomm__semiring]) ).
fof(f_1088_2,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1088_1]) ).
cnf(f_1088_3,plain,
class_Rings_Ocomm__semiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1088_2]) ).
fof(f_1089_1,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Ozero__neq__one]) ).
fof(f_1089_2,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1089_1]) ).
cnf(f_1089_3,plain,
class_Rings_Ozero__neq__one(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1089_2]) ).
fof(f_1090_1,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Opreorder]) ).
fof(f_1090_2,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1090_1]) ).
cnf(f_1090_3,plain,
class_Orderings_Opreorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1090_2]) ).
fof(f_1091_1,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Olinorder]) ).
fof(f_1091_2,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1091_1]) ).
cnf(f_1091_3,plain,
class_Orderings_Olinorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1091_2]) ).
fof(f_1092_1,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__mult]) ).
fof(f_1092_2,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1092_1]) ).
cnf(f_1092_3,plain,
class_Groups_Omonoid__mult(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1092_2]) ).
fof(f_1093_1,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Omonoid__add]) ).
fof(f_1093_2,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1093_1]) ).
cnf(f_1093_3,plain,
class_Groups_Omonoid__add(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1093_2]) ).
fof(f_1094_1,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring__0]) ).
fof(f_1094_2,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1094_1]) ).
cnf(f_1094_3,plain,
class_Rings_Osemiring__0(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1094_2]) ).
fof(f_1095_1,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Omult__zero]) ).
fof(f_1095_2,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1095_1]) ).
cnf(f_1095_3,plain,
class_Rings_Omult__zero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1095_2]) ).
fof(f_1096_1,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oorder]) ).
fof(f_1096_2,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1096_1]) ).
cnf(f_1096_3,plain,
class_Orderings_Oorder(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1096_2]) ).
fof(f_1097_1,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Osemiring]) ).
fof(f_1097_2,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1097_1]) ).
cnf(f_1097_3,plain,
class_Rings_Osemiring(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1097_2]) ).
fof(f_1098_1,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Orderings_Oord]) ).
fof(f_1098_2,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1098_1]) ).
cnf(f_1098_3,plain,
class_Orderings_Oord(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1098_2]) ).
fof(f_1099_1,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ominus]) ).
fof(f_1099_2,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1099_1]) ).
cnf(f_1099_3,plain,
class_Groups_Ominus(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1099_2]) ).
fof(f_1100_1,plain,
class_Power_Opower(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Power_Opower]) ).
fof(f_1100_2,plain,
class_Power_Opower(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1100_1]) ).
cnf(f_1100_3,plain,
class_Power_Opower(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1100_2]) ).
fof(f_1101_1,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Ozero]) ).
fof(f_1101_2,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1101_1]) ).
cnf(f_1101_3,plain,
class_Groups_Ozero(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1101_2]) ).
fof(f_1102_1,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Groups_Oone]) ).
fof(f_1102_2,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1102_1]) ).
cnf(f_1102_3,plain,
class_Groups_Oone(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1102_2]) ).
fof(f_1103_1,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(fof_nnf,[status(thm)],[arity_Nat__Onat__Rings_Odvd]) ).
fof(f_1103_2,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(definitional_conversion,[status(esa)],[f_1103_1]) ).
cnf(f_1103_3,plain,
class_Rings_Odvd(tc_Nat_Onat),
inference(clausify,[status(thm)],[f_1103_2]) ).
fof(f_1104_1,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Lattices_Oboolean__algebra]) ).
fof(f_1104_2,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1104_1]) ).
cnf(f_1104_3,plain,
class_Lattices_Oboolean__algebra(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1104_2]) ).
fof(f_1105_1,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Opreorder]) ).
fof(f_1105_2,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1105_1]) ).
cnf(f_1105_3,plain,
class_Orderings_Opreorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1105_2]) ).
fof(f_1106_1,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oorder]) ).
fof(f_1106_2,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1106_1]) ).
cnf(f_1106_3,plain,
class_Orderings_Oorder(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1106_2]) ).
fof(f_1107_1,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Orderings_Oord]) ).
fof(f_1107_2,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1107_1]) ).
cnf(f_1107_3,plain,
class_Orderings_Oord(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1107_2]) ).
fof(f_1108_1,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ouminus]) ).
fof(f_1108_2,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1108_1]) ).
cnf(f_1108_3,plain,
class_Groups_Ouminus(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1108_2]) ).
fof(f_1109_1,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(fof_nnf,[status(thm)],[arity_HOL__Obool__Groups_Ominus]) ).
fof(f_1109_2,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(definitional_conversion,[status(esa)],[f_1109_1]) ).
cnf(f_1109_3,plain,
class_Groups_Ominus(tc_HOL_Obool),
inference(clausify,[status(thm)],[f_1109_2]) ).
fof(f_1110_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_1110_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1110_1]) ).
cnf(f_1110_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1110_2]) ).
fof(f_1111_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_1111_2,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1111_1]) ).
cnf(f_1111_3,plain,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1111_2]) ).
fof(f_1112_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_1112_2,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1112_1]) ).
cnf(f_1112_3,plain,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1112_2]) ).
fof(f_1113_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_1113_2,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1113_1]) ).
cnf(f_1113_3,plain,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1113_2]) ).
fof(f_1114_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_1114_2,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1114_1]) ).
cnf(f_1114_3,plain,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1114_2]) ).
fof(f_1115_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_1115_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1115_1]) ).
cnf(f_1115_3,plain,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1115_2]) ).
fof(f_1116_1,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__strict]) ).
fof(f_1116_2,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1116_1]) ).
cnf(f_1116_3,plain,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1116_2]) ).
fof(f_1117_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_1117_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1117_1]) ).
cnf(f_1117_3,plain,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1117_2]) ).
fof(f_1118_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_1118_2,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1118_1]) ).
cnf(f_1118_3,plain,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1118_2]) ).
fof(f_1119_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_1119_2,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1119_1]) ).
cnf(f_1119_3,plain,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1119_2]) ).
fof(f_1120_1,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__algebra]) ).
fof(f_1120_2,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1120_1]) ).
cnf(f_1120_3,plain,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1120_2]) ).
fof(f_1121_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_1121_2,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1121_1]) ).
cnf(f_1121_3,plain,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1121_2]) ).
fof(f_1122_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_1122_2,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1122_1]) ).
cnf(f_1122_3,plain,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1122_2]) ).
fof(f_1123_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_1123_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1123_1]) ).
cnf(f_1123_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1123_2]) ).
fof(f_1124_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_1124_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1124_1]) ).
cnf(f_1124_3,plain,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1124_2]) ).
fof(f_1125_1,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__cancel__semiring]) ).
fof(f_1125_2,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1125_1]) ).
cnf(f_1125_3,plain,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1125_2]) ).
fof(f_1126_1,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__RealVector_Oreal__normed__vector]) ).
fof(f_1126_2,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1126_1]) ).
cnf(f_1126_3,plain,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1126_2]) ).
fof(f_1127_1,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring__strict]) ).
fof(f_1127_2,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1127_1]) ).
cnf(f_1127_3,plain,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1127_2]) ).
fof(f_1128_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_1128_2,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1128_1]) ).
cnf(f_1128_3,plain,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1128_2]) ).
fof(f_1129_1,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__comm__semiring]) ).
fof(f_1129_2,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1129_1]) ).
cnf(f_1129_3,plain,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1129_2]) ).
fof(f_1130_1,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring__1]) ).
fof(f_1130_2,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1130_1]) ).
cnf(f_1130_3,plain,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1130_2]) ).
fof(f_1131_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_1131_2,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1131_1]) ).
cnf(f_1131_3,plain,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1131_2]) ).
fof(f_1132_1,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocancel__semigroup__add]) ).
fof(f_1132_2,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1132_1]) ).
cnf(f_1132_3,plain,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1132_2]) ).
fof(f_1133_1,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semiring]) ).
fof(f_1133_2,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1133_1]) ).
cnf(f_1133_3,plain,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1133_2]) ).
fof(f_1134_1,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__semidom]) ).
fof(f_1134_2,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1134_1]) ).
cnf(f_1134_3,plain,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1134_2]) ).
fof(f_1135_1,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__mult]) ).
fof(f_1135_2,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1135_1]) ).
cnf(f_1135_3,plain,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1135_2]) ).
fof(f_1136_1,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__mult]) ).
fof(f_1136_2,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1136_1]) ).
cnf(f_1136_3,plain,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1136_2]) ).
fof(f_1137_1,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__semigroup__add]) ).
fof(f_1137_2,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1137_1]) ).
cnf(f_1137_3,plain,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1137_2]) ).
fof(f_1138_1,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__semiring]) ).
fof(f_1138_2,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1138_1]) ).
cnf(f_1138_3,plain,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1138_2]) ).
fof(f_1139_1,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring__abs]) ).
fof(f_1139_2,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1139_1]) ).
cnf(f_1139_3,plain,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1139_2]) ).
fof(f_1140_1,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ono__zero__divisors]) ).
fof(f_1140_2,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1140_1]) ).
cnf(f_1140_3,plain,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1140_2]) ).
fof(f_1141_1,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ocomm__monoid__add]) ).
fof(f_1141_2,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1141_1]) ).
cnf(f_1141_3,plain,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1141_2]) ).
fof(f_1142_1,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__ring]) ).
fof(f_1142_2,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1142_1]) ).
cnf(f_1142_3,plain,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1142_2]) ).
fof(f_1143_1,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Olinordered__idom]) ).
fof(f_1143_2,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1143_1]) ).
cnf(f_1143_3,plain,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1143_2]) ).
fof(f_1144_1,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__1]) ).
fof(f_1144_2,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1144_1]) ).
cnf(f_1144_3,plain,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1144_2]) ).
fof(f_1145_1,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring__0]) ).
fof(f_1145_2,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1145_1]) ).
cnf(f_1145_3,plain,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1145_2]) ).
fof(f_1146_1,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__semiring]) ).
fof(f_1146_2,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1146_1]) ).
cnf(f_1146_3,plain,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1146_2]) ).
fof(f_1147_1,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oab__group__add]) ).
fof(f_1147_2,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1147_1]) ).
cnf(f_1147_3,plain,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1147_2]) ).
fof(f_1148_1,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ozero__neq__one]) ).
fof(f_1148_2,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1148_1]) ).
cnf(f_1148_3,plain,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1148_2]) ).
fof(f_1149_1,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oordered__ring]) ).
fof(f_1149_2,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1149_1]) ).
cnf(f_1149_3,plain,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1149_2]) ).
fof(f_1150_1,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Opreorder]) ).
fof(f_1150_2,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1150_1]) ).
cnf(f_1150_3,plain,
class_Orderings_Opreorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1150_2]) ).
fof(f_1151_1,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Olinorder]) ).
fof(f_1151_2,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1151_1]) ).
cnf(f_1151_3,plain,
class_Orderings_Olinorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1151_2]) ).
fof(f_1152_1,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__mult]) ).
fof(f_1152_2,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1152_1]) ).
cnf(f_1152_3,plain,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1152_2]) ).
fof(f_1153_1,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring__1]) ).
fof(f_1153_2,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1153_1]) ).
cnf(f_1153_3,plain,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1153_2]) ).
fof(f_1154_1,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Omonoid__add]) ).
fof(f_1154_2,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1154_1]) ).
cnf(f_1154_3,plain,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1154_2]) ).
fof(f_1155_1,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring__0]) ).
fof(f_1155_2,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1155_1]) ).
cnf(f_1155_3,plain,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1155_2]) ).
fof(f_1156_1,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ogroup__add]) ).
fof(f_1156_2,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1156_1]) ).
cnf(f_1156_3,plain,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1156_2]) ).
fof(f_1157_1,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Omult__zero]) ).
fof(f_1157_2,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1157_1]) ).
cnf(f_1157_3,plain,
class_Rings_Omult__zero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1157_2]) ).
fof(f_1158_1,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Ocomm__ring]) ).
fof(f_1158_2,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1158_1]) ).
cnf(f_1158_3,plain,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1158_2]) ).
fof(f_1159_1,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oorder]) ).
fof(f_1159_2,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1159_1]) ).
cnf(f_1159_3,plain,
class_Orderings_Oorder(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1159_2]) ).
fof(f_1160_1,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Int_Oring__char__0]) ).
fof(f_1160_2,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1160_1]) ).
cnf(f_1160_3,plain,
class_Int_Oring__char__0(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1160_2]) ).
fof(f_1161_1,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Osemiring]) ).
fof(f_1161_2,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1161_1]) ).
cnf(f_1161_3,plain,
class_Rings_Osemiring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1161_2]) ).
fof(f_1162_1,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Orderings_Oord]) ).
fof(f_1162_2,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1162_1]) ).
cnf(f_1162_3,plain,
class_Orderings_Oord(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1162_2]) ).
fof(f_1163_1,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ouminus]) ).
fof(f_1163_2,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1163_1]) ).
cnf(f_1163_3,plain,
class_Groups_Ouminus(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1163_2]) ).
fof(f_1164_1,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Osgn__if]) ).
fof(f_1164_2,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1164_1]) ).
cnf(f_1164_3,plain,
class_Groups_Osgn__if(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1164_2]) ).
fof(f_1165_1,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oabs__if]) ).
fof(f_1165_2,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1165_1]) ).
cnf(f_1165_3,plain,
class_Groups_Oabs__if(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1165_2]) ).
fof(f_1166_1,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring__1]) ).
fof(f_1166_2,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1166_1]) ).
cnf(f_1166_3,plain,
class_Rings_Oring__1(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1166_2]) ).
fof(f_1167_1,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ominus]) ).
fof(f_1167_2,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1167_1]) ).
cnf(f_1167_3,plain,
class_Groups_Ominus(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1167_2]) ).
fof(f_1168_1,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Power_Opower]) ).
fof(f_1168_2,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1168_1]) ).
cnf(f_1168_3,plain,
class_Power_Opower(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1168_2]) ).
fof(f_1169_1,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Ozero]) ).
fof(f_1169_2,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1169_1]) ).
cnf(f_1169_3,plain,
class_Groups_Ozero(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1169_2]) ).
fof(f_1170_1,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oring]) ).
fof(f_1170_2,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1170_1]) ).
cnf(f_1170_3,plain,
class_Rings_Oring(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1170_2]) ).
fof(f_1171_1,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Oidom]) ).
fof(f_1171_2,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1171_1]) ).
cnf(f_1171_3,plain,
class_Rings_Oidom(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1171_2]) ).
fof(f_1172_1,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Groups_Oone]) ).
fof(f_1172_2,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1172_1]) ).
cnf(f_1172_3,plain,
class_Groups_Oone(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1172_2]) ).
fof(f_1173_1,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(fof_nnf,[status(thm)],[arity_RealDef__Oreal__Rings_Odvd]) ).
fof(f_1173_2,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(definitional_conversion,[status(esa)],[f_1173_1]) ).
cnf(f_1173_3,plain,
class_Rings_Odvd(tc_RealDef_Oreal),
inference(clausify,[status(thm)],[f_1173_2]) ).
fof(f_1174_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_1174_2,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1174_1]) ).
cnf(f_1174_3,plain,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1174_2]) ).
fof(f_1175_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_1175_2,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1175_1]) ).
cnf(f_1175_3,plain,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1175_2]) ).
fof(f_1176_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_1176_2,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1176_1]) ).
cnf(f_1176_3,plain,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1176_2]) ).
fof(f_1177_1,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra]) ).
fof(f_1177_2,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1177_1]) ).
cnf(f_1177_3,plain,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1177_2]) ).
fof(f_1178_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_1178_2,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1178_1]) ).
cnf(f_1178_3,plain,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1178_2]) ).
fof(f_1179_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_1179_2,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1179_1]) ).
cnf(f_1179_3,plain,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1179_2]) ).
fof(f_1180_1,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__RealVector_Oreal__normed__vector]) ).
fof(f_1180_2,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1180_1]) ).
cnf(f_1180_3,plain,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1180_2]) ).
fof(f_1181_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_1181_2,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1181_1]) ).
cnf(f_1181_3,plain,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1181_2]) ).
fof(f_1182_1,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add]) ).
fof(f_1182_2,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1182_1]) ).
cnf(f_1182_3,plain,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1182_2]) ).
fof(f_1183_1,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__mult]) ).
fof(f_1183_2,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1183_1]) ).
cnf(f_1183_3,plain,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1183_2]) ).
fof(f_1184_1,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult]) ).
fof(f_1184_2,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1184_1]) ).
cnf(f_1184_3,plain,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1184_2]) ).
fof(f_1185_1,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__semigroup__add]) ).
fof(f_1185_2,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1185_1]) ).
cnf(f_1185_3,plain,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1185_2]) ).
fof(f_1186_1,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ono__zero__divisors]) ).
fof(f_1186_2,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1186_1]) ).
cnf(f_1186_3,plain,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1186_2]) ).
fof(f_1187_1,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ocomm__monoid__add]) ).
fof(f_1187_2,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1187_1]) ).
cnf(f_1187_3,plain,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1187_2]) ).
fof(f_1188_1,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__1]) ).
fof(f_1188_2,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1188_1]) ).
cnf(f_1188_3,plain,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1188_2]) ).
fof(f_1189_1,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring__0]) ).
fof(f_1189_2,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1189_1]) ).
cnf(f_1189_3,plain,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1189_2]) ).
fof(f_1190_1,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__semiring]) ).
fof(f_1190_2,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1190_1]) ).
cnf(f_1190_3,plain,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1190_2]) ).
fof(f_1191_1,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oab__group__add]) ).
fof(f_1191_2,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1191_1]) ).
cnf(f_1191_3,plain,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1191_2]) ).
fof(f_1192_1,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ozero__neq__one]) ).
fof(f_1192_2,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1192_1]) ).
cnf(f_1192_3,plain,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1192_2]) ).
fof(f_1193_1,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__mult]) ).
fof(f_1193_2,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1193_1]) ).
cnf(f_1193_3,plain,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1193_2]) ).
fof(f_1194_1,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring__1]) ).
fof(f_1194_2,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1194_1]) ).
cnf(f_1194_3,plain,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1194_2]) ).
fof(f_1195_1,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Omonoid__add]) ).
fof(f_1195_2,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1195_1]) ).
cnf(f_1195_3,plain,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1195_2]) ).
fof(f_1196_1,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring__0]) ).
fof(f_1196_2,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1196_1]) ).
cnf(f_1196_3,plain,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1196_2]) ).
fof(f_1197_1,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ogroup__add]) ).
fof(f_1197_2,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1197_1]) ).
cnf(f_1197_3,plain,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1197_2]) ).
fof(f_1198_1,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Omult__zero]) ).
fof(f_1198_2,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1198_1]) ).
cnf(f_1198_3,plain,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1198_2]) ).
fof(f_1199_1,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Ocomm__ring]) ).
fof(f_1199_2,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1199_1]) ).
cnf(f_1199_3,plain,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1199_2]) ).
fof(f_1200_1,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Int_Oring__char__0]) ).
fof(f_1200_2,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1200_1]) ).
cnf(f_1200_3,plain,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1200_2]) ).
fof(f_1201_1,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Osemiring]) ).
fof(f_1201_2,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1201_1]) ).
cnf(f_1201_3,plain,
class_Rings_Osemiring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1201_2]) ).
fof(f_1202_1,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ouminus]) ).
fof(f_1202_2,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1202_1]) ).
cnf(f_1202_3,plain,
class_Groups_Ouminus(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1202_2]) ).
fof(f_1203_1,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring__1]) ).
fof(f_1203_2,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1203_1]) ).
cnf(f_1203_3,plain,
class_Rings_Oring__1(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1203_2]) ).
fof(f_1204_1,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ominus]) ).
fof(f_1204_2,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1204_1]) ).
cnf(f_1204_3,plain,
class_Groups_Ominus(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1204_2]) ).
fof(f_1205_1,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Power_Opower]) ).
fof(f_1205_2,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1205_1]) ).
cnf(f_1205_3,plain,
class_Power_Opower(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1205_2]) ).
fof(f_1206_1,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Ozero]) ).
fof(f_1206_2,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1206_1]) ).
cnf(f_1206_3,plain,
class_Groups_Ozero(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1206_2]) ).
fof(f_1207_1,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oring]) ).
fof(f_1207_2,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1207_1]) ).
cnf(f_1207_3,plain,
class_Rings_Oring(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1207_2]) ).
fof(f_1208_1,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Oidom]) ).
fof(f_1208_2,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1208_1]) ).
cnf(f_1208_3,plain,
class_Rings_Oidom(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1208_2]) ).
fof(f_1209_1,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Groups_Oone]) ).
fof(f_1209_2,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1209_1]) ).
cnf(f_1209_3,plain,
class_Groups_Oone(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1209_2]) ).
fof(f_1210_1,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(fof_nnf,[status(thm)],[arity_Complex__Ocomplex__Rings_Odvd]) ).
fof(f_1210_2,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(definitional_conversion,[status(esa)],[f_1210_1]) ).
cnf(f_1210_3,plain,
class_Rings_Odvd(tc_Complex_Ocomplex),
inference(clausify,[status(thm)],[f_1210_2]) ).
fof(f_1211_1,plain,
! [T_1] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct]) ).
fof(f_1211_2,plain,
! [U_3155] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3155))
| ~ class_Rings_Oidom(U_3155) ),
inference(variable_rename,[status(thm)],[f_1211_1]) ).
fof(f_1211_3,plain,
! [U_3155] :
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3155))
| ~ class_Rings_Oidom(U_3155) ),
inference(definitional_conversion,[status(esa)],[f_1211_2]) ).
cnf(f_1211_4,plain,
( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Polynomial_Opoly(U_3155))
| ~ class_Rings_Oidom(U_3155) ),
inference(clausify,[status(thm)],[f_1211_3]) ).
fof(f_1212_1,plain,
! [T_1] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__cancel__ab__semigroup__add]) ).
fof(f_1212_2,plain,
! [U_3156] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3156))
| ~ class_Rings_Olinordered__idom(U_3156) ),
inference(variable_rename,[status(thm)],[f_1212_1]) ).
fof(f_1212_3,plain,
! [U_3156] :
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3156))
| ~ class_Rings_Olinordered__idom(U_3156) ),
inference(definitional_conversion,[status(esa)],[f_1212_2]) ).
cnf(f_1212_4,plain,
( class_Groups_Oordered__cancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3156))
| ~ class_Rings_Olinordered__idom(U_3156) ),
inference(clausify,[status(thm)],[f_1212_3]) ).
fof(f_1213_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add__imp__le]) ).
fof(f_1213_2,plain,
! [U_3157] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3157))
| ~ class_Rings_Olinordered__idom(U_3157) ),
inference(variable_rename,[status(thm)],[f_1213_1]) ).
fof(f_1213_3,plain,
! [U_3157] :
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3157))
| ~ class_Rings_Olinordered__idom(U_3157) ),
inference(definitional_conversion,[status(esa)],[f_1213_2]) ).
cnf(f_1213_4,plain,
( class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Polynomial_Opoly(U_3157))
| ~ class_Rings_Olinordered__idom(U_3157) ),
inference(clausify,[status(thm)],[f_1213_3]) ).
fof(f_1214_1,plain,
! [T_1] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__comm__semiring__strict]) ).
fof(f_1214_2,plain,
! [U_3158] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3158))
| ~ class_Rings_Olinordered__idom(U_3158) ),
inference(variable_rename,[status(thm)],[f_1214_1]) ).
fof(f_1214_3,plain,
! [U_3158] :
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3158))
| ~ class_Rings_Olinordered__idom(U_3158) ),
inference(definitional_conversion,[status(esa)],[f_1214_2]) ).
cnf(f_1214_4,plain,
( class_Rings_Olinordered__comm__semiring__strict(tc_Polynomial_Opoly(U_3158))
| ~ class_Rings_Olinordered__idom(U_3158) ),
inference(clausify,[status(thm)],[f_1214_3]) ).
fof(f_1215_1,plain,
! [T_1] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1__strict]) ).
fof(f_1215_2,plain,
! [U_3159] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3159))
| ~ class_Rings_Olinordered__idom(U_3159) ),
inference(variable_rename,[status(thm)],[f_1215_1]) ).
fof(f_1215_3,plain,
! [U_3159] :
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3159))
| ~ class_Rings_Olinordered__idom(U_3159) ),
inference(definitional_conversion,[status(esa)],[f_1215_2]) ).
cnf(f_1215_4,plain,
( class_Rings_Olinordered__semiring__1__strict(tc_Polynomial_Opoly(U_3159))
| ~ class_Rings_Olinordered__idom(U_3159) ),
inference(clausify,[status(thm)],[f_1215_3]) ).
fof(f_1216_1,plain,
! [T_1] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__strict]) ).
fof(f_1216_2,plain,
! [U_3160] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3160))
| ~ class_Rings_Olinordered__idom(U_3160) ),
inference(variable_rename,[status(thm)],[f_1216_1]) ).
fof(f_1216_3,plain,
! [U_3160] :
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3160))
| ~ class_Rings_Olinordered__idom(U_3160) ),
inference(definitional_conversion,[status(esa)],[f_1216_2]) ).
cnf(f_1216_4,plain,
( class_Rings_Olinordered__semiring__strict(tc_Polynomial_Opoly(U_3160))
| ~ class_Rings_Olinordered__idom(U_3160) ),
inference(clausify,[status(thm)],[f_1216_3]) ).
fof(f_1217_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__semigroup__add]) ).
fof(f_1217_2,plain,
! [U_3161] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3161))
| ~ class_Rings_Olinordered__idom(U_3161) ),
inference(variable_rename,[status(thm)],[f_1217_1]) ).
fof(f_1217_3,plain,
! [U_3161] :
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3161))
| ~ class_Rings_Olinordered__idom(U_3161) ),
inference(definitional_conversion,[status(esa)],[f_1217_2]) ).
cnf(f_1217_4,plain,
( class_Groups_Oordered__ab__semigroup__add(tc_Polynomial_Opoly(U_3161))
| ~ class_Rings_Olinordered__idom(U_3161) ),
inference(clausify,[status(thm)],[f_1217_3]) ).
fof(f_1218_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add__abs]) ).
fof(f_1218_2,plain,
! [U_3162] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3162))
| ~ class_Rings_Olinordered__idom(U_3162) ),
inference(variable_rename,[status(thm)],[f_1218_1]) ).
fof(f_1218_3,plain,
! [U_3162] :
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3162))
| ~ class_Rings_Olinordered__idom(U_3162) ),
inference(definitional_conversion,[status(esa)],[f_1218_2]) ).
cnf(f_1218_4,plain,
( class_Groups_Oordered__ab__group__add__abs(tc_Polynomial_Opoly(U_3162))
| ~ class_Rings_Olinordered__idom(U_3162) ),
inference(clausify,[status(thm)],[f_1218_3]) ).
fof(f_1219_1,plain,
! [T_1] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__comm__monoid__add]) ).
fof(f_1219_2,plain,
! [U_3163] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3163))
| ~ class_Rings_Olinordered__idom(U_3163) ),
inference(variable_rename,[status(thm)],[f_1219_1]) ).
fof(f_1219_3,plain,
! [U_3163] :
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3163))
| ~ class_Rings_Olinordered__idom(U_3163) ),
inference(definitional_conversion,[status(esa)],[f_1219_2]) ).
cnf(f_1219_4,plain,
( class_Groups_Oordered__comm__monoid__add(tc_Polynomial_Opoly(U_3163))
| ~ class_Rings_Olinordered__idom(U_3163) ),
inference(clausify,[status(thm)],[f_1219_3]) ).
fof(f_1220_1,plain,
! [T_1] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Olinordered__ab__group__add]) ).
fof(f_1220_2,plain,
! [U_3164] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3164))
| ~ class_Rings_Olinordered__idom(U_3164) ),
inference(variable_rename,[status(thm)],[f_1220_1]) ).
fof(f_1220_3,plain,
! [U_3164] :
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3164))
| ~ class_Rings_Olinordered__idom(U_3164) ),
inference(definitional_conversion,[status(esa)],[f_1220_2]) ).
cnf(f_1220_4,plain,
( class_Groups_Olinordered__ab__group__add(tc_Polynomial_Opoly(U_3164))
| ~ class_Rings_Olinordered__idom(U_3164) ),
inference(clausify,[status(thm)],[f_1220_3]) ).
fof(f_1221_1,plain,
! [T_1] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__ab__semigroup__add]) ).
fof(f_1221_2,plain,
! [U_3165] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3165))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3165) ),
inference(variable_rename,[status(thm)],[f_1221_1]) ).
fof(f_1221_3,plain,
! [U_3165] :
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3165))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3165) ),
inference(definitional_conversion,[status(esa)],[f_1221_2]) ).
cnf(f_1221_4,plain,
( class_Groups_Ocancel__ab__semigroup__add(tc_Polynomial_Opoly(U_3165))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3165) ),
inference(clausify,[status(thm)],[f_1221_3]) ).
fof(f_1222_1,plain,
! [T_1] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1__no__zero__divisors]) ).
fof(f_1222_2,plain,
! [U_3166] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3166))
| ~ class_Rings_Oidom(U_3166) ),
inference(variable_rename,[status(thm)],[f_1222_1]) ).
fof(f_1222_3,plain,
! [U_3166] :
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3166))
| ~ class_Rings_Oidom(U_3166) ),
inference(definitional_conversion,[status(esa)],[f_1222_2]) ).
cnf(f_1222_4,plain,
( class_Rings_Oring__1__no__zero__divisors(tc_Polynomial_Opoly(U_3166))
| ~ class_Rings_Oidom(U_3166) ),
inference(clausify,[status(thm)],[f_1222_3]) ).
fof(f_1223_1,plain,
! [T_1] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__cancel__semiring]) ).
fof(f_1223_2,plain,
! [U_3167] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3167))
| ~ class_Rings_Olinordered__idom(U_3167) ),
inference(variable_rename,[status(thm)],[f_1223_1]) ).
fof(f_1223_3,plain,
! [U_3167] :
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3167))
| ~ class_Rings_Olinordered__idom(U_3167) ),
inference(definitional_conversion,[status(esa)],[f_1223_2]) ).
cnf(f_1223_4,plain,
( class_Rings_Oordered__cancel__semiring(tc_Polynomial_Opoly(U_3167))
| ~ class_Rings_Olinordered__idom(U_3167) ),
inference(clausify,[status(thm)],[f_1223_3]) ).
fof(f_1224_1,plain,
! [T_1] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring__strict]) ).
fof(f_1224_2,plain,
! [U_3168] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3168))
| ~ class_Rings_Olinordered__idom(U_3168) ),
inference(variable_rename,[status(thm)],[f_1224_1]) ).
fof(f_1224_3,plain,
! [U_3168] :
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3168))
| ~ class_Rings_Olinordered__idom(U_3168) ),
inference(definitional_conversion,[status(esa)],[f_1224_2]) ).
cnf(f_1224_4,plain,
( class_Rings_Olinordered__ring__strict(tc_Polynomial_Opoly(U_3168))
| ~ class_Rings_Olinordered__idom(U_3168) ),
inference(clausify,[status(thm)],[f_1224_3]) ).
fof(f_1225_1,plain,
! [T_1] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__no__zero__divisors]) ).
fof(f_1225_2,plain,
! [U_3169] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3169))
| ~ class_Rings_Oidom(U_3169) ),
inference(variable_rename,[status(thm)],[f_1225_1]) ).
fof(f_1225_3,plain,
! [U_3169] :
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3169))
| ~ class_Rings_Oidom(U_3169) ),
inference(definitional_conversion,[status(esa)],[f_1225_2]) ).
cnf(f_1225_4,plain,
( class_Rings_Oring__no__zero__divisors(tc_Polynomial_Opoly(U_3169))
| ~ class_Rings_Oidom(U_3169) ),
inference(clausify,[status(thm)],[f_1225_3]) ).
fof(f_1226_1,plain,
! [T_1] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__comm__semiring]) ).
fof(f_1226_2,plain,
! [U_3170] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3170))
| ~ class_Rings_Olinordered__idom(U_3170) ),
inference(variable_rename,[status(thm)],[f_1226_1]) ).
fof(f_1226_3,plain,
! [U_3170] :
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3170))
| ~ class_Rings_Olinordered__idom(U_3170) ),
inference(definitional_conversion,[status(esa)],[f_1226_2]) ).
cnf(f_1226_4,plain,
( class_Rings_Oordered__comm__semiring(tc_Polynomial_Opoly(U_3170))
| ~ class_Rings_Olinordered__idom(U_3170) ),
inference(clausify,[status(thm)],[f_1226_3]) ).
fof(f_1227_1,plain,
! [T_1] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring__1]) ).
fof(f_1227_2,plain,
! [U_3171] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3171))
| ~ class_Rings_Olinordered__idom(U_3171) ),
inference(variable_rename,[status(thm)],[f_1227_1]) ).
fof(f_1227_3,plain,
! [U_3171] :
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3171))
| ~ class_Rings_Olinordered__idom(U_3171) ),
inference(definitional_conversion,[status(esa)],[f_1227_2]) ).
cnf(f_1227_4,plain,
( class_Rings_Olinordered__semiring__1(tc_Polynomial_Opoly(U_3171))
| ~ class_Rings_Olinordered__idom(U_3171) ),
inference(clausify,[status(thm)],[f_1227_3]) ).
fof(f_1228_1,plain,
! [T_1] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oordered__ab__group__add]) ).
fof(f_1228_2,plain,
! [U_3172] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3172))
| ~ class_Rings_Olinordered__idom(U_3172) ),
inference(variable_rename,[status(thm)],[f_1228_1]) ).
fof(f_1228_3,plain,
! [U_3172] :
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3172))
| ~ class_Rings_Olinordered__idom(U_3172) ),
inference(definitional_conversion,[status(esa)],[f_1228_2]) ).
cnf(f_1228_4,plain,
( class_Groups_Oordered__ab__group__add(tc_Polynomial_Opoly(U_3172))
| ~ class_Rings_Olinordered__idom(U_3172) ),
inference(clausify,[status(thm)],[f_1228_3]) ).
fof(f_1229_1,plain,
! [T_1] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocancel__comm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocancel__semigroup__add]) ).
fof(f_1229_2,plain,
! [U_3173] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3173))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3173) ),
inference(variable_rename,[status(thm)],[f_1229_1]) ).
fof(f_1229_3,plain,
! [U_3173] :
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3173))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3173) ),
inference(definitional_conversion,[status(esa)],[f_1229_2]) ).
cnf(f_1229_4,plain,
( class_Groups_Ocancel__semigroup__add(tc_Polynomial_Opoly(U_3173))
| ~ class_Groups_Ocancel__comm__monoid__add(U_3173) ),
inference(clausify,[status(thm)],[f_1229_3]) ).
fof(f_1230_1,plain,
! [T_1] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semiring]) ).
fof(f_1230_2,plain,
! [U_3174] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3174))
| ~ class_Rings_Olinordered__idom(U_3174) ),
inference(variable_rename,[status(thm)],[f_1230_1]) ).
fof(f_1230_3,plain,
! [U_3174] :
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3174))
| ~ class_Rings_Olinordered__idom(U_3174) ),
inference(definitional_conversion,[status(esa)],[f_1230_2]) ).
cnf(f_1230_4,plain,
( class_Rings_Olinordered__semiring(tc_Polynomial_Opoly(U_3174))
| ~ class_Rings_Olinordered__idom(U_3174) ),
inference(clausify,[status(thm)],[f_1230_3]) ).
fof(f_1231_1,plain,
! [T_1] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__semidom]) ).
fof(f_1231_2,plain,
! [U_3175] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3175))
| ~ class_Rings_Olinordered__idom(U_3175) ),
inference(variable_rename,[status(thm)],[f_1231_1]) ).
fof(f_1231_3,plain,
! [U_3175] :
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3175))
| ~ class_Rings_Olinordered__idom(U_3175) ),
inference(definitional_conversion,[status(esa)],[f_1231_2]) ).
cnf(f_1231_4,plain,
( class_Rings_Olinordered__semidom(tc_Polynomial_Opoly(U_3175))
| ~ class_Rings_Olinordered__idom(U_3175) ),
inference(clausify,[status(thm)],[f_1231_3]) ).
fof(f_1232_1,plain,
! [T_1] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__mult]) ).
fof(f_1232_2,plain,
! [U_3176] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3176))
| ~ class_Rings_Ocomm__semiring__0(U_3176) ),
inference(variable_rename,[status(thm)],[f_1232_1]) ).
fof(f_1232_3,plain,
! [U_3176] :
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3176))
| ~ class_Rings_Ocomm__semiring__0(U_3176) ),
inference(definitional_conversion,[status(esa)],[f_1232_2]) ).
cnf(f_1232_4,plain,
( class_Groups_Oab__semigroup__mult(tc_Polynomial_Opoly(U_3176))
| ~ class_Rings_Ocomm__semiring__0(U_3176) ),
inference(clausify,[status(thm)],[f_1232_3]) ).
fof(f_1233_1,plain,
! [T_1] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__mult]) ).
fof(f_1233_2,plain,
! [U_3177] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3177))
| ~ class_Rings_Ocomm__semiring__1(U_3177) ),
inference(variable_rename,[status(thm)],[f_1233_1]) ).
fof(f_1233_3,plain,
! [U_3177] :
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3177))
| ~ class_Rings_Ocomm__semiring__1(U_3177) ),
inference(definitional_conversion,[status(esa)],[f_1233_2]) ).
cnf(f_1233_4,plain,
( class_Groups_Ocomm__monoid__mult(tc_Polynomial_Opoly(U_3177))
| ~ class_Rings_Ocomm__semiring__1(U_3177) ),
inference(clausify,[status(thm)],[f_1233_3]) ).
fof(f_1234_1,plain,
! [T_1] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocomm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__semigroup__add]) ).
fof(f_1234_2,plain,
! [U_3178] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3178))
| ~ class_Groups_Ocomm__monoid__add(U_3178) ),
inference(variable_rename,[status(thm)],[f_1234_1]) ).
fof(f_1234_3,plain,
! [U_3178] :
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3178))
| ~ class_Groups_Ocomm__monoid__add(U_3178) ),
inference(definitional_conversion,[status(esa)],[f_1234_2]) ).
cnf(f_1234_4,plain,
( class_Groups_Oab__semigroup__add(tc_Polynomial_Opoly(U_3178))
| ~ class_Groups_Ocomm__monoid__add(U_3178) ),
inference(clausify,[status(thm)],[f_1234_3]) ).
fof(f_1235_1,plain,
! [T_1] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__semiring]) ).
fof(f_1235_2,plain,
! [U_3179] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3179))
| ~ class_Rings_Olinordered__idom(U_3179) ),
inference(variable_rename,[status(thm)],[f_1235_1]) ).
fof(f_1235_3,plain,
! [U_3179] :
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3179))
| ~ class_Rings_Olinordered__idom(U_3179) ),
inference(definitional_conversion,[status(esa)],[f_1235_2]) ).
cnf(f_1235_4,plain,
( class_Rings_Oordered__semiring(tc_Polynomial_Opoly(U_3179))
| ~ class_Rings_Olinordered__idom(U_3179) ),
inference(clausify,[status(thm)],[f_1235_3]) ).
fof(f_1236_1,plain,
! [T_1] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring__abs]) ).
fof(f_1236_2,plain,
! [U_3180] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3180))
| ~ class_Rings_Olinordered__idom(U_3180) ),
inference(variable_rename,[status(thm)],[f_1236_1]) ).
fof(f_1236_3,plain,
! [U_3180] :
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3180))
| ~ class_Rings_Olinordered__idom(U_3180) ),
inference(definitional_conversion,[status(esa)],[f_1236_2]) ).
cnf(f_1236_4,plain,
( class_Rings_Oordered__ring__abs(tc_Polynomial_Opoly(U_3180))
| ~ class_Rings_Olinordered__idom(U_3180) ),
inference(clausify,[status(thm)],[f_1236_3]) ).
fof(f_1237_1,plain,
! [T_1] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ono__zero__divisors]) ).
fof(f_1237_2,plain,
! [U_3181] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3181))
| ~ class_Rings_Oidom(U_3181) ),
inference(variable_rename,[status(thm)],[f_1237_1]) ).
fof(f_1237_3,plain,
! [U_3181] :
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3181))
| ~ class_Rings_Oidom(U_3181) ),
inference(definitional_conversion,[status(esa)],[f_1237_2]) ).
cnf(f_1237_4,plain,
( class_Rings_Ono__zero__divisors(tc_Polynomial_Opoly(U_3181))
| ~ class_Rings_Oidom(U_3181) ),
inference(clausify,[status(thm)],[f_1237_3]) ).
fof(f_1238_1,plain,
! [T_1] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocomm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ocomm__monoid__add]) ).
fof(f_1238_2,plain,
! [U_3182] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3182))
| ~ class_Groups_Ocomm__monoid__add(U_3182) ),
inference(variable_rename,[status(thm)],[f_1238_1]) ).
fof(f_1238_3,plain,
! [U_3182] :
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3182))
| ~ class_Groups_Ocomm__monoid__add(U_3182) ),
inference(definitional_conversion,[status(esa)],[f_1238_2]) ).
cnf(f_1238_4,plain,
( class_Groups_Ocomm__monoid__add(tc_Polynomial_Opoly(U_3182))
| ~ class_Groups_Ocomm__monoid__add(U_3182) ),
inference(clausify,[status(thm)],[f_1238_3]) ).
fof(f_1239_1,plain,
! [T_1] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__ring]) ).
fof(f_1239_2,plain,
! [U_3183] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3183))
| ~ class_Rings_Olinordered__idom(U_3183) ),
inference(variable_rename,[status(thm)],[f_1239_1]) ).
fof(f_1239_3,plain,
! [U_3183] :
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3183))
| ~ class_Rings_Olinordered__idom(U_3183) ),
inference(definitional_conversion,[status(esa)],[f_1239_2]) ).
cnf(f_1239_4,plain,
( class_Rings_Olinordered__ring(tc_Polynomial_Opoly(U_3183))
| ~ class_Rings_Olinordered__idom(U_3183) ),
inference(clausify,[status(thm)],[f_1239_3]) ).
fof(f_1240_1,plain,
! [T_1] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Olinordered__idom]) ).
fof(f_1240_2,plain,
! [U_3184] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3184))
| ~ class_Rings_Olinordered__idom(U_3184) ),
inference(variable_rename,[status(thm)],[f_1240_1]) ).
fof(f_1240_3,plain,
! [U_3184] :
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3184))
| ~ class_Rings_Olinordered__idom(U_3184) ),
inference(definitional_conversion,[status(esa)],[f_1240_2]) ).
cnf(f_1240_4,plain,
( class_Rings_Olinordered__idom(tc_Polynomial_Opoly(U_3184))
| ~ class_Rings_Olinordered__idom(U_3184) ),
inference(clausify,[status(thm)],[f_1240_3]) ).
fof(f_1241_1,plain,
! [T_1] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__1]) ).
fof(f_1241_2,plain,
! [U_3185] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3185))
| ~ class_Rings_Ocomm__semiring__1(U_3185) ),
inference(variable_rename,[status(thm)],[f_1241_1]) ).
fof(f_1241_3,plain,
! [U_3185] :
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3185))
| ~ class_Rings_Ocomm__semiring__1(U_3185) ),
inference(definitional_conversion,[status(esa)],[f_1241_2]) ).
cnf(f_1241_4,plain,
( class_Rings_Ocomm__semiring__1(tc_Polynomial_Opoly(U_3185))
| ~ class_Rings_Ocomm__semiring__1(U_3185) ),
inference(clausify,[status(thm)],[f_1241_3]) ).
fof(f_1242_1,plain,
! [T_1] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring__0]) ).
fof(f_1242_2,plain,
! [U_3186] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3186))
| ~ class_Rings_Ocomm__semiring__0(U_3186) ),
inference(variable_rename,[status(thm)],[f_1242_1]) ).
fof(f_1242_3,plain,
! [U_3186] :
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3186))
| ~ class_Rings_Ocomm__semiring__0(U_3186) ),
inference(definitional_conversion,[status(esa)],[f_1242_2]) ).
cnf(f_1242_4,plain,
( class_Rings_Ocomm__semiring__0(tc_Polynomial_Opoly(U_3186))
| ~ class_Rings_Ocomm__semiring__0(U_3186) ),
inference(clausify,[status(thm)],[f_1242_3]) ).
fof(f_1243_1,plain,
! [T_1] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__semiring]) ).
fof(f_1243_2,plain,
! [U_3187] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3187))
| ~ class_Rings_Ocomm__semiring__0(U_3187) ),
inference(variable_rename,[status(thm)],[f_1243_1]) ).
fof(f_1243_3,plain,
! [U_3187] :
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3187))
| ~ class_Rings_Ocomm__semiring__0(U_3187) ),
inference(definitional_conversion,[status(esa)],[f_1243_2]) ).
cnf(f_1243_4,plain,
( class_Rings_Ocomm__semiring(tc_Polynomial_Opoly(U_3187))
| ~ class_Rings_Ocomm__semiring__0(U_3187) ),
inference(clausify,[status(thm)],[f_1243_3]) ).
fof(f_1244_1,plain,
! [T_1] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oab__group__add]) ).
fof(f_1244_2,plain,
! [U_3188] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3188))
| ~ class_Groups_Oab__group__add(U_3188) ),
inference(variable_rename,[status(thm)],[f_1244_1]) ).
fof(f_1244_3,plain,
! [U_3188] :
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3188))
| ~ class_Groups_Oab__group__add(U_3188) ),
inference(definitional_conversion,[status(esa)],[f_1244_2]) ).
cnf(f_1244_4,plain,
( class_Groups_Oab__group__add(tc_Polynomial_Opoly(U_3188))
| ~ class_Groups_Oab__group__add(U_3188) ),
inference(clausify,[status(thm)],[f_1244_3]) ).
fof(f_1245_1,plain,
! [T_1] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ozero__neq__one]) ).
fof(f_1245_2,plain,
! [U_3189] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3189))
| ~ class_Rings_Ocomm__semiring__1(U_3189) ),
inference(variable_rename,[status(thm)],[f_1245_1]) ).
fof(f_1245_3,plain,
! [U_3189] :
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3189))
| ~ class_Rings_Ocomm__semiring__1(U_3189) ),
inference(definitional_conversion,[status(esa)],[f_1245_2]) ).
cnf(f_1245_4,plain,
( class_Rings_Ozero__neq__one(tc_Polynomial_Opoly(U_3189))
| ~ class_Rings_Ocomm__semiring__1(U_3189) ),
inference(clausify,[status(thm)],[f_1245_3]) ).
fof(f_1246_1,plain,
! [T_1] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oordered__ring]) ).
fof(f_1246_2,plain,
! [U_3190] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3190))
| ~ class_Rings_Olinordered__idom(U_3190) ),
inference(variable_rename,[status(thm)],[f_1246_1]) ).
fof(f_1246_3,plain,
! [U_3190] :
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3190))
| ~ class_Rings_Olinordered__idom(U_3190) ),
inference(definitional_conversion,[status(esa)],[f_1246_2]) ).
cnf(f_1246_4,plain,
( class_Rings_Oordered__ring(tc_Polynomial_Opoly(U_3190))
| ~ class_Rings_Olinordered__idom(U_3190) ),
inference(clausify,[status(thm)],[f_1246_3]) ).
fof(f_1247_1,plain,
! [T_1] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Opreorder]) ).
fof(f_1247_2,plain,
! [U_3191] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3191))
| ~ class_Rings_Olinordered__idom(U_3191) ),
inference(variable_rename,[status(thm)],[f_1247_1]) ).
fof(f_1247_3,plain,
! [U_3191] :
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3191))
| ~ class_Rings_Olinordered__idom(U_3191) ),
inference(definitional_conversion,[status(esa)],[f_1247_2]) ).
cnf(f_1247_4,plain,
( class_Orderings_Opreorder(tc_Polynomial_Opoly(U_3191))
| ~ class_Rings_Olinordered__idom(U_3191) ),
inference(clausify,[status(thm)],[f_1247_3]) ).
fof(f_1248_1,plain,
! [T_1] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Olinorder]) ).
fof(f_1248_2,plain,
! [U_3192] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3192))
| ~ class_Rings_Olinordered__idom(U_3192) ),
inference(variable_rename,[status(thm)],[f_1248_1]) ).
fof(f_1248_3,plain,
! [U_3192] :
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3192))
| ~ class_Rings_Olinordered__idom(U_3192) ),
inference(definitional_conversion,[status(esa)],[f_1248_2]) ).
cnf(f_1248_4,plain,
( class_Orderings_Olinorder(tc_Polynomial_Opoly(U_3192))
| ~ class_Rings_Olinordered__idom(U_3192) ),
inference(clausify,[status(thm)],[f_1248_3]) ).
fof(f_1249_1,plain,
! [T_1] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__mult]) ).
fof(f_1249_2,plain,
! [U_3193] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3193))
| ~ class_Rings_Ocomm__semiring__1(U_3193) ),
inference(variable_rename,[status(thm)],[f_1249_1]) ).
fof(f_1249_3,plain,
! [U_3193] :
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3193))
| ~ class_Rings_Ocomm__semiring__1(U_3193) ),
inference(definitional_conversion,[status(esa)],[f_1249_2]) ).
cnf(f_1249_4,plain,
( class_Groups_Omonoid__mult(tc_Polynomial_Opoly(U_3193))
| ~ class_Rings_Ocomm__semiring__1(U_3193) ),
inference(clausify,[status(thm)],[f_1249_3]) ).
fof(f_1250_1,plain,
! [T_1] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring__1]) ).
fof(f_1250_2,plain,
! [U_3194] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3194))
| ~ class_Rings_Ocomm__ring__1(U_3194) ),
inference(variable_rename,[status(thm)],[f_1250_1]) ).
fof(f_1250_3,plain,
! [U_3194] :
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3194))
| ~ class_Rings_Ocomm__ring__1(U_3194) ),
inference(definitional_conversion,[status(esa)],[f_1250_2]) ).
cnf(f_1250_4,plain,
( class_Rings_Ocomm__ring__1(tc_Polynomial_Opoly(U_3194))
| ~ class_Rings_Ocomm__ring__1(U_3194) ),
inference(clausify,[status(thm)],[f_1250_3]) ).
fof(f_1251_1,plain,
! [T_1] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ocomm__monoid__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Omonoid__add]) ).
fof(f_1251_2,plain,
! [U_3195] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3195))
| ~ class_Groups_Ocomm__monoid__add(U_3195) ),
inference(variable_rename,[status(thm)],[f_1251_1]) ).
fof(f_1251_3,plain,
! [U_3195] :
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3195))
| ~ class_Groups_Ocomm__monoid__add(U_3195) ),
inference(definitional_conversion,[status(esa)],[f_1251_2]) ).
cnf(f_1251_4,plain,
( class_Groups_Omonoid__add(tc_Polynomial_Opoly(U_3195))
| ~ class_Groups_Ocomm__monoid__add(U_3195) ),
inference(clausify,[status(thm)],[f_1251_3]) ).
fof(f_1252_1,plain,
! [T_1] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring__0]) ).
fof(f_1252_2,plain,
! [U_3196] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3196))
| ~ class_Rings_Ocomm__semiring__0(U_3196) ),
inference(variable_rename,[status(thm)],[f_1252_1]) ).
fof(f_1252_3,plain,
! [U_3196] :
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3196))
| ~ class_Rings_Ocomm__semiring__0(U_3196) ),
inference(definitional_conversion,[status(esa)],[f_1252_2]) ).
cnf(f_1252_4,plain,
( class_Rings_Osemiring__0(tc_Polynomial_Opoly(U_3196))
| ~ class_Rings_Ocomm__semiring__0(U_3196) ),
inference(clausify,[status(thm)],[f_1252_3]) ).
fof(f_1253_1,plain,
! [T_1] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ogroup__add]) ).
fof(f_1253_2,plain,
! [U_3197] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3197))
| ~ class_Groups_Oab__group__add(U_3197) ),
inference(variable_rename,[status(thm)],[f_1253_1]) ).
fof(f_1253_3,plain,
! [U_3197] :
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3197))
| ~ class_Groups_Oab__group__add(U_3197) ),
inference(definitional_conversion,[status(esa)],[f_1253_2]) ).
cnf(f_1253_4,plain,
( class_Groups_Ogroup__add(tc_Polynomial_Opoly(U_3197))
| ~ class_Groups_Oab__group__add(U_3197) ),
inference(clausify,[status(thm)],[f_1253_3]) ).
fof(f_1254_1,plain,
! [T_1] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Omult__zero]) ).
fof(f_1254_2,plain,
! [U_3198] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3198))
| ~ class_Rings_Ocomm__semiring__0(U_3198) ),
inference(variable_rename,[status(thm)],[f_1254_1]) ).
fof(f_1254_3,plain,
! [U_3198] :
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3198))
| ~ class_Rings_Ocomm__semiring__0(U_3198) ),
inference(definitional_conversion,[status(esa)],[f_1254_2]) ).
cnf(f_1254_4,plain,
( class_Rings_Omult__zero(tc_Polynomial_Opoly(U_3198))
| ~ class_Rings_Ocomm__semiring__0(U_3198) ),
inference(clausify,[status(thm)],[f_1254_3]) ).
fof(f_1255_1,plain,
! [T_1] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Ocomm__ring]) ).
fof(f_1255_2,plain,
! [U_3199] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3199))
| ~ class_Rings_Ocomm__ring(U_3199) ),
inference(variable_rename,[status(thm)],[f_1255_1]) ).
fof(f_1255_3,plain,
! [U_3199] :
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3199))
| ~ class_Rings_Ocomm__ring(U_3199) ),
inference(definitional_conversion,[status(esa)],[f_1255_2]) ).
cnf(f_1255_4,plain,
( class_Rings_Ocomm__ring(tc_Polynomial_Opoly(U_3199))
| ~ class_Rings_Ocomm__ring(U_3199) ),
inference(clausify,[status(thm)],[f_1255_3]) ).
fof(f_1256_1,plain,
! [T_1] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oorder]) ).
fof(f_1256_2,plain,
! [U_3200] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3200))
| ~ class_Rings_Olinordered__idom(U_3200) ),
inference(variable_rename,[status(thm)],[f_1256_1]) ).
fof(f_1256_3,plain,
! [U_3200] :
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3200))
| ~ class_Rings_Olinordered__idom(U_3200) ),
inference(definitional_conversion,[status(esa)],[f_1256_2]) ).
cnf(f_1256_4,plain,
( class_Orderings_Oorder(tc_Polynomial_Opoly(U_3200))
| ~ class_Rings_Olinordered__idom(U_3200) ),
inference(clausify,[status(thm)],[f_1256_3]) ).
fof(f_1257_1,plain,
! [T_1] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Int_Oring__char__0]) ).
fof(f_1257_2,plain,
! [U_3201] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3201))
| ~ class_Rings_Olinordered__idom(U_3201) ),
inference(variable_rename,[status(thm)],[f_1257_1]) ).
fof(f_1257_3,plain,
! [U_3201] :
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3201))
| ~ class_Rings_Olinordered__idom(U_3201) ),
inference(definitional_conversion,[status(esa)],[f_1257_2]) ).
cnf(f_1257_4,plain,
( class_Int_Oring__char__0(tc_Polynomial_Opoly(U_3201))
| ~ class_Rings_Olinordered__idom(U_3201) ),
inference(clausify,[status(thm)],[f_1257_3]) ).
fof(f_1258_1,plain,
! [T_1] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__0(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Osemiring]) ).
fof(f_1258_2,plain,
! [U_3202] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3202))
| ~ class_Rings_Ocomm__semiring__0(U_3202) ),
inference(variable_rename,[status(thm)],[f_1258_1]) ).
fof(f_1258_3,plain,
! [U_3202] :
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3202))
| ~ class_Rings_Ocomm__semiring__0(U_3202) ),
inference(definitional_conversion,[status(esa)],[f_1258_2]) ).
cnf(f_1258_4,plain,
( class_Rings_Osemiring(tc_Polynomial_Opoly(U_3202))
| ~ class_Rings_Ocomm__semiring__0(U_3202) ),
inference(clausify,[status(thm)],[f_1258_3]) ).
fof(f_1259_1,plain,
! [T_1] :
( class_Orderings_Oord(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Orderings_Oord]) ).
fof(f_1259_2,plain,
! [U_3203] :
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3203))
| ~ class_Rings_Olinordered__idom(U_3203) ),
inference(variable_rename,[status(thm)],[f_1259_1]) ).
fof(f_1259_3,plain,
! [U_3203] :
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3203))
| ~ class_Rings_Olinordered__idom(U_3203) ),
inference(definitional_conversion,[status(esa)],[f_1259_2]) ).
cnf(f_1259_4,plain,
( class_Orderings_Oord(tc_Polynomial_Opoly(U_3203))
| ~ class_Rings_Olinordered__idom(U_3203) ),
inference(clausify,[status(thm)],[f_1259_3]) ).
fof(f_1260_1,plain,
! [T_1] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ouminus]) ).
fof(f_1260_2,plain,
! [U_3204] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_3204))
| ~ class_Groups_Oab__group__add(U_3204) ),
inference(variable_rename,[status(thm)],[f_1260_1]) ).
fof(f_1260_3,plain,
! [U_3204] :
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_3204))
| ~ class_Groups_Oab__group__add(U_3204) ),
inference(definitional_conversion,[status(esa)],[f_1260_2]) ).
cnf(f_1260_4,plain,
( class_Groups_Ouminus(tc_Polynomial_Opoly(U_3204))
| ~ class_Groups_Oab__group__add(U_3204) ),
inference(clausify,[status(thm)],[f_1260_3]) ).
fof(f_1261_1,plain,
! [T_1] :
( class_Groups_Osgn__if(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Osgn__if]) ).
fof(f_1261_2,plain,
! [U_3205] :
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3205))
| ~ class_Rings_Olinordered__idom(U_3205) ),
inference(variable_rename,[status(thm)],[f_1261_1]) ).
fof(f_1261_3,plain,
! [U_3205] :
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3205))
| ~ class_Rings_Olinordered__idom(U_3205) ),
inference(definitional_conversion,[status(esa)],[f_1261_2]) ).
cnf(f_1261_4,plain,
( class_Groups_Osgn__if(tc_Polynomial_Opoly(U_3205))
| ~ class_Rings_Olinordered__idom(U_3205) ),
inference(clausify,[status(thm)],[f_1261_3]) ).
fof(f_1262_1,plain,
! [T_1] :
( class_Groups_Oabs__if(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Olinordered__idom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oabs__if]) ).
fof(f_1262_2,plain,
! [U_3206] :
( class_Groups_Oabs__if(tc_Polynomial_Opoly(U_3206))
| ~ class_Rings_Olinordered__idom(U_3206) ),
inference(variable_rename,[status(thm)],[f_1262_1]) ).
fof(f_1262_3,plain,
! [U_3206] :
( class_Groups_Oabs__if(tc_Polynomial_Opoly(U_3206))
| ~ class_Rings_Olinordered__idom(U_3206) ),
inference(definitional_conversion,[status(esa)],[f_1262_2]) ).
cnf(f_1262_4,plain,
( class_Groups_Oabs__if(tc_Polynomial_Opoly(U_3206))
| ~ class_Rings_Olinordered__idom(U_3206) ),
inference(clausify,[status(thm)],[f_1262_3]) ).
fof(f_1263_1,plain,
! [T_1] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring__1]) ).
fof(f_1263_2,plain,
! [U_3207] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3207))
| ~ class_Rings_Ocomm__ring__1(U_3207) ),
inference(variable_rename,[status(thm)],[f_1263_1]) ).
fof(f_1263_3,plain,
! [U_3207] :
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3207))
| ~ class_Rings_Ocomm__ring__1(U_3207) ),
inference(definitional_conversion,[status(esa)],[f_1263_2]) ).
cnf(f_1263_4,plain,
( class_Rings_Oring__1(tc_Polynomial_Opoly(U_3207))
| ~ class_Rings_Ocomm__ring__1(U_3207) ),
inference(clausify,[status(thm)],[f_1263_3]) ).
fof(f_1264_1,plain,
! [T_1] :
( class_Groups_Ominus(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Oab__group__add(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ominus]) ).
fof(f_1264_2,plain,
! [U_3208] :
( class_Groups_Ominus(tc_Polynomial_Opoly(U_3208))
| ~ class_Groups_Oab__group__add(U_3208) ),
inference(variable_rename,[status(thm)],[f_1264_1]) ).
fof(f_1264_3,plain,
! [U_3208] :
( class_Groups_Ominus(tc_Polynomial_Opoly(U_3208))
| ~ class_Groups_Oab__group__add(U_3208) ),
inference(definitional_conversion,[status(esa)],[f_1264_2]) ).
cnf(f_1264_4,plain,
( class_Groups_Ominus(tc_Polynomial_Opoly(U_3208))
| ~ class_Groups_Oab__group__add(U_3208) ),
inference(clausify,[status(thm)],[f_1264_3]) ).
fof(f_1265_1,plain,
! [T_1] :
( class_Power_Opower(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Power_Opower]) ).
fof(f_1265_2,plain,
! [U_3209] :
( class_Power_Opower(tc_Polynomial_Opoly(U_3209))
| ~ class_Rings_Ocomm__semiring__1(U_3209) ),
inference(variable_rename,[status(thm)],[f_1265_1]) ).
fof(f_1265_3,plain,
! [U_3209] :
( class_Power_Opower(tc_Polynomial_Opoly(U_3209))
| ~ class_Rings_Ocomm__semiring__1(U_3209) ),
inference(definitional_conversion,[status(esa)],[f_1265_2]) ).
cnf(f_1265_4,plain,
( class_Power_Opower(tc_Polynomial_Opoly(U_3209))
| ~ class_Rings_Ocomm__semiring__1(U_3209) ),
inference(clausify,[status(thm)],[f_1265_3]) ).
fof(f_1266_1,plain,
! [T_1] :
( class_Groups_Ozero(tc_Polynomial_Opoly(T_1))
| ~ class_Groups_Ozero(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Ozero]) ).
fof(f_1266_2,plain,
! [U_3210] :
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3210))
| ~ class_Groups_Ozero(U_3210) ),
inference(variable_rename,[status(thm)],[f_1266_1]) ).
fof(f_1266_3,plain,
! [U_3210] :
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3210))
| ~ class_Groups_Ozero(U_3210) ),
inference(definitional_conversion,[status(esa)],[f_1266_2]) ).
cnf(f_1266_4,plain,
( class_Groups_Ozero(tc_Polynomial_Opoly(U_3210))
| ~ class_Groups_Ozero(U_3210) ),
inference(clausify,[status(thm)],[f_1266_3]) ).
fof(f_1267_1,plain,
! [T_1] :
( class_Rings_Oring(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__ring(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oring]) ).
fof(f_1267_2,plain,
! [U_3211] :
( class_Rings_Oring(tc_Polynomial_Opoly(U_3211))
| ~ class_Rings_Ocomm__ring(U_3211) ),
inference(variable_rename,[status(thm)],[f_1267_1]) ).
fof(f_1267_3,plain,
! [U_3211] :
( class_Rings_Oring(tc_Polynomial_Opoly(U_3211))
| ~ class_Rings_Ocomm__ring(U_3211) ),
inference(definitional_conversion,[status(esa)],[f_1267_2]) ).
cnf(f_1267_4,plain,
( class_Rings_Oring(tc_Polynomial_Opoly(U_3211))
| ~ class_Rings_Ocomm__ring(U_3211) ),
inference(clausify,[status(thm)],[f_1267_3]) ).
fof(f_1268_1,plain,
! [T_1] :
( class_Rings_Oidom(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Oidom(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Oidom]) ).
fof(f_1268_2,plain,
! [U_3212] :
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3212))
| ~ class_Rings_Oidom(U_3212) ),
inference(variable_rename,[status(thm)],[f_1268_1]) ).
fof(f_1268_3,plain,
! [U_3212] :
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3212))
| ~ class_Rings_Oidom(U_3212) ),
inference(definitional_conversion,[status(esa)],[f_1268_2]) ).
cnf(f_1268_4,plain,
( class_Rings_Oidom(tc_Polynomial_Opoly(U_3212))
| ~ class_Rings_Oidom(U_3212) ),
inference(clausify,[status(thm)],[f_1268_3]) ).
fof(f_1269_1,plain,
! [T_1] :
( class_Groups_Oone(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Groups_Oone]) ).
fof(f_1269_2,plain,
! [U_3213] :
( class_Groups_Oone(tc_Polynomial_Opoly(U_3213))
| ~ class_Rings_Ocomm__semiring__1(U_3213) ),
inference(variable_rename,[status(thm)],[f_1269_1]) ).
fof(f_1269_3,plain,
! [U_3213] :
( class_Groups_Oone(tc_Polynomial_Opoly(U_3213))
| ~ class_Rings_Ocomm__semiring__1(U_3213) ),
inference(definitional_conversion,[status(esa)],[f_1269_2]) ).
cnf(f_1269_4,plain,
( class_Groups_Oone(tc_Polynomial_Opoly(U_3213))
| ~ class_Rings_Ocomm__semiring__1(U_3213) ),
inference(clausify,[status(thm)],[f_1269_3]) ).
fof(f_1270_1,plain,
! [T_1] :
( class_Rings_Odvd(tc_Polynomial_Opoly(T_1))
| ~ class_Rings_Ocomm__semiring__1(T_1) ),
inference(fof_nnf,[status(thm)],[arity_Polynomial__Opoly__Rings_Odvd]) ).
fof(f_1270_2,plain,
! [U_3214] :
( class_Rings_Odvd(tc_Polynomial_Opoly(U_3214))
| ~ class_Rings_Ocomm__semiring__1(U_3214) ),
inference(variable_rename,[status(thm)],[f_1270_1]) ).
fof(f_1270_3,plain,
! [U_3214] :
( class_Rings_Odvd(tc_Polynomial_Opoly(U_3214))
| ~ class_Rings_Ocomm__semiring__1(U_3214) ),
inference(definitional_conversion,[status(esa)],[f_1270_2]) ).
cnf(f_1270_4,plain,
( class_Rings_Odvd(tc_Polynomial_Opoly(U_3214))
| ~ class_Rings_Ocomm__semiring__1(U_3214) ),
inference(clausify,[status(thm)],[f_1270_3]) ).
fof(f_1271_1,plain,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(c_fequal(V_x_2,V_y_2)) ),
inference(fof_nnf,[status(thm)],[help_c__fequal__1]) ).
fof(f_1271_2,plain,
! [U_3216,U_3215] :
( U_3215 = U_3216
| ~ hBOOL(c_fequal(U_3215,U_3216)) ),
inference(variable_rename,[status(thm)],[f_1271_1]) ).
fof(f_1271_3,plain,
! [U_3215,U_3216] :
( U_3215 = U_3216
| ~ hBOOL(c_fequal(U_3215,U_3216)) ),
inference(definitional_conversion,[status(esa)],[f_1271_2]) ).
cnf(f_1271_4,plain,
( U_3215 = U_3216
| ~ hBOOL(c_fequal(U_3215,U_3216)) ),
inference(clausify,[status(thm)],[f_1271_3]) ).
fof(f_1272_1,plain,
! [V_y_2,V_x_2] :
( hBOOL(c_fequal(V_x_2,V_y_2))
| V_x_2 != V_y_2 ),
inference(fof_nnf,[status(thm)],[help_c__fequal__2]) ).
fof(f_1272_2,plain,
! [U_3218,U_3217] :
( hBOOL(c_fequal(U_3217,U_3218))
| U_3217 != U_3218 ),
inference(variable_rename,[status(thm)],[f_1272_1]) ).
fof(f_1272_3,plain,
! [U_3217,U_3218] :
( hBOOL(c_fequal(U_3217,U_3218))
| U_3217 != U_3218 ),
inference(definitional_conversion,[status(esa)],[f_1272_2]) ).
cnf(f_1272_4,plain,
( hBOOL(c_fequal(U_3217,U_3218))
| U_3217 != U_3218 ),
inference(clausify,[status(thm)],[f_1272_3]) ).
fof(f_1273_1,negated_conjecture,
~ ? [B_m] :
( ! [B_z] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r)
=> c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),B_z)),B_m) )
& c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_1273_2,negated_conjecture,
! [B_m] :
( ? [B_z] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),B_z)),B_m)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,B_z),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),B_m) ),
inference(fof_nnf,[status(thm)],[f_1273_1]) ).
fof(f_1273_3,negated_conjecture,
! [U_3220] :
( ? [U_3219] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),U_3219)),U_3220)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,U_3219),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3220) ),
inference(variable_rename,[status(thm)],[f_1273_2]) ).
fof(f_1273_4,negated_conjecture,
! [U_3220] :
( ( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK52(U_3220))),U_3220)
& c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK52(U_3220)),v_r) )
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3220) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_3219,sK52(U_3220))],[f_1273_3]) ).
fof(f_1273_5,negated_conjecture,
( ! [U_3220] :
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK52(U_3220))),U_3220)
| ~ sP303(U_3220) )
& ! [U_3220] :
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK52(U_3220)),v_r)
| ~ sP303(U_3220) )
& ! [U_3220] :
( sP303(U_3220)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3220) ) ),
inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP303])],[f_1273_4]) ).
cnf(f_1273_6,negated_conjecture,
( sP303(U_3220)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),U_3220) ),
inference(clausify,[status(thm)],[f_1273_5]) ).
cnf(f_1273_7,negated_conjecture,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,sK52(U_3220)),v_r)
| ~ sP303(U_3220) ),
inference(clausify,[status(thm)],[f_1273_5]) ).
cnf(f_1273_8,negated_conjecture,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,hAPP(c_Polynomial_Opoly(tc_Complex_Ocomplex,c_Polynomial_OpCons(tc_Complex_Ocomplex,v_c____,v_cs____)),sK52(U_3220))),U_3220)
| ~ sP303(U_3220) ),
inference(clausify,[status(thm)],[f_1273_5]) ).
cnf(f_587_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_587_4]) ).
cnf(f_589_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_589_4]) ).
cnf(f_594_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_594_4]) ).
cnf(f_595_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_595_4]) ).
cnf(f_596_4_true,plain,
$true,
inference(clause_is_true,[status(thm)],[f_596_4]) ).
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_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_6,axiom,
( c_Polynomial_Opoly(Eq_x_0,Eq_x_1) = c_Polynomial_Opoly(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_7,axiom,
( c_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_8,axiom,
( tc_Polynomial_Opoly(Eq_x_0) = tc_Polynomial_Opoly(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_9,axiom,
( c_Polynomial_OpCons(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_OpCons(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_10,axiom,
( 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_11,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_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_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_14,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_15,axiom,
( c_Polynomial_Oorder(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Oorder(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_16,axiom,
( c_Polynomial_Opoly__rec(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Polynomial_Opoly__rec(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_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_functions]) ).
cnf(equality_17,axiom,
( c_fequal(Eq_x_0,Eq_x_1) = c_fequal(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_18,axiom,
( c_If(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = c_If(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_19,axiom,
( c_Polynomial_Osynthetic__div(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Osynthetic__div(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_20,axiom,
( c_Polynomial_Opcompose(Eq_x_0,Eq_x_1,Eq_x_2) = c_Polynomial_Opcompose(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_21,axiom,
( c_Groups_Ouminus__class_Ouminus(Eq_x_0,Eq_x_1) = c_Groups_Ouminus__class_Ouminus(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_22,axiom,
( c_Groups_Osgn__class_Osgn(Eq_x_0,Eq_x_1) = c_Groups_Osgn__class_Osgn(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_23,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_24,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_25,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_26,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_27,axiom,
( c_RComplete_Onatfloor(Eq_x_0) = c_RComplete_Onatfloor(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_28,axiom,
( c_RealDef_Oreal(Eq_x_0,Eq_x_1) = c_RealDef_Oreal(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_29,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_30,axiom,
( c_Nat__Transfer_Otsub(Eq_x_0,Eq_x_1) = c_Nat__Transfer_Otsub(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_31,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_32,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_33,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_34,axiom,
( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_35,axiom,
( sK7(Eq_x_0,Eq_x_1) = sK7(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_36,axiom,
( sK8(Eq_x_0,Eq_x_1) = sK8(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_37,axiom,
( sK9(Eq_x_0,Eq_x_1) = 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_38,axiom,
( sK10(Eq_x_0,Eq_x_1) = sK10(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_39,axiom,
( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_40,axiom,
( sK12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK12(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_41,axiom,
( sK13(Eq_x_0,Eq_x_1) = sK13(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_42,axiom,
( sK14(Eq_x_0,Eq_x_1) = sK14(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_43,axiom,
( sK15(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK15(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_44,axiom,
( sK16(Eq_x_0) = sK16(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_45,axiom,
( sK17(Eq_x_0,Eq_x_1) = sK17(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_46,axiom,
( sK18(Eq_x_0,Eq_x_1) = sK18(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_47,axiom,
( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_48,axiom,
( sK20(Eq_x_0,Eq_x_1,Eq_x_2) = sK20(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_49,axiom,
( sK21(Eq_x_0,Eq_x_1) = sK21(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_50,axiom,
( sK22(Eq_x_0,Eq_x_1) = sK22(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_51,axiom,
( sK23(Eq_x_0,Eq_x_1) = sK23(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_52,axiom,
( sK24(Eq_x_0) = sK24(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_53,axiom,
( sK25(Eq_x_0,Eq_x_1) = sK25(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_54,axiom,
( sK26(Eq_x_0,Eq_x_1,Eq_x_2) = sK26(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_55,axiom,
( sK27(Eq_x_0,Eq_x_1,Eq_x_2) = sK27(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_56,axiom,
( sK28(Eq_x_0,Eq_x_1) = sK28(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_57,axiom,
( sK29(Eq_x_0,Eq_x_1) = sK29(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_58,axiom,
( sK30(Eq_x_0,Eq_x_1) = sK30(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_59,axiom,
( sK31(Eq_x_0) = sK31(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_60,axiom,
( sK32(Eq_x_0,Eq_x_1) = sK32(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_61,axiom,
( sK33(Eq_x_0,Eq_x_1,Eq_x_2) = sK33(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_62,axiom,
( sK34(Eq_x_0,Eq_x_1) = sK34(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_63,axiom,
( sK35(Eq_x_0,Eq_x_1,Eq_x_2) = sK35(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_64,axiom,
( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_65,axiom,
( sK37(Eq_x_0,Eq_x_1,Eq_x_2) = sK37(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_66,axiom,
( sK38(Eq_x_0,Eq_x_1,Eq_x_2) = sK38(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_67,axiom,
( sK39(Eq_x_0,Eq_x_1) = sK39(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_68,axiom,
( sK40(Eq_x_0,Eq_x_1,Eq_x_2) = sK40(Eq_y_0,Eq_y_1,Eq_y_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_69,axiom,
( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_70,axiom,
( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(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_71,axiom,
( sK43(Eq_x_0,Eq_x_1) = sK43(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_72,axiom,
( sK44(Eq_x_0,Eq_x_1,Eq_x_2) = sK44(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_73,axiom,
( sK45(Eq_x_0,Eq_x_1) = sK45(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_74,axiom,
( sK46(Eq_x_0) = sK46(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_75,axiom,
( sK47(Eq_x_0,Eq_x_1) = sK47(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_76,axiom,
( sK48(Eq_x_0,Eq_x_1) = sK48(Eq_y_0,Eq_y_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_77,axiom,
( sK49(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK49(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_78,axiom,
( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(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_79,axiom,
( sK51(Eq_x_0,Eq_x_1,Eq_x_2) = sK51(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_80,axiom,
( sK52(Eq_x_0) = sK52(Eq_y_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_functions]) ).
cnf(equality_81,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_82,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_83,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_84,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_85,axiom,
( class_Rings_Ocomm__semiring__0(Eq_y_0)
| ~ class_Rings_Ocomm__semiring__0(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_86,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_87,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_88,axiom,
( class_Rings_Oidom(Eq_y_0)
| ~ class_Rings_Oidom(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_89,axiom,
( class_Orderings_Olinorder(Eq_y_0)
| ~ class_Orderings_Olinorder(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_90,axiom,
( class_Orderings_Oord(Eq_y_0)
| ~ class_Orderings_Oord(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_91,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_92,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_93,axiom,
( c_Polynomial_Opos__poly(Eq_y_0,Eq_y_1)
| ~ c_Polynomial_Opos__poly(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_94,axiom,
( c_SEQ_OBseq(Eq_y_0,Eq_y_1)
| ~ c_SEQ_OBseq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_95,axiom,
( class_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_96,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_97,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_98,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_99,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_100,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_101,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_102,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_103,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_104,axiom,
( class_Groups_Oab__semigroup__add(Eq_y_0)
| ~ class_Groups_Oab__semigroup__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_105,axiom,
( class_Groups_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_106,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_107,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_108,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_109,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_110,axiom,
( class_Groups_Ocomm__monoid__add(Eq_y_0)
| ~ class_Groups_Ocomm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_111,axiom,
( class_Groups_Omonoid__add(Eq_y_0)
| ~ class_Groups_Omonoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_112,axiom,
( class_Groups_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_113,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_114,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_115,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_116,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_117,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_118,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_119,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_120,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_121,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_122,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_123,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_124,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_125,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_126,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_127,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_128,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_129,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_130,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_131,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_132,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_133,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_134,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_135,axiom,
( hBOOL(Eq_y_0)
| ~ hBOOL(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_136,axiom,
( class_Rings_Ocomm__ring(Eq_y_0)
| ~ class_Rings_Ocomm__ring(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_137,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_138,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_139,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_140,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_141,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_142,axiom,
( class_Groups_Oabs__if(Eq_y_0)
| ~ class_Groups_Oabs__if(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_143,axiom,
( c_SEQ_Odecseq(Eq_y_0,Eq_y_1)
| ~ c_SEQ_Odecseq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_144,axiom,
( class_Lattices_Oboolean__algebra(Eq_y_0)
| ~ class_Lattices_Oboolean__algebra(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_145,axiom,
( class_Groups_Osgn__if(Eq_y_0)
| ~ class_Groups_Osgn__if(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_146,axiom,
( class_Lattices_Oab__semigroup__idem__mult(Eq_y_0)
| ~ class_Lattices_Oab__semigroup__idem__mult(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_147,axiom,
( class_Groups_Ouminus(Eq_y_0)
| ~ class_Groups_Ouminus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_148,axiom,
( c_Rings_Odvd__class_Odvd(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Rings_Odvd__class_Odvd(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,
( class_Rings_Odvd(Eq_y_0)
| ~ class_Rings_Odvd(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_150,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_151,axiom,
( c_SEQ_Oincseq(Eq_y_0,Eq_y_1)
| ~ c_SEQ_Oincseq(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_152,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_153,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_154,axiom,
( class_Groups_Ominus(Eq_y_0)
| ~ class_Groups_Ominus(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_155,axiom,
( class_Groups_Ocancel__comm__monoid__add(Eq_y_0)
| ~ class_Groups_Ocancel__comm__monoid__add(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_156,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_157,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_158,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_159,axiom,
( sP3(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP3(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,
( sP4(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP4(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,
( sP5(Eq_y_0,Eq_y_1)
| ~ sP5(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,
( sP6(Eq_y_0,Eq_y_1)
| ~ sP6(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_163,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_164,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_165,axiom,
( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP9(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,
( sP10(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP10(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_167,axiom,
( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP11(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,
( 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_169,axiom,
( sP13(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP13(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_170,axiom,
( sP14(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP14(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,
( 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_172,axiom,
( sP16(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP16(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_173,axiom,
( sP17(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP17(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_174,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_175,axiom,
( sP19(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP19(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,
( sP20(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP20(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,
( 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_178,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_179,axiom,
( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP23(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,
( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP24(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_181,axiom,
( sP25(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP25(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_182,axiom,
( sP26(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP26(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,
( 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_184,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_185,axiom,
( sP29(Eq_y_0,Eq_y_1)
| ~ sP29(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_186,axiom,
( sP30(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP30(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_187,axiom,
( sP31(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP31(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_188,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_189,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_190,axiom,
( sP34(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP34(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,
( 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_192,axiom,
( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP36(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_193,axiom,
( sP37(Eq_y_0,Eq_y_1)
| ~ sP37(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,
( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP38(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_195,axiom,
( sP39(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP39(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_196,axiom,
( sP40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP40(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_197,axiom,
( sP41(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP41(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_198,axiom,
( sP42(Eq_y_0,Eq_y_1)
| ~ sP42(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_199,axiom,
( sP43(Eq_y_0,Eq_y_1)
| ~ sP43(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_200,axiom,
( sP44(Eq_y_0,Eq_y_1)
| ~ sP44(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,
( sP45(Eq_y_0,Eq_y_1)
| ~ sP45(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,
( 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_203,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_204,axiom,
( sP48(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP48(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_205,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_206,axiom,
( sP50(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP50(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_207,axiom,
( sP51(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP51(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_208,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_209,axiom,
( sP53(Eq_y_0,Eq_y_1)
| ~ sP53(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_210,axiom,
( sP54(Eq_y_0,Eq_y_1)
| ~ sP54(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_211,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_212,axiom,
( sP56(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP56(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_213,axiom,
( sP57(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP57(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_214,axiom,
( sP58(Eq_y_0,Eq_y_1)
| ~ sP58(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_215,axiom,
( sP59(Eq_y_0,Eq_y_1)
| ~ sP59(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_216,axiom,
( sP60(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP60(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_217,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_218,axiom,
( sP62(Eq_y_0,Eq_y_1)
| ~ sP62(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_219,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_220,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_221,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_222,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_223,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_224,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_225,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_226,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_227,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_228,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_229,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_230,axiom,
( sP74(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP74(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_231,axiom,
( sP75(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP75(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,
( sP76(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP76(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,
( sP77(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP77(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,
( sP78(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP78(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_235,axiom,
( sP79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP79(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,
( sP80(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP80(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,
( sP81(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP81(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,
( sP82(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP82(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_239,axiom,
( sP83(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP83(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,
( sP84(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP84(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_241,axiom,
( sP85(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP85(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_242,axiom,
( sP86(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP86(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,
( sP87(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP87(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,
( sP88(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP88(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,
( 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_246,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_247,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_248,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_249,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_250,axiom,
( sP94(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP94(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_251,axiom,
( sP95(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP95(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_252,axiom,
( sP96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP96(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,
( sP97(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP97(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_254,axiom,
( sP98(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP98(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,
( sP99(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP99(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_256,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_257,axiom,
( sP101(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP101(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_258,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_259,axiom,
( sP103(Eq_y_0,Eq_y_1)
| ~ sP103(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_260,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_261,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_262,axiom,
( sP106(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP106(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_263,axiom,
( sP107(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP107(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_264,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_265,axiom,
( sP109(Eq_y_0,Eq_y_1)
| ~ sP109(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_266,axiom,
( sP110(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP110(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_267,axiom,
( sP111(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP111(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_268,axiom,
( sP112(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP112(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_269,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_270,axiom,
( sP114(Eq_y_0,Eq_y_1)
| ~ sP114(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,
( 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_272,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_273,axiom,
( sP117(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP117(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,
( sP118(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP118(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,
( sP119(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP119(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,
( 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_277,axiom,
( sP121(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP121(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_278,axiom,
( sP122(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP122(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_279,axiom,
( sP123(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP123(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_280,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_281,axiom,
( sP125(Eq_y_0,Eq_y_1)
| ~ sP125(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_282,axiom,
( sP126(Eq_y_0,Eq_y_1)
| ~ sP126(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_283,axiom,
( sP127(Eq_y_0,Eq_y_1)
| ~ sP127(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_284,axiom,
( sP128(Eq_y_0,Eq_y_1)
| ~ sP128(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_285,axiom,
( sP129(Eq_y_0,Eq_y_1)
| ~ sP129(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_286,axiom,
( sP130(Eq_y_0,Eq_y_1)
| ~ sP130(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_287,axiom,
( sP131(Eq_y_0,Eq_y_1)
| ~ sP131(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_288,axiom,
( sP132(Eq_y_0,Eq_y_1)
| ~ sP132(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_289,axiom,
( sP133(Eq_y_0,Eq_y_1)
| ~ sP133(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_290,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_291,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_292,axiom,
( sP136(Eq_y_0,Eq_y_1)
| ~ sP136(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_293,axiom,
( sP137(Eq_y_0,Eq_y_1)
| ~ sP137(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_294,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_295,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_296,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_297,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_298,axiom,
( sP142(Eq_y_0,Eq_y_1)
| ~ sP142(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_299,axiom,
( sP143(Eq_y_0,Eq_y_1)
| ~ sP143(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_300,axiom,
( sP144(Eq_y_0,Eq_y_1)
| ~ sP144(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_301,axiom,
( sP145(Eq_y_0,Eq_y_1)
| ~ sP145(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_302,axiom,
( sP146(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP146(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,
( sP147(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP147(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,
( 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_305,axiom,
( sP149(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP149(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,
( sP150(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP150(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_307,axiom,
( sP151(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP151(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_308,axiom,
( sP152(Eq_y_0,Eq_y_1)
| ~ sP152(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_309,axiom,
( sP153(Eq_y_0,Eq_y_1)
| ~ sP153(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_310,axiom,
( sP154(Eq_y_0,Eq_y_1)
| ~ sP154(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_311,axiom,
( sP155(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP155(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,
( sP156(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP156(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,
( sP157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP157(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_314,axiom,
( sP158(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP158(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_315,axiom,
( sP159(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP159(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_316,axiom,
( sP160(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP160(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_317,axiom,
( sP161(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP161(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_318,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_319,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_320,axiom,
( sP164(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP164(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_321,axiom,
( sP165(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP165(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_322,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_323,axiom,
( sP167(Eq_y_0,Eq_y_1)
| ~ sP167(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_324,axiom,
( sP168(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP168(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,
( 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_326,axiom,
( sP170(Eq_y_0,Eq_y_1)
| ~ sP170(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_327,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_328,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_329,axiom,
( sP173(Eq_y_0,Eq_y_1)
| ~ sP173(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_330,axiom,
( sP174(Eq_y_0,Eq_y_1)
| ~ sP174(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_331,axiom,
( sP175(Eq_y_0,Eq_y_1)
| ~ sP175(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_332,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_333,axiom,
( sP177(Eq_y_0,Eq_y_1)
| ~ sP177(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_334,axiom,
( sP178(Eq_y_0,Eq_y_1)
| ~ sP178(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_335,axiom,
( sP179(Eq_y_0,Eq_y_1)
| ~ sP179(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,
( sP180(Eq_y_0,Eq_y_1)
| ~ sP180(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_337,axiom,
( sP181(Eq_y_0,Eq_y_1)
| ~ sP181(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_338,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_339,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_340,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_341,axiom,
( sP185(Eq_y_0)
| ~ sP185(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_342,axiom,
( sP186(Eq_y_0)
| ~ sP186(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_343,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_344,axiom,
( sP188(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP188(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_345,axiom,
( sP189(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP189(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_346,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_347,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_348,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_349,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_350,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_351,axiom,
( sP195(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP195(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,
( sP196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP196(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,
( sP197(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP197(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_354,axiom,
( sP198(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP198(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,
( 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_356,axiom,
( sP200(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP200(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_357,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_358,axiom,
( sP202(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP202(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,
( sP203(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP203(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_360,axiom,
( sP204(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP204(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,
( sP205(Eq_y_0,Eq_y_1)
| ~ sP205(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_362,axiom,
( sP206(Eq_y_0,Eq_y_1)
| ~ sP206(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_363,axiom,
( sP207(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP207(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_364,axiom,
( sP208(Eq_y_0,Eq_y_1)
| ~ sP208(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_365,axiom,
( sP209(Eq_y_0,Eq_y_1)
| ~ sP209(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_366,axiom,
( sP210(Eq_y_0,Eq_y_1)
| ~ sP210(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_367,axiom,
( sP211(Eq_y_0,Eq_y_1)
| ~ sP211(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_368,axiom,
( sP212(Eq_y_0,Eq_y_1)
| ~ sP212(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_369,axiom,
( sP213(Eq_y_0,Eq_y_1)
| ~ sP213(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_370,axiom,
( sP214(Eq_y_0,Eq_y_1)
| ~ sP214(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_371,axiom,
( sP215(Eq_y_0,Eq_y_1)
| ~ sP215(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_372,axiom,
( sP216(Eq_y_0,Eq_y_1)
| ~ sP216(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_373,axiom,
( sP217(Eq_y_0,Eq_y_1)
| ~ sP217(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_374,axiom,
( sP218(Eq_y_0,Eq_y_1)
| ~ sP218(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_375,axiom,
( sP219(Eq_y_0,Eq_y_1)
| ~ sP219(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_376,axiom,
( sP220(Eq_y_0,Eq_y_1)
| ~ sP220(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_377,axiom,
( sP221(Eq_y_0,Eq_y_1)
| ~ sP221(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_378,axiom,
( sP222(Eq_y_0,Eq_y_1)
| ~ sP222(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_379,axiom,
( sP223(Eq_y_0,Eq_y_1)
| ~ sP223(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_380,axiom,
( sP224(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP224(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_381,axiom,
( sP225(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP225(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,
( 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_383,axiom,
( sP227(Eq_y_0,Eq_y_1)
| ~ sP227(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_384,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_385,axiom,
( sP229(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP229(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,
( 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_387,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_388,axiom,
( sP232(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP232(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_389,axiom,
( sP233(Eq_y_0,Eq_y_1)
| ~ sP233(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_390,axiom,
( sP234(Eq_y_0,Eq_y_1)
| ~ sP234(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_391,axiom,
( sP235(Eq_y_0)
| ~ sP235(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_392,axiom,
( sP236(Eq_y_0,Eq_y_1)
| ~ sP236(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_393,axiom,
( sP237(Eq_y_0,Eq_y_1)
| ~ sP237(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_394,axiom,
( sP238(Eq_y_0,Eq_y_1)
| ~ sP238(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_395,axiom,
( sP239(Eq_y_0,Eq_y_1)
| ~ sP239(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_396,axiom,
( sP240(Eq_y_0,Eq_y_1)
| ~ sP240(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_397,axiom,
( sP241(Eq_y_0,Eq_y_1)
| ~ sP241(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_398,axiom,
( sP242(Eq_y_0,Eq_y_1)
| ~ sP242(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_399,axiom,
( sP243(Eq_y_0,Eq_y_1)
| ~ sP243(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_400,axiom,
( sP244(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP244(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_401,axiom,
( sP245(Eq_y_0,Eq_y_1)
| ~ sP245(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_402,axiom,
( sP246(Eq_y_0,Eq_y_1)
| ~ sP246(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_403,axiom,
( sP247(Eq_y_0,Eq_y_1)
| ~ sP247(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_404,axiom,
( sP248(Eq_y_0,Eq_y_1)
| ~ sP248(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_405,axiom,
( sP249(Eq_y_0,Eq_y_1)
| ~ sP249(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_406,axiom,
( sP250(Eq_y_0,Eq_y_1)
| ~ sP250(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_407,axiom,
( sP251(Eq_y_0,Eq_y_1)
| ~ sP251(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_408,axiom,
( sP252(Eq_y_0,Eq_y_1)
| ~ sP252(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_409,axiom,
( sP253(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP253(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_410,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_411,axiom,
( sP255(Eq_y_0,Eq_y_1)
| ~ sP255(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_412,axiom,
( sP256(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP256(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_413,axiom,
( sP257(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP257(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_414,axiom,
( sP258(Eq_y_0,Eq_y_1)
| ~ sP258(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,
( sP259(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP259(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,
( sP260(Eq_y_0,Eq_y_1)
| ~ sP260(Eq_x_0,Eq_x_1)
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_417,axiom,
( sP261(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP261(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_418,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_419,axiom,
( sP263(Eq_y_0,Eq_y_1)
| ~ sP263(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,
( sP264(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP264(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_421,axiom,
( sP265(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP265(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_422,axiom,
( sP266(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP266(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,
( sP267(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP267(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_424,axiom,
( sP268(Eq_y_0)
| ~ sP268(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(equality_425,axiom,
( sP269(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP269(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_426,axiom,
( sP270(Eq_y_0,Eq_y_1)
| ~ sP270(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,
( sP271(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP271(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_428,axiom,
( sP272(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP272(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_429,axiom,
( sP273(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP273(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_430,axiom,
( sP274(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP274(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_431,axiom,
( sP275(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP275(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| 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_432,axiom,
( sP276(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
| ~ sP276(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
| Eq_x_7 != Eq_y_7
| Eq_x_6 != Eq_y_6
| 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_433,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_434,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_435,axiom,
( sP279(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP279(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_436,axiom,
( sP280(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP280(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_437,axiom,
( sP281(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
| ~ sP281(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_438,axiom,
( sP282(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP282(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_439,axiom,
( sP283(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
| ~ sP283(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_440,axiom,
( sP284(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP284(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_441,axiom,
( sP285(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP285(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_442,axiom,
( sP286(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP286(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_443,axiom,
( sP287(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP287(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_444,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_445,axiom,
( sP289(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP289(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_446,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_447,axiom,
( sP291(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP291(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_448,axiom,
( sP292(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP292(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_449,axiom,
( sP293(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP293(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_450,axiom,
( sP294(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP294(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_451,axiom,
( sP295(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP295(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_452,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_453,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_454,axiom,
( sP298(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP298(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_455,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_456,axiom,
( sP300(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP300(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_457,axiom,
( sP301(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ sP301(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_458,axiom,
( sP302(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
| ~ sP302(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_459,axiom,
( sP303(Eq_y_0)
| ~ sP303(Eq_x_0)
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW181+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 20 05:06:16 UTC 2026
% 0.10/0.36 % CPUTime :
% 240.36/240.61 % SZS status Theorem for theBenchmark
% 240.36/240.61 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------